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|
<?xml version='1.0' encoding='utf-8'?>
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<rfc category="info" docName="draft-summermatter-set-union-03" ipr="trust200902"
obsoletes="" updates="" submissionType="IETF" xml:lang="en" version="3">
<!-- xml2rfc v2v3 conversion 2.26.0 -->
<front>
<title abbrev="Set Union">
Byzantine Fault Tolerant Set Reconciliation
</title>
<seriesInfo name="Internet-Draft" value="draft-summermatter-set-union-01"/>
<author fullname="Elias Summermatter" initials="E." surname="Summermatter">
<organization>Seccom GmbH</organization>
<address>
<postal>
<street>Brunnmattstrasse 44</street>
<city>Bern</city>
<code>3007</code>
<country>CH</country>
</postal>
<email>elias.summermatter@seccom.ch</email>
</address>
</author>
<author fullname="Christian Grothoff" initials="C." surname="Grothoff">
<organization>Berner Fachhochschule</organization>
<address>
<postal>
<street>Hoeheweg 80</street>
<city>Biel/Bienne</city>
<code>2501</code>
<country>CH</country>
</postal>
<email>grothoff@gnunet.org</email>
</address>
</author>
<!-- Meta-data Declarations -->
<area>General</area>
<workgroup>Independent Stream</workgroup>
<keyword>name systems</keyword>
<abstract>
<t>This document contains a protocol specification for Byzantine fault-tolerant
Set Reconciliation.
</t>
</abstract>
</front>
<middle>
<section anchor="introduction" numbered="true" toc="default">
<name>Introduction</name>
<t>
This document describes a byzantine fault tolerant set reconciliation protocol used to efficient and securely
compute the union of two sets across a network.
</t>
<t>
This byzantine fault tolerant set reconciliation
protocol can be used in a variety of applications.
Our primary envisioned application domain is the
distribution of revocation messages in the GNU Name
System (GNS) <xref target="GNS" format="default" />. In GNS,
key revocation messages are usually flooded across the
peer-to-peer overlay network to all connected peers
whenever a key is revoked. However, as peers may be
offline or the network might have been partitioned,
there is a need to reconcile revocation lists whenever
network partitions are healed or peers go online. The
GNU Name System uses the protocol described in this
specification to efficiently distribute revocation
messages whenever network partitions are healed.
Another application domain for the protocol described
in this specification are Byzantine fault-tolerant
bulletin boards, like those required in some secure
multiparty computations. A well-known example for
secure multiparty computations are various E-voting
protocols <xref target="CryptographicallySecureVoting" format="default"/> which
use a bulletin board to share the votes and intermediate
computational results. We note that for such systems,
the set reconciliation protocol is merely a component of
a multiparty consensus protocol, such as the one
described in Dold's "Byzantine set-union consensus using
efficient set reconciliation" <xref target="ByzantineSetUnionConsensusUsingEfficientSetReconciliation" format="default"/>.
</t>
<t>
The protocol described in this report is generic and
suitable for a wide range of applications. As a result,
the internal structure of the elements in the sets MUST
be defined and verified by the application using the
protocol. This document thus does not cover the element
structure, except for imposing a limit on the maximum
size of an element.
</t>
<t>
The protocol faces an inherent trade-off between minimizing
the number of network round-trips and the number of bytes
sent over the network. Thus, for the protocol to choose
the right parameters for a given situation, applications
using an implementation of the protocol SHOULD provide a
parameter that specifies
the cost-ratio of round-trips vs. bandwidth usage. Given
this trade-off factor, an implementation CAN then choose parameters
that minimize total execution cost. In particular, there
is one major choice to be made, namely between sending the
complete set of elements, or computing the set differences and
transmitting only the elements in the set differences.
In the latter case, our design is basically a concrete
implementation of a proposal by Eppstein.<xref target="Eppstein" format="default" />
</t>
<t>
We say that our set reconciliation protocol is Byzantine
fault-tolerant because it provides cryptographic and
probabilistic methods to discover if the other peer
is dishonest or misbehaving.
Here, the security objective is to limit resources wasted on
malicious actors. Malicious actors could send malformed
messages, including malformed set elements, claim to
have much larger numbers of valid set elements than they
actually hold, or request the retransmission of elements
that they have already received in previous
interactions. Bounding resources consumed by malicous
actors is important to ensure that higher-level protocols
can use set reconciliation and still meet their resource
targets. This can be particularly critical in multi-round
synchronous consensus protocols where peers that cannot
answer in a timely fashion would have to be treated as
failed or malicious.
</t>
<t>
To defend against some of these attacks, applications
SHOULD remember the number of elements previously
shared with a peer, and SHOULD provide a way to check that
elements are well-formed. Applications MAY also
provide an upper bound on the total number of valid
elements that exist. For example, in E-voting, the
number of eligible voters MAY be used to provide such
an upper bound.
</t>
<t>
A first draft of this RFC is part of Elias Summermatter's
bachelor thesis. Many of the algorithms and parameters
documented in this RFC are derived from experiments
detailed in this thesis.
<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>
</t>
<t>
This document defines the normative wire format of resource records, resolution processes,
cryptographic routines and security considerations for use by implementors.
SETU requires a bidirectional secure communication channel between the two parties.
Specification of the communication channel is out of scope of this document.
</t>
<t>
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL
NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described
in <xref target="RFC2119"/>.
</t>
</section>
<section anchor="background" numbered="true" toc="default">
<name>Background</name>
<section anchor="bf" numbered="true" toc="default">
<name>Bloom Filter</name>
<t>
A Bloom filter (BF) is a space-efficient probabilistic
datastructure to test if an element is part of a set of elements.
Elements are identified by an element ID.
Since a BF is a probabilistic datastructure, it is possible to have false-positives: when asked
if an element is in the set, the answer from a BF is either "no" or "maybe".
</t>
<t>
A BF consists of L buckets. Every bucket is a binary value that can be either 0 or 1. All buckets are initialized
to 0. A mapping function M is used to map each ID of each element from the set to a subset of k buckets. In the original proposal by Bloom, M is non-injective
and can thus map the same element multiple times to the same bucket.
The type of the mapping function can thus be described by the following mathematical notation:
</t>
<figure anchor="bf_mapping_function_math">
<artwork name="" type="" align="left" alt=""><![CDATA[
------------------------------------
# M: E->B^k
------------------------------------
# L = Number of buckets
# B = 0,1,2,3,4,...L-1 (the buckets)
# k = Number of buckets per element
# E = Set of elements
------------------------------------
Example: L=256, k=3
M('element-data') = {4,6,255}
]]></artwork>
</figure>
<t>
A typical mapping function is constructed by hashing the element, for example
using the well-known <relref section="2" target="RFC5869" displayFormat="of">HKDF construction</relref>.
</t>
<t>
To add an element to the BF, the corresponding buckets under the map M are set to 1.
To check if an element may be in the set, one tests if all buckets under the map M are set to 1.
</t>
<t>
In the BF the buckets are set to 1 if the corresponding bit in the bitstream is 1.
If there is a collision and a bucket is already set to 1, the bucket stays at 1.
</t>
<t>
In the following example the element e0 with M(e0) = {1,3} has been added:
</t>
<figure anchor="figure_bf_insert_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
| 0 | 1 | 0 | 1 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
It is easy to see that an element e1 with M(e1) = {0,3}
could have been added to the BF below, while an element e2
with M(e2) = {0,2} cannot be in the set represented by the
BF below:
</t>
<figure anchor="figure_bf_contains">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
| 1 | 0 | 0 | 1 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
The parameters L and k depend on the set size and MUST be
chosen carefully to ensure that the BF does not return too
many false-positives.
</t>
<t>
It is not possible to remove an element from the BF because buckets can only be set to 1 or 0. Hence it is impossible to
differentiate between buckets containing one or more elements. To remove elements from the BF a <xref target="cbf" format="title" />
is required.
</t>
</section>
<section anchor="cbf" numbered="true" toc="default">
<name>Counting Bloom Filter</name>
<t>
A Counting Bloom Filter (CBF) is a variation on the idea
of a <xref target="bf" format="title" />. With a CBF, buckets are
unsigned numbers instead of binary values.
This allows the removal of an element from the CBF.
</t>
<t>
Adding an element to the CBF is similar to the adding operation of the BF.
However, instead of setting the buckets to 1 the
numeric value stored in the bucket is increased by 1.
For example, if two colliding elements M(e1) = {1,3} and
M(e2) = {0,3} are added to the CBF, bucket 0 and 1 are set
to 1 and bucket 3 (the colliding bucket) is set to 2:
</t>
<figure anchor="figure_cbf_insert_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
| 1 | 1 | 0 | 2 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
The counter stored in the bucket is also called the order of the bucket.
</t>
<t>
To remove an element form the CBF the counters of all buckets
the element is mapped to are decreased by 1.
</t>
<t>
For example, removing M(e2) = {1,3} from the CBF above
results in:
</t>
<figure anchor="figure_cbf_remove_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
| 1 | 0 | 0 | 1 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
In practice, the number of bits available for the counters
is often finite. For example, given a 4-bit
counter, a CBF bucket would overflow 16 elements are mapped
to the same bucket. To handle this case, the maximum value
(15 in our example) is considered to represent "infinity". Once the
order of a bucket reaches "infinity", it is no longer incremented or decremented.
</t>
<t>
The parameters L and k and the number of bits allocated to the counters
SHOULD depend on the set size.
A CBF will degenerate when subjected to insert and remove iterations of
different elements, and eventually all buckets will reach "infinity".
The speed of the degradation will depend on the choice of L and k in
relation to the number of elements stored in the IBF.
</t>
</section>
</section>
<section anchor="ibf" numbered="true" toc="default">
<name>Invertible Bloom Filter</name>
<t>
An Invertible Bloom Filter (IBF) is a further extension of the <xref target="cbf" format="title" />.
An IBF extends the <xref target="cbf" format="title" /> with two more operations:
decode and set difference. This two extra operations are key to efficiently obtain
small differences between large sets.
</t>
<section anchor="ibf_structure" numbered="true" toc="default">
<name>Structure</name>
<t>
An IBF consists of an injective mapping function M mapping
elements to k out of L buckets. Each of the L buckets stores
a signed COUNTER, an IDSUM and an XHASH.
An IDSUM is the XOR of various element IDs.
An XHASH is the XOR of various hash values.
As before, the values used for k, L and the number of bits used
for the signed counter and the XHASH depend
on the set size and various other trade-offs.
</t>
<t>
If the IBF size is too small or the mapping
function does not spread out the elements
uniformly, the signed counter can overflow or
underflow. As with the CBF, the "maximum" value is
thus used to represent "infinite". As there is no
need to distinguish between overflow and
underflow, the most canonical representation of
"infinite" would be the minimum value of the
counter in the canonical 2-complement
interpretation. For example, given a 4-bit
counter a value of -8 would be used to represent
"infinity".
</t>
<figure anchor="figure_ibf_structure">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+-------
count | COUNTER | COUNTER | COUNTER | COUNTER | C...
+-------------+-------------+-------------+-------------+------
idSum | IDSUM | IDSUM | IDSUM | IDSUM | I...
+-------------+-------------+-------------+-------------+------
hashSum | HASHSUM | HASHSUM | HASHSUM | HASHSUM | H..
+-------------+-------------+-------------+-------------+-------
]]></artwork>
</figure>
</section>
<section anchor="ibf_format_id_generation" numbered="true" toc="default">
<name>Salted Element ID Calculation</name>
<t>
IBFs are a probabilistic data structure, hence it can be necessary to
recompute the IBF in case operations fail, and then try again. The
recomputed IBF would ideally be statistically independent of the
failed IBF. This is achieved by introducing an IBF-salt. Given that with
benign peers failures should be rare, and that we need to be able to
"invert" the application of the IBF-salt to the element IDs, we use an
unsigned 32 bit non-random IBF-salt value of which the lowest 6 bits will
be used to rotate bits in the element ID computation.
</t>
<t>
64-bit element IDs are generated from a
<relref section="2" target="RFC5869" displayFormat="of">HKDF construction</relref>
with HMAC-SHA512 as XTR and HMAC-SHA256 as PRF with a 16-bit KDF-salt set to a
unsigned 16-bit representation of zero.
The output of the KDF is then truncated to 64-bit.
Finally, salting is done by calculating the IBF-salt modulo 64
(effectively using only the lowest 6-bits of the IBF-salt)
and doing a bitwise right rotation of the output of KDF. We
note that this operation was chosen as it is easily inverted,
allowing applications to easily derive element IDs with one
IBF-salt value from element IDs generated with a different
IBF-salt value.
</t>
<t>
In case the IBF does not decode, the IBF-salt can be changed to
compute different element IDs, which will (likely) be mapped
to different buckets, likely allowing the IBF to decode in a
subsequent iteration.
</t>
<figure anchor="ibf_format_id_generation_pseudo_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# INPUTS:
# key: Pre calculated and truncated key from id_calculation function
# ibf_salt: Salt of the IBF
# OUTPUT:
# value: salted key
FUNCTION salt_key(key,ibf_salt):
s = ibf_salt % 64;
/* rotate key */
return (key >> s) | (key << (64 - s))
# INPUTS:
# element: element for which we are to calculate the element ID
# ibf_salt: Salt of the IBF
# OUTPUT:
# value: the ID of the element
FUNCTION id_calculation (element,ibf_salt):
kdf_salt = 0 // 16 bits
XTR=HMAC-SHA256
PRF=HMAC-SHA256
key = HKDF(XTR, PRF, kdf_salt, element) modulo 2^64
return salt_key(key, ibf_salt)
]]></artwork>
</figure>
</section>
<section anchor="ibf_format_HASH_calculation" numbered="true" toc="default">
<name>HASH calculation</name>
<t>
The HASH of an element ID is computed by calculating the
CRC32 checksum of the 64-bit ID value,
which returns a 32-bit value.CRC32 is well-known and described in <relref section="4.1" target="RFC3385" displayFormat="of">the RFC</relref>.
</t>
</section>
<section anchor="ibf_m" numbered="true" toc="default">
<name>Mapping Function</name>
<t>
The mapping function M decides which buckets a given ID is mapped to.
For an IBF, it is beneficial to use an injective mapping function M.
</t>
<t>
The first index is simply the CRC32 of the ID modulo the IBF size. The second
index is calculated by creating a new 64-bit value by shifting the previous 32-bit
value left and setting the lower 32 bits to the number of indices already processed.
From the resulting 64-bit value, another CRC32 checksum is computed.
The subsequent index is the modulo of this CRC32 output.
The process is repeated until the desired number of indices is generated.
In the case the process computes the same index twice,
which would mean this bucket could not get pure again,
the second hit is just skipped and the next iteration is used instead,
creating an injective mapping function.
</t>
<figure anchor="ibf_format_bucket_identification_pseudo_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# INPUTS:
# key: the ID of the element calculated
# k: numbers of buckets per element
# L: total number of buckets in the IBF
# OUTPUT:
# dst: Array with k bucket IDs
FUNCTION get_bucket_id (key, k, L)
bucket = CRC32(key)
i = 0 // unsigned 32-bit index
filled = 0
WHILE filled < k
element_already_in_bucket = false
j = 0
WHILE j < filled
IF dst[j] == bucket modulo L THEN
element_already_in_bucket = true
ENDIF
j++
ENDWHILE
IF !element_already_in_bucket THEN
dst[filled] = bucket modulo L
filled = filled + 1
ENDIF
x = (bucket << 32) | i // 64 bit result
bucket = CRC32(x)
i = i + 1
ENDWHILE
return dst
]]></artwork>
</figure>
</section>
<section anchor="ibf_operations" numbered="true" toc="default">
<name>Operations</name>
<t>
When an IBF is created, all counters and IDSUM and HASHSUM values of
all buckets are initialized to zero.
</t>
<section anchor="ibv_operations_insert" numbered="true" toc="default">
<name>Insert Element</name>
<t>
To add an element to an IBF, the element is mapped to a subset of k buckets using
the injective mapping function M as described in section <xref target="ibf_m" format="title" />. For the buckets selected by the mapping function, the counter is increased by one and the
IDSUM field is set to the XOR of the element ID
computed as described in section <xref target="ibf_format_id_generation" format="title" />
and the previously stored IDSUM. Furthermore,
the HASHSUM is set to the XOR of the previously stored HASHSUM
and the hash of the element ID computed as described
in section <xref target="ibf_format_HASH_calculation" format="title" />.
</t>
<t>
In the following example, the insert operation is illustrated using an element with the
ID 0x0102 mapped to {1,3} with a hash of 0x4242, and a second element with the
ID 0x0304 mapped to {0,1} and a hash of 0x0101.
</t>
<t>Empty IBF:</t>
<figure anchor="figure_ibf_insert_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 0 | 0 | 0 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x0000 | 0x0000 | 0x0000 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x0000 | 0x0000 | 0x0000 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>Insert first element with ID 0x0102 and hash 0x4242 into {1,3}:</t>
<figure anchor="figure_ibf_insert_1">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 1 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x0102 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x4242 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>Insert second element with ID 0x0304 and hash 0101 into {0,1}:</t>
<figure anchor="figure_ibf_insert_2">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 1 | 2 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0304 | 0x0206 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0101 | 0x4343 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
</section>
<section anchor="ibf_operations_remove" numbered="true" toc="default">
<name>Remove Element</name>
<t>
To remove an element from the IBF the element is again mapped to a subset of the buckets using M.
Then all the counters of the buckets selected by M are reduced by one, the IDSUM is
replaced by the XOR of the old IDSUM and the ID of the element being removed, and the
HASHSUM is similarly replaced with the XOR of the old HASHSUM and the hash of the ID.
</t>
<t>
In the following example the remove operation is illustrated.
</t>
<t>IBF with two encoded elements:</t>
<figure anchor="figure_ibf_remove_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 1 | 2 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0304 | 0x0206 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0101 | 0x4343 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>After removal of element with ID 0x0304 and hash 0x0101 mapped to {0,1} from the IBF:</t>
<figure anchor="figure_ibf_remove_1">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 1 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x0102 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x4242 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
Note that it is possible to "remove" elements from an IBF that were never present
in the IBF in the first place. A negative counter value is thus indicative of
elements that were removed without having been added. Note that an IBF bucket
counter of zero no longer guarantees that an element mapped to that bucket is not
present in the set: a bucket with a counter of zero can be the result of one
element being added and a different element (mapped to the same bucket) being removed.
To check that an element is not present requires a counter of zero and an
IDSUM and HASHSUM of zero --- and some certainty that there was no collision due
to the limited number of bits in IDSUM and HASHSUM. Thus,
IBFs are not suitable to replace BFs or IBFs.
</t>
<t>
Buckets in an IBF with a counter of 1 or -1 are crucial for decoding an IBF, as
they MIGHT represent only a single element, with the IDSUM being the ID of that element.
Following Eppstein <xref target="Eppstein" format="default" />, we will call buckets that only represent a single
element <em>pure buckets</em>.
Note that due to the possibility of multiple insertion and removal operations
affecting the same bucket, not all buckets with a counter of 1 or -1 are
actually pure buckets. Sometimes a counter can be 1 or -1 because N elements
mapped to that bucket were added while N-1 or N+1 different elements also
mapped to that bucket were removed.
</t>
</section>
<section anchor="ibf_operations_decode" numbered="true" toc="default">
<name>Extracting elements</name>
<t>
Extracting elements from an IBF yields IDs of elements from the IBF.
Elements are extracted from an IBF by repeatedly performing a
decode operation on the IBF.
</t>
<t>
A decode operation requires a pure bucket, that is a bucket to which M
only mapped a single element, to succeed. Thus, if there is no bucket with
a counter of 1 or -1, decoding fails. However, as a counter of 1 or -1 is
not a guarantee that the bucket is pure, there is also a chance that the
decoder returns an IDSUM value that is actually the XOR of several IDSUMs.
This is primarily detected by checking that the HASHSUM is the hash of the IDSUM.
Only if the HASHSUM also matches, the bucket could be pure. Additionally,
one MUST check that the IDSUM value actually would be mapped by M to
the respective bucket. If not, there was a hash collision and the bucket
is also not pure.
</t>
<t>
The very rare case that after all these checks a bucket is still
falsely identified as pure MUST be detected (say by determining that
extracted element IDs do not match any actual elements), and addressed
at a higher level in the protocol. As these failures are probabilistic
and depend on element IDs and the IBF construction, they can typically
be avoided by retrying with different parameters, such as a different
way to assign element IDs to elements (by varying the IBF-salt),
using a larger value for L, or a different mapping function M.
A more common scenario (especially if L was too small) is that
IBF decoding fails because there is no pure bucket. In this case, the
higher-level protocol generally MUST also retry using different
parameters (except if an attack is detected).
</t>
<t>
Suppose the IBF contains a pure bucket. In this case, the IDSUM in the
bucket is the ID of an element. Furthermore, it is then possible
to remove that element from the IBF (by inserting it if the counter
was negative, and by removing it if the counter was positive). This
is likely to cause other buckets to become pure, allowing further
elements to be decoded. Eventually, decoding ought to finish with
all counters and IDSUM and HASHSUM values reach zero. However, it is also
possible that an IBF only partly decodes and then decoding fails due
to the lack of pure buckets after extracting some element IDs.
</t>
<t>
In the following example the successful decoding of an IBF containing
the two elements previously added in our running example.
</t>
<t>
We begin with an IBF with two elements added:
</t>
<figure anchor="figure_ibf_decode_0">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 1 | 2 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0304 | 0x0206 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0101 | 0x4343 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
In the IBF are two pure buckets to decode (buckets 0 and 3) we choose to start with
decoding bucket 0. This yields the element with the hash ID 0x0304 and
hash 1010. This element ID is mapped to buckets
{0,1}.
Subtracting this element results in bucket 1 becoming pure:
</t>
<figure anchor="figure_ibf_decode_1">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 1 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x0102 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x4242 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>
We can now decoding bucket 2 and extract the element
with the ID 0x0102 and hash 0x4242. Now the IBF is
empty. Extraction completes with the status that
the IBF has been successfully decoded.
</t>
<figure anchor="figure_ibf_decode_2">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 0 | 0 | 0 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x0000 | 0x0000 | 0x0000 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x0000 | 0x0000 | 0x0000 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
</section>
<section anchor="ibv_operations_setdiff" numbered="true" toc="default">
<name>Set Difference</name>
<t>
Given addition and removal as defined above, it is possible to define an operation on IBFs
that computes an IBF representing the set difference. Suppose IBF1 represents set A, and
IBF2 represents set B. Then this set difference operation will compute IBF3 which
represents the set A - B. Note that this computation can be done only on the IBFs,
and does not require access to the elements from set A or B.
To calculate the IBF representing this set difference, both IBFs MUST have the same
length L, the same number of buckets per element k and use the same map M.
Naturally, all IDs must have been computed using the same IBF-salt. Given this,
one can compute the IBF representing the set difference by taking the XOR of the IDSUM and HASHSUM values
of the respective buckets and subtracting the respective counters. Care MUST be taken
to handle overflows and underflows by setting the counter to "infinity" as necessary.
The result is a new IBF with the same number of buckets representing the set difference.
</t>
<t>
This new IBF can be decoded as described in section <xref target="ibf_operations_decode" format="counter" />.
The new IBF can have two types of pure buckets with counter set to 1 or -1. If the counter is set to 1
the element is missing in the secondary set, and if the counter is set to -1 the element is missing in
the primary set.
</t>
<t>
To demonstrate the set difference operation we compare IBF-A with IBF-B and generate as described
IBF-AB
</t>
<t>IBF-A contains the elements with ID 0x0304 and hash 0x0101 mapped to {0,1},
and ID 0x0102 and hash 0x4242 mapped to {1,3}:</t>
<figure anchor="figure_ibf_setdiff_A">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 1 | 2 | 0 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0304 | 0x0206 | 0x0000 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0101 | 0x4343 | 0x0000 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>IBF-B also contains the element with ID 0x0102 and
and another element with ID 0x1345 and hash 0x5050
mapped to {1,2}.</t>
<figure anchor="figure_ibf_setdiff_B">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 0 | 1 | 1 | 1 |
+-------------+-------------+-------------+-------------+
idSum | 0x0000 | 0x1447 | 0x1345 | 0x0102 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0000 | 0x9292 | 0x5050 | 0x4242 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>IBF-A minus IBF-B is then:</t>
<figure anchor="figure_ibf_setdiff_AB">
<artwork name="" type="" align="left" alt=""><![CDATA[
bucket-0 bucket-1 bucket-2 bucket-3
+-------------+-------------+-------------+-------------+
count | 1 | 0 | -1 | 0 |
+-------------+-------------+-------------+-------------+
idSum | 0x0304 | 0x1049 | 0x1345 | 0x0000 |
+-------------+-------------+-------------+-------------+
hashSum | 0x0101 | 0x5151 | 0x5050 | 0x0000 |
+-------------+-------------+-------------+-------------+
]]></artwork>
</figure>
<t>After calculating and decoding the IBF-AB shows clear that in IBF-A the element with the hash 0x5050
is missing (-1 in bucket 2) while in IBF-B the element with the hash 0101 is missing
(1 in bucket 0). The element with hash 0x4242 is present in IBF-A and IBF-B and is
removed by the set difference operation. Bucket 2 is not empty.
</t>
</section>
</section>
<section anchor="ibf_format" numbered="true" toc="default">
<name>Wire format</name>
<t>
For the counter field, we use a variable-size encoding to ensure
that even for very large sets the counter should never reach
"infinity", while also ensuring that the encoding is compact for
small sets.
Hence, the counter size transmitted over the wire
varies between 1 and 64 bits, depending on the
maximum counter in the IBF. A range of 1 to 64 bits
should cover most areas of application and can be
efficiently implemented on most contemporary CPU
architectures and programming languages.
The bit length for the transmitted IBF
will be communicated in the header of the
<em><xref target="messages_ibf" format="title" /></em> message
in the "IMCS" field as unsigned 8-bit integer.
For implementation details see section <xref target="performance_counter_variable_size" format="title" />.
</t>
<t>
For the "IDSUM", we always use a 64-bit representation.
The IDSUM value MUST have sufficient entropy for the
mapping function M to yield reasonably random buckets
even for very large values of L. With a 32 bit
value the chance that multiple elements may be mapped
to the same ID would be quite high, even for moderately
large sets. Using more than 64 bits would at best make
sense for very large sets, but then it is likely always
better to simply afford additional round trips to handle
the occasional collision. 64 bits are also a reasonable
size for many CPU architectures.
</t>
<t>
For the "HASHSUM", we always use a 32-bit
representation. Here, it is most important to
avoid collisions, where different elements are
mapped to the same hash, possibly resulting in
a bucket being falsely classified as pure.
While with 32 bits there remains a non-negligible chance of
accidental collisions, our protocol is designed
to handle occasional collisions. Hence, at 32 bit the chance is
believed to be sufficiently small enough
for the protocol to handle those cases efficiently. Smaller hash
values would safe bandwidth, but also substantially
increase the chance of collisions. 32 bits are
also again a reasonable size for many CPU
architectures.
</t>
</section>
</section>
<section anchor="se" numbered="true" toc="default">
<name>Strata Estimator</name>
<t>
Strata Estimators help estimate the size of the set difference between two sets of elements.
This is necessary to efficiently determinate the tuning parameters for an IBF, in particular
a good value for L.
</t>
<t>
Basically a Strata Estimator (SE) is a series of IBFs (with a rather small value of L=79)
in which increasingly large subsets of the full set
of elements are added to each IBF. For the n-th IBF, the function selecting the
subset of elements MUST sample to select (probabilistically) 1/(2^n) of all
elements. This can be done by counting the number of trailing bits set to "1"
in an element ID, and then inserting the element into the IBF identified by that
counter. As a result, all elements will be mapped to one IBF, with the n-th
IBF being statistically expected to contain 1/(2^n) elements.
</t>
<t>
Given two SEs, the set size difference can be estimated by attempting to decode all of the
IBFs. Given that L is set to a fixed and rather small value, IBFs containing large strata
will likely fail to decode. For IBFs that failed to decode, one simply
extrapolates the number of elements by scaling the numbers obtained from the
other IBFs that did decode. If none of the IBFs of the SE decoded (which given
a reasonable number of IBFs in the SE should be highly unlikely), one can theoretically
retry using a different IBF-salt.
</t>
<t>
When decoding the IBFs in the strata estimator, it is possible to determine
on which side which part of the difference is. For this purpose, the pure buckets with
counter 1 and -1 must be distinguished and assigned to the respective side when decoding
the IBFs.
</t>
</section>
<section anchor="modeofoperation" numbered="true" toc="default">
<name>Mode of Operation</name>
<t>
Depending on the state of the two sets the set union
protocol uses different modes of operation to efficiently
determinate missing elements between the two sets.
</t>
<t>
The simplest mode is the <em>full synchronisation mode</em>.
If the difference between the sets of the two
peers exceeds a certain threshold, the overhead to determine
which elements are different would outweigh the overhead of
simply sending the complete set. Hence, the protocol may
determine that the most efficient method is to exchange the full sets.
</t>
<t>
The second possibility is that the difference between the sets
is relatively small compared to the set size.
In this case, the <em>differential synchronisation mode</em> is more efficient.
Given these two possibilities, the first steps of the protocol are used to
determine which mode MUST be used.
</t>
<t>
Thus, the set union protocol always begins with the following operation mode independent steps:
</t>
<t>
The initiating peer begins in the <strong>Initiating Connection</strong> state and the receiving peer in the <strong>Expecting Connection</strong>
state. The first step for the initiating peer in the protocol is to send an <em><xref target="messages_operation_request" format="title" /></em> to the receiving peer and
transition into the <strong>Expect SE</strong> state. After receiving the <em><xref target="messages_operation_request" format="title" /></em> the receiving peer
transitions to the <strong>Expecting IBF</strong> state and answers with the
<em><xref target="messages_se" format="title" /></em> message. When the initiating peer receives the <em><xref target="messages_se" format="title" /></em> message,
it decides with some heuristics which operation mode is likely more suitable for the estimated set difference and the application-provided latency-bandwidth tradeoff.
The detailed algorithm used to choose between the <xref target="modeofoperation_full-sync" format="title" /> and the <xref target="modeofoperation_individual-elements" format="title" />
is explained in the section <xref target="modeofoperation_combined-mode" format="title" /> below.
</t>
<section anchor="modeofoperation_full-sync" numbered="true" toc="default">
<name>Full Synchronisation Mode</name>
<t>
When the initiating peer decides to use the full synchronisation mode and it is better that the other peer sends his set first, the initiating
peer sends a <em><xref target="messages_request_full" format="title" /></em> message, and transitions from <strong>Expecting SE</strong> to the <strong>Full Receiving</strong> state.
If it has been determined that it is better that the initiating peer sends his set first, the initiating peer sends a <em><xref target="messages_send_full" format="title" /></em> message followed by all
set elements in <em><xref target="messages_full_element" format="title" /></em> messages to the other peer, followed by the <em><xref target="messages_full_done" format="title" /></em> message, and transitions into the <strong>Full Sending</strong> state.
</t>
<t>
A state diagram illustrating the state machine used during full synchronization
is provided
<eref target="https://git.gnunet.org/lsd0003.git/plain/statemachine/state_machine_full.png">here</eref>.
</t>
<t><strong>The behavior of the participants the different state is described below:</strong></t>
<dl>
<dt><strong>Expecting IBF:</strong></dt>
<dd>
If a peer in the <strong>Expecting IBF</strong> state receives a <em><xref target="messages_request_full" format="title" /></em> message from the other peer, the
peer sends all the elements of his set followed by a <em><xref target="messages_full_done" format="title" /></em> message to the other peer, and transitions to the
<strong>Full Sending</strong> state. If the peer receives an <em><xref target="messages_send_full" format="title" /></em> message followed by
<em><xref target="messages_full_element" format="title" /></em> messages, the peer processes the element and transitions to the <strong>Full Receiving</strong> state.
</dd>
<dt><strong>Full Sending:</strong></dt>
<dd>
While a peer is in <strong>Full Sending</strong> state the peer expects to continuously receive elements from the other
peer. As soon as a the <em><xref target="messages_full_done" format="title" /></em> message is received, the peer transitions into
the <strong>Finished</strong> state.
</dd>
<dt><strong>Full Receiving: </strong></dt>
<dd>
While a peer is in the <strong>Full Receiving</strong> state, it expects to continuously receive elements from the other
peer. As soon as a the <em><xref target="messages_full_done" format="title" /></em> message is received, it sends
the remaining elements (those it did not receive) from his set to the other
peer, followed by a <em><xref target="messages_full_done" format="title" /></em>.
After sending the last message, the peer transitions into the <strong>Finished</strong> state.
</dd>
</dl>
</section>
<section anchor="modeofoperation_individual-elements" numbered="true" toc="default">
<name>Differential Synchronisation Mode</name>
<t>
The message format used by the protocol limits the maximum message size to
64 kb. Given that L can be large, an IBF will not always fit within that
size limit. To deal with this, larger IBFs are split into multiple messages.
</t>
<t>
When the initiating peer in the <strong>Expected SE</strong> state decides to use the differential synchronisation mode, it
sends an IBF, which may
consist of several <em><xref target="messages_ibf" format="title" /></em> messages,
to the receiving peer and transitions into the <strong>Passive Decoding</strong> state.
</t>
<t>
The receiving peer in the <strong>Expecting IBF</strong> state receives the
first <em><xref target="messages_ibf" format="title" /></em> message from
the initiating peer, and transitions into the <strong>Expecting IBF Last</strong> state
if the IBF was split into multiple <em><xref target="messages_ibf" format="title" /></em>
messages. If there is just a single <em><xref target="messages_ibf" format="title" /></em>
message, the receiving peer
transitions directly to the <strong>Active Decoding</strong> state.
</t>
<t>
The peer that is in the <strong>Active Decoding</strong>, <strong>Finish Closing</strong> or in the <strong>Expecting IBF Last</strong>
state is called the active peer, and the peer that is in either the <strong>Passive Decoding</strong> or the <strong>Finish Waiting</strong> state
is called the passive peer.
</t>
<t>
A state diagram illustrating the state machine used during differential synchronization
is provided
<eref target="https://git.gnunet.org/lsd0003.git/plain/statemachine/differential_state_machine.png">here</eref>.
</t>
<t><strong>The behavior of the participants the different states is described below:</strong></t>
<dl>
<dt><strong>Passive Decoding:</strong></dt>
<dd>
<t>
In the <strong>Passive Decoding</strong> state the passive peer reacts to requests from the active peer.
The action the passive peer executes depends on the message the passive peer receives in the <strong>Passive Decoding</strong> state from the active peer
and is described below on a per message basis.
</t>
<dl>
<dt><em><xref target="messages_inquiry" format="title" /></em> message:</dt>
<dd>
The <em><xref target="messages_inquiry" format="title" /></em> message
is received if the active peer requests the SHA-512 hash of one or more elements (by sending the 64 bit element ID)
that are missing from the active peer's set.
In this case the passive peer answers with <em><xref target="messages_offer" format="title" /></em> messages
which contain the SHA-512 hash of the requested element. If the passive peer does not have an element with
a matching element ID, it MUST ignore the inquiry (in this case, a bucket was falsely classified as pure, decoding the IBF will eventually fail, and roles will be swapped).
It should be verified that after an falsely classified pure bucket a role change is made.
If multiple elements match the 64 bit element ID, the passive
peer MUST send offers for all of the matching elements.
</dd>
<dt><em><xref target="messages_demand" format="title" /></em> message:</dt>
<dd>
The <em><xref target="messages_demand" format="title" /></em> message
is received if the active peer requests a complete element that is missing in the active peers set in response to an offer. If the requested element is known and has not yet been transmitted
the passive peer answers with an <em><xref target="messages_elements" format="title" /></em> message which contains the full,
application-dependent data of the requested element. If the passive peer receives a demand for a SHA-512 hash for which
it has no corresponding element, a protocol violation is detected and the protocol MUST be aborted.
Implementations MUST also abort when facing demands without previous matching offers or for which the passive peer previously transmitted the element to the active peer.
</dd>
<dt><em><xref target="messages_offer" format="title" /></em> message:</dt>
<dd>
The <em><xref target="messages_offer" format="title" /></em> message
is received if the active peer has decoded an element that is present in the active peers set and is likely be missing in the
set of the passive peer. If the SHA-512 hash of the offer is indeed not a hash of any of the elements from the set of
the passive peer, the passive peer MUST answer with a <em><xref target="messages_demand" format="title" /></em> message
for that SHA-512 hash and remember that it issued this demand. The demand thus needs to be added to a list with unsatisfied demands.
</dd>
<dt><em><xref target="messages_elements" format="title" /></em> message:</dt>
<dd>
When a new <em><xref target="messages_elements" format="title" /></em> message has been received the peer checks if a corresponding
<em><xref target="messages_demand" format="title" /></em> for the element has been sent
and the demand is still unsatisfied.
If the element has been demanded the peer checks the element for validity, removes it from the list
of pending demands and then saves the element to the set. Otherwise the peer
ignores the element.
</dd>
<dt><em><xref target="messages_ibf" format="title" /></em> message:</dt>
<dd>
If an <em><xref target="messages_ibf" format="title" /></em> message is received, this
indicates that decoding of the IBF on the active site has failed and roles will be swapped.
The receiving passive peer transitions into the <strong>Expecting IBF Last</strong> state,
and waits for more <em><xref target="messages_ibf" format="title" /></em> messages.
There, once the final <em><xref target="messages_ibf_last" format="title" /></em> message has been received, it transitions to <strong>Active Decoding</strong>.
</dd>
<dt><em><xref target="messages_ibf_last" format="title" /></em> message:</dt>
<dd>
If an <em><xref target="messages_ibf_last" format="title" /></em> message is received this
indicates that there is just one IBF slice left and a direct state and role transition from
<strong>Passive Decoding</strong> to <strong>Active Decoding</strong> is initiated.
</dd>
<dt><em><xref target="messages_done" format="title" /></em> message:</dt>
<dd>
Receiving the <em><xref target="messages_done" format="title" /></em> message signals
the passive peer that all demands of the active peer have been satisfied. Alas, the
active peer will continue to process demands from the passive peer.
Upon receiving this message, the passive peer transitions into the
<strong>Finish Waiting</strong> state.
</dd>
</dl>
</dd>
<dt><strong>Active Decoding:</strong></dt>
<dd>
<t>
In the <strong>Active Decoding</strong> state the active peer decodes the IBFs and evaluates the set difference
between the active and passive peer. Whenever an element ID is obtained by decoding the IBF, the active peer
sends either an offer or an inquiry to the passive peer, depending on which site the decoded element is missing.
</t>
<t>
If the IBF decodes a positive (1) pure bucket, the element is missing on the passive peers site.
Thus, the active peer sends an <em><xref target="messages_offer" format="title" /></em> to the passive peer.
A negative (-1) pure bucket indicates that an element is missing in the active peers set, so the active peer
sends a <em><xref target="messages_inquiry" format="title" /></em> to the passive peer.
</t>
<t>
In case the IBF does not successfully decode anymore, the active peer sends a new IBF computed with a different IBF-salt to the passive peer
and changes into <strong>Passive Decoding</strong> state. This initiates a role swap.
To reduce overhead and prevent double transmission of offers and elements, the new IBF is created
on the local set after updating it with the all of the elements that have been successfully demanded. Note that the active peer MUST NOT wait for all active demands to be satisfied, as demands can fail if a bucket was falsely classified as pure.
</t>
<t>
As soon as the active peer successfully finished decoding the IBF, the active peer sends a
<em><xref target="messages_done" format="title" /></em> message to the passive peer.
</t>
<t>
All other actions taken by the active peer depend on the message the active peer receives from
the passive peer. The actions are described below on a per message basis:
</t>
<dl>
<dt><em><xref target="messages_offer" format="title" /></em> message:</dt>
<dd>
The <em><xref target="messages_offer" format="title" /></em> message indicates that the
passive peer received a <em><xref target="messages_inquiry" format="title" /></em> message from
the active peer. If a inquiry has been sent and
the offered element is missing in the active peers set,
the active peer sends a <em><xref target="messages_demand" format="title" /></em> message to the
passive peer. The demand needs to be added to a list of unsatisfied demands.
In case the received offer is for an element that is already in the set of the peer, the offer MUST BE ignored.
</dd>
<dt><em><xref target="messages_demand" format="title" /></em> message:</dt>
<dd>
The <em><xref target="messages_demand" format="title" /></em> message indicates that the
passive peer received a <em><xref target="messages_offer" format="title" /></em> from
the active peer. The active peer satisfies the demand of the passive peer by sending an
<em><xref target="messages_elements" format="title" /></em> message if a offer request
for the element was sent earlier. Otherwise, the protocol MUST be aborted, as peers must never send demands for hashes that they have never been offered.
</dd>
<dt><em><xref target="messages_elements" format="title" /></em> message:</dt>
<dd>
If element is received that was not demanded or for which
the application-specific validation logic fails, the protocol
MUST be aborted. Otherwise, the corresponding demand is marked
as satisfied. Note that this applies only to the differential
synchronization mode. In full synchronization, it is perfectly
normal to receive
<xref target="messages_full_element" format="title" />
messages for elements that were not demanded and that might
even already be known locally.
</dd>
<dt><em><xref target="messages_done" format="title" /></em> message:</dt>
<dd>
Receiving the message <em><xref target="messages_done" format="title" /></em> indicates
that all demands of the passive peer have been satisfied. The active peer then changes into the
<strong>Finish Closing</strong> state.
If the IBF has not finished decoding and the <em><xref target="messages_done" format="title" /></em>
is received, the other peer is not in compliance with the protocol and the protocol MUST be aborted.
</dd>
</dl>
</dd>
<dt><strong>Expecing IBF Last</strong></dt>
<dd>
<t>
In this state the active peer continuously receives <em><xref target="messages_ibf" format="title" /></em>
messages from the passive peer. When the last <em><xref target="messages_ibf_last" format="title" /></em> message is received,
the peer changes into the <strong>Active Decoding</strong> state.
</t>
</dd>
<dt><strong>Finish Closing</strong> / <strong>Finish Waiting</strong></dt>
<dd>
<t>
In this states the peers are waiting for all demands to be satisfied and for the synchronisation
to be completed. When all demands are satisfied the peer changes into <strong>Finished</strong> state.
</t>
</dd>
</dl>
</section>
<section anchor="modeofoperation_combined-mode" numbered="true" toc="default">
<name>Combined Mode</name>
<t>
In the <em>combined mode</em> the protocol decides between
<xref target="modeofoperation_full-sync" format="title" /> and
the <xref target="modeofoperation_individual-elements" format="title" />
to minimize resource consumption. Typically, the protocol always runs
in combined mode, but implementations MAY allow applications to force
the use of one of the modes for testing. In this case, applications MUST
ensure that the respective options to force a particular mode are used by
both participants.
</t>
<t>
The <xref target="modeofoperation_individual-elements" format="title" /> is only efficient on small set
differences or if the byte-size of the elements is large. If the set difference is estimated to be large
the <xref target="modeofoperation_full-sync" format="title" /> is
more efficient. The exact heuristics and parameters on which the protocol decides which mode
MUST be used are described in the <xref target="performance" format="title" /> section of this document.
</t>
<t>
There are two main cases when a <xref target="modeofoperation_full-sync" format="title" />
is always used.
The first case is when one of the peers announces having an empty set. This is announced by setting
the SETSIZE field in the <em><xref target="messages_se" format="title" /></em> to 0.
<!-- FIXME: why not also do this if sending the elements is about as
expensive as sending the SE? Should be a simple calculation. (thesis summermatter: future work) -->
The second case is if the application requests full synchronisation explicitly.
This is useful for testing and MUST NOT be used in production.
</t>
<t>
The state diagram illustrating the combined mode can be found
<eref target="https://git.gnunet.org/lsd0003.git/plain/statemachine/full_state_machine.png">here</eref>.
</t>
</section>
</section>
<section anchor="messages" numbered="true" toc="default">
<name>Messages</name>
<t>
This section describes the various message formats used by the protocol.
</t>
<section anchor="messages_operation_request" numbered="true" toc="default">
<name>Operation Request</name>
<section anchor="messages_operation_request_description" numbered="true" toc="default">
<name>Description</name>
<t>
This message is the first message of the protocol and it is sent to signal to the receiving peer
that the initiating peer wants to initialize a new connection.
</t>
<t>
This message is sent in the transition between the <strong>Initiating Connection</strong> state and the <strong>Expect SE</strong> state.
</t>
<t>
If a peer receives this message and is willing to run the protocol, it answers by sending back a <em><xref target="messages_se" format="title" /></em> message.
Otherwise it simply closes the connection.
</t>
</section>
<section anchor="messages_operation_request_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_operation_request">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | ELEMENT COUNT |
+-----+-----+-----+-----+-----+-----+-----+-----+
| APX
+-----+-----+-----+-----+-----+-----+-----+-----+ /
/ APPLICATION DATA /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is the type of SETU_P2P_OPERATION_REQUEST as registered in <xref target="gana" format="title" />, in network byte order.
</dd>
<dt>ELEMENT COUNT</dt>
<dd>
is the number of the elements the requesting party has in its set, as a 32-bit unsigned integer in network byte order.
</dd>
<dt>APX</dt>
<dd>
is a SHA-512 hash that identifies the application.
</dd>
<dt>APPLICATION DATA</dt>
<dd>
is optional, variable-size application specific data that can be used
by the application to decide if it would like to answer the request.
</dd>
</dl>
</section>
</section>
<section anchor="messages_ibf" numbered="true" toc="default">
<name>IBF</name>
<section anchor="messages_ibf_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <xref target="messages_ibf" format="title" /> message contains a slice of the IBF.
</t>
<t>
The <em>IBF</em> message is sent at the start of the protocol from the initiating peer in the transaction
between <strong>Expect SE</strong> -> <strong>Expecting IBF Last</strong> or when the IBF does not
decode and there is a role change in the transition between <strong>Active Decoding</strong> -> <strong>Expecting IBF Last</strong>.
This message is only sent if there is more than one IBF slice to be sent. If there is just
one slice, then only the <xref target="messages_ibf_last" format="title" /> message is sent.
</t>
</section>
<section anchor="messages_ibf_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_ibf">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | IBF SIZE |
+-----+-----+-----+-----+-----+-----+-----+-----+
| OFFSET | SALT | IMCS |
+-----+-----+-----+-----+-----+-----+-----+-----+
| IBF-SLICE
+-----+-----+-----+-----+-----+-----+-----+-----+ /
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte orderwhichdescribes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
the type of SETU_P2P_REQUEST_IBF as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>IBF SIZE</dt>
<dd>
is a 32-bit unsigned integer which signals the total number of buckets in the IBF. The minimal number of buckets is 37.
</dd>
<dt>OFFSET</dt>
<dd>
is a 32-bit unsigned integer which signals the offset of the following IBF slices in the original.
</dd>
<dt>SALT</dt>
<dd>
is a 16-bit unsigned integer that contains the IBF-salt which was used to create the
IBF.
</dd>
<dt>IMCS</dt>
<dd>
is a 16-bit unsigned integer, which describes the number of bits that
are required to store a single counter. This is used for the unpacking function as described
in the <xref target="performance_counter_variable_size" format="title" /> section.
</dd>
<dt>IBF-SLICE</dt>
<dd>
<t>
are variable numbers of slices in an array. A single slice contains multiple 64-bit IDSUMS,
32-bit HASHSUMS and (1-64)-bit COUNTERS of variable size. All values are in the network byte order. The array of IDSUMS is serialized first, followed
by an array of HASHSUMS. Last comes an array of unsigned COUNTERS (details of the COUNTERS encoding are described in section
<xref target="performance_counter_variable_size" format="default"/>). The length of the array is
defined by MIN( SIZE - OFFSET, MAX_BUCKETS_PER_MESSAGE). MAX_BUCKETS_PER_MESSAGE is defined as
32768 divided by the BUCKET_SIZE which ranges between 97-bits when counter uses bit 1 (IMCS=1) and 160-bit when counter size uses 64 bit (IMCS=64).
</t>
<t>
To get the IDSUM field, all IDs (computed with the IBF-salt) hitting a bucket under the map M are added up with a binary XOR operation.
See <xref target="ibf_format_id_generation" format="title" /> details about ID generation.
</t>
<t>
The calculation of the HASHSUM field is done accordingly to the calculation of the IDSUM field:
all HASHes are added up with a binary XOR operation.
The HASH value is calculated as described in detail in section <xref target="ibf_format_HASH_calculation" format="title" />.
</t>
<t>
The algorithm to find the correct bucket in which the ID and the HASH have to be added
is described in detail in section <xref target="ibf_m" format="title" />.
</t>
<t>
Test vectors for an implementation can be found in the <xref target="test_vectors" format="title" /> section
</t>
</dd>
</dl>
<figure anchor="figure_ibf_slice">
<artwork name="" type="" align="left" alt=""><![CDATA[
IBF-SLICE
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| IDSUMS |
+-----+-----+-----+-----+-----+-----+-----+-----+
| IDSUMS |
+-----+-----+-----+-----+-----+-----+-----+-----+
| HASHSUMS | HASHSUMS |
+-----+-----+-----+-----+-----+-----+-----+-----+
| COUNTERS* | COUNTERS* |
+-----+-----+-----+-----+-----+-----+-----+-----+
/ /
/ /
* Counter size is variable. In this example the IMCS is 32 (4 bytes).
]]></artwork>
</figure>
</section>
</section>
<section anchor="messages_ibf_last" numbered="true" toc="default">
<name>IBF Last</name>
<section anchor="messages_ibf_last_description" numbered="true" toc="default">
<name>Description</name>
<t>
This message indicates to the remote peer that this is the last slice
of the Bloom filter. The receiving peer MUST check that the sizes and
offsets of all received IBF slices add up to the total IBF SIZE that was
given.
</t>
<t>
Receiving this message initiates the state transmissions
<strong>Expecting IBF Last</strong> -> <strong>Active Decoding</strong>,
<strong>Expecting IBF</strong> -> <strong>Active Decoding</strong> and
<strong>Passive Decoding</strong> -> <strong>Active Decoding</strong>. This message
can initiate a peer the roll change from <strong>Active Decoding</strong> to
<strong>Passive Decoding</strong>.
</t>
</section>
<section anchor="messages_ibf_last_structure" numbered="true" toc="default">
<name>Structure</name>
<t>
The binary structure is exactly the same as the <xref target="messages_ibf_structure" format="title" /> of
the message <xref target="messages_ibf" format="title" /> with a different "MSG TYPE"
which is defined in <xref target="gana" format="title" /> "SETU_P2P_IBF_LAST".
</t>
</section>
</section>
<section anchor="messages_elements" numbered="true" toc="default">
<name>Element</name>
<section anchor="messages_elements_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_elements" format="title" /></em> message contains an element that is synchronized in the <xref target="modeofoperation_individual-elements" format="title" />
and transmits a full element between the peers.
</t>
<t>
This message is sent in the state <strong>Active Decoding</strong> and <strong>Passive Decoding</strong>
as answer to a <em><xref target="messages_demand" format="title" /></em> message from the remote peer.
The <em><xref target="messages_elements" format="title" /></em> message can also be received in the <strong>Finish Closing</strong> or <strong>Finish Waiting</strong>
state after receiving a <em><xref target="messages_done" format="title" /></em> message from the remote peer. In this
case the peer changes to the <strong>Finished</strong> state as soon as all demands for elements have been satisfied.
</t>
<t>
This message is exclusively used in the <xref target="modeofoperation_individual-elements" format="title" />.
</t>
</section>
<section anchor="messages_elements_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_elements">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | E TYPE | PADDING |
+-----+-----+-----+-----+-----+-----+-----+-----+
| E SIZE | DATA
+-----+-----+ /
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_ELEMENTS as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>E TYPE</dt>
<dd>
is a 16-bit unsigned integer which defines the element type for
the application.
</dd>
<dt>PADDING</dt>
<dd>
is 16-bit always set to zero.
</dd>
<dt>E SIZE</dt>
<dd>
is a 16-bit unsigned integer that signals the size of the elements data part.
</dd>
<dt>DATA</dt>
<dd>
is a field with variable length that contains the data of the element.
</dd>
</dl>
</section>
</section>
<section anchor="messages_offer" numbered="true" toc="default">
<name>Offer</name>
<section anchor="messages_offer_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_offer" format="title" /></em> message is an answer to an <em><xref target="messages_inquiry" format="title" /></em> message
and transmits the full hash of an element that has been requested by the other peer.
This full hash enables the other peer to check if the element is really missing in his set and
eventually sends a <em><xref target="messages_demand" format="title" /></em> message for that element.
</t>
<t>
The offer is sent and received only in the <strong>Active Decoding</strong> and in the <strong>Passive Decoding</strong>
state.
</t>
<t>
This message is exclusively sent in the <xref target="modeofoperation_individual-elements" format="title" />.
</t>
</section>
<section anchor="messages_offer_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_offer">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | HASH 1
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| HASH 1 | HASH 2
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| HASH 2 | HASH n
+-----+-----+-----+-----+-----+-----+-----+-----+
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_OFFER as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>HASHES</dt>
<dd>
contains one or more successive SHA 512-bit hashes of the elements that are being requested with <em><xref target="messages_inquiry" format="title" /></em> messages.
</dd>
</dl>
</section>
</section>
<section anchor="messages_inquiry" numbered="true" toc="default">
<name>Inquiry</name>
<section anchor="messages_inquiry_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_inquiry" format="title" /></em> message is exclusively sent by the active peer in <strong>Active Decoding</strong> state
to request the full hash of an element that is missing in the active peers set. This is normally answered
by the passive peer with <em><xref target="messages_offer" format="title" /></em> message.
</t>
<t>
This message is exclusively sent in the <xref target="modeofoperation_individual-elements" format="title" />.
</t>
</section>
<section anchor="messages_inquiry_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_inquiry">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | SALT |
+-----+-----+-----+-----+-----+-----+-----+-----+
| IBF KEY 1 |
+-----+-----+-----+-----+-----+-----+-----+-----+
| IBF KEY 2 |
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| IBF KEY n |
+-----+-----+-----+-----+-----+-----+-----+-----+
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_INQUIRY as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>IBF KEY</dt>
<dd>
contains one or more successive ibf keys (64-bit unsigned integer) for which the inquiry is sent.
</dd>
</dl>
</section>
</section>
<section anchor="messages_demand" numbered="true" toc="default">
<name>Demand</name>
<section anchor="messages_demand_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_demand" format="title" /></em> message is sent in the <strong>Active Decoding</strong> and in the <strong>Passive Decoding</strong>
state. It is an answer to a received <em><xref target="messages_offer" format="title" /></em> message
and is sent if the element described in the <em><xref target="messages_offer" format="title" /></em> message
is missing in the peers set. In the normal workflow the answer to the <em><xref target="messages_demand" format="title" /></em> message is an
<em><xref target="messages_elements" format="title" /></em> message.
</t>
<t>
This message is exclusively sent in the <xref target="modeofoperation_individual-elements" format="title" />.
</t>
</section>
<section anchor="messages_demand_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_demand">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | HASH
+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| HASH 1 | HASH 2
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| HASH 2 | HASH n
+-----+-----+-----+-----+-----+-----+-----+-----+
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes and the header is included.
</dd>
<dt>MSG TYPE</dt>
<dd>
the type of SETU_P2P_DEMAND as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>HASH</dt>
<dd>
contains one or more successive SHA 512-bit hashes of the elements that are being demanded.
</dd>
</dl>
</section>
</section>
<section anchor="messages_done" numbered="true" toc="default">
<name>Done</name>
<section anchor="messages_done_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_done" format="title" /></em> message is sent when all <em><xref target="messages_demand" format="title" /></em> messages
have been successfully satisfied and from the perspective of the sender the set is completely synchronized.
</t>
<t>
This message is exclusively sent in the <xref target="modeofoperation_individual-elements" format="title" />.
</t>
</section>
<section anchor="messages_done_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_done">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE |
+-----+-----+-----+-----+-----+-----+-----+-----+
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included. The value is always 4 for this message type.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_DONE as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
</dl>
</section>
</section>
<section anchor="messages_full_done" numbered="true" toc="default">
<name>Full Done</name>
<section anchor="messages_full_done_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_full_done" format="title" /></em> message is sent in the <xref target="modeofoperation_full-sync" format="title" />
to signal that all remaining elements of the set have been sent. The message is received and sent in the
<strong>Full Sending</strong> and in the <strong>Full Receiving</strong> state. When the <em><xref target="messages_full_done" format="title" /></em> message is received
in <strong>Full Sending</strong> state the peer changes directly into <strong>Finished</strong> state. In
<strong>Full Receiving</strong> state receiving a <em><xref target="messages_full_done" format="title" /></em> message initiates the sending of
the remaining elements that are missing in the set of the other peer.
</t>
</section>
<section anchor="messages_full_done_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_full_done">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE |
+-----+-----+-----+-----+-----+-----+-----+-----+
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included. The value is always 4 for this message type.
</dd>
<dt>MSG TYPE</dt>
<dd>
the type of SETU_P2P_FULL_DONE as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
</dl>
</section>
</section>
<section anchor="messages_request_full" numbered="true" toc="default">
<name>Request Full</name>
<section anchor="messages_request_full_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_request_full" format="title" /></em> message is sent by the initiating peer in <strong>Expect SE</strong> state to the receiving peer, if
the operation mode "<xref target="modeofoperation_full-sync" format="title" />" is
determined to be the superior <xref target="modeofoperation" format="title" /> and that it is the better choice that
the other peer sends his elements first. The initiating peer changes after sending the <em><xref target="messages_request_full" format="title" /></em> message into
<strong>Full Receiving</strong> state.
</t>
<t>
The receiving peer receives the <em><xref target="messages_request_full" format="title" /></em> message in the <strong>Expecting IBF</strong>, afterwards the receiving peer
starts sending his complete set in <xref target="messages_full_element" format="title" /> messages to the initiating peer.
</t>
</section>
<section anchor="messages_request_full_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_request_full">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | REMOTE SET DIFF |
+-----+-----+-----+-----+-----+-----+-----+-----+
| REMOTE SET SIZE | LOCAL SET DIFF |
+-----+-----+-----+-----+-----+-----+-----+-----+
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included. The value is always 16 for this message type.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_REQUEST_FULL as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>REMOTE SET DIFF</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the remote (from the perspective of the
sending peer) set difference calculated with strata estimator.
</dd>
<dt>REMOTE SET SIZE</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the total remote
(from the perspective of the sending peer) set size.
</dd>
<dt>LOCAL SET DIFF</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the local
(from the perspective of the sending peer) set difference calculated with strata estimator.
</dd>
</dl>
</section>
</section>
<section anchor="messages_send_full" numbered="true" toc="default">
<name>Send Full</name>
<section anchor="messages_send_full_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_send_full" format="title" /></em> message is sent by the initiating peer in <strong>Expect SE</strong> state to the receiving peer if
the operation mode "<xref target="modeofoperation_full-sync" format="title" />" is
determined as superior <xref target="modeofoperation" format="title" /> and that it is the better choice that the
peer sends his elements first. The initiating peer changes after sending the <em><xref target="messages_request_full" format="title" /></em> message into
<strong>Full Sending</strong> state.
</t>
<t>
The receiving peer receives the <em><xref target="messages_send_full" format="title" /></em> message in the <strong>Expecting IBF</strong> state, afterwards the receiving peer
changes into <strong>Full Receiving</strong> state and expects to receive the set of the remote peer.
</t>
</section>
<section anchor="messages_send_full_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_send_full">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | REMOTE SET DIFF |
+-----+-----+-----+-----+-----+-----+-----+-----+
| REMOTE SET SIZE | LOCAL SET DIFF |
+-----+-----+-----+-----+-----+-----+-----+-----+
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included. The value is always 16 for this message type.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_REQUEST_FULL as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>REMOTE SET DIFF</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the remote (from the perspective of the sending peer)
set difference calculated with strata estimator.
</dd>
<dt>REMOTE SET SIZE</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the total remote (from the perspective
of the sending peer) set size.
</dd>
<dt>LOCAL SET DIFF</dt>
<dd>
is a 32-bit unsigned integer in network byte order, which represents the local (from the perspective of the sending peer)
set difference calculated with strata estimator.
</dd>
</dl>
</section>
</section>
<section anchor="messages_se" numbered="true" toc="default">
<name>Strata Estimator</name>
<section anchor="messages_se_description" numbered="true" toc="default">
<name>Description</name>
<t>
The strata estimator is sent by the receiving peer at the start of the protocol, right after the
<xref target="messages_operation_request" format="title" /> message has been received.
</t>
<t>
The strata estimator is used to estimate the difference between the two sets as described in section <xref target="se" format="title" />.
</t>
<t>
When the initiating peer receives the strata estimator, the peer decides which <xref target="modeofoperation" format="title" /> to use
for the synchronisation. Depending on the size of the set difference and the <xref target="modeofoperation" format="title" /> the initiating peer
changes into <strong>Full Sending</strong>, <strong>Full Receiving</strong> or <strong>Passive Decoding</strong> state.
</t>
<t>
The <em><xref target="messages_se" format="title" /></em> message can contain one, two, four or eight strata estimators with different salts, depending on the initial size of the sets.
More details can be found in section <xref target="performance_multi_se" format="title" />.
</t>
<t>
The IBFs in a strata estimator always have 79 buckets. The reason why can be found in <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> in section 3.4.2.
</t>
<!-- Give a more precise reference into the thesis for this, do not cite the whole thesis! -->
</section>
<section anchor="messages_se_structure" numbered="true" toc="default">
<name>Structure</name>
<figure anchor="figure_se">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | SEC | SETSIZE
+-----+-----+-----+-----+-----+-----+-----+-----+
SETSIZE | SE-SLICES
+-----+-----+-----+-----+
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_SE as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>SEC</dt>
<dd>
is a 8-bit unsigned integer in networkf byte order, which indicates how many strata estimators
with different salts are attached to the message. Valid values are 1,2,4 or 8, more details can be found
in the section <xref target="performance_multi_se" format="title" />.
</dd>
<dt>SETSIZE</dt>
<dd>
is a 64-bit unsigned integer that is defined by the size of the set the SE is
</dd>
<dt>SE-SLICES</dt>
<dd>
<t>
are variable numbers of slices in an array. A slice can contain one or more Strata Estimators which
contain multiple IBFs as described in IBF-SLICES in <xref target="messages_ibf_structure" format="default"/>.
A SE slice can contain one to eight Strata Estimators which contain 32 (Defined as Constant SE_STRATA_COUNT) IBFs. Every IBF in
a SE contains 79 Buckets.
</t>
<t>
The different SEs are built as in detail described in <xref target="performance_multi_se" format="default"/>.
Simply put, the IBFs in each SE are serialized as described in <xref target="messages_ibf_structure" format="default"/> starting with the highest stratum.
Then the created SEs are appended one after the other starting with the SE that was created with a salt of zero.
</t>
</dd>
</dl>
<figure anchor="figure_se_slice">
<artwork name="" type="" align="left" alt=""><![CDATA[
SE-SLICE
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| SE 1 [IBF 1] |
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
+-----+-----+-----+-----+-----+-----+-----+-----+
| SE 1 [IBF 30] |
+-----+-----+-----+-----+-----+-----+-----+-----+
| SE 2 [IBF 1] |
+-----+-----+-----+-----+-----+-----+-----+-----+
... ...
/ /
/ /
]]></artwork>
</figure>
</section>
</section>
<section anchor="messages_sec" numbered="true" toc="default">
<name>Strata Estimator Compressed</name>
<section anchor="messages_sec_description" numbered="true" toc="default">
<name>Description</name>
<t>
The Strata Estimator can be compressed with gzip as
described in <xref target="RFC1951"/> to improve performance. This can be recognized
by the different message type number from <xref target="gana" format="title" />.
</t>
<section anchor="messages_sec_structure" numbered="true" toc="default">
<name>Structure</name>
<t>
The key difference between the compressed and the uncompressed Strata Estimator is that the
SE slices are compressed with gzip (<xref target="RFC1951"/>) in the compressed SE.
But the header remains uncompressed with both.
</t>
<t>
Since the content of the message is the same as the uncompressed Strata Estimator, the details
are not repeated here. For details see section <xref target="messages_se" format="counter" />.
</t>
</section>
</section>
</section>
<section anchor="messages_full_element" numbered="true" toc="default">
<name>Full Element</name>
<section anchor="messages_full_element_description" numbered="true" toc="default">
<name>Description</name>
<t>
The <em><xref target="messages_full_element" format="title" /></em> message is the equivalent of the <xref target="messages_elements" format="title" /> message in
the <xref target="modeofoperation_full-sync" format="title" />. It contains a complete element that is missing
in the set of the peer that receives this message.
</t>
<t>
The <em><xref target="messages_full_element" format="title" /></em> message is exclusively sent in the transitions <strong>Expecting IBF</strong> -> <strong>Full Receiving</strong> and
<strong>Full Receiving</strong> -> <strong>Finished</strong>. The message is only received in the <strong> Full Sending</strong> and
<strong>Full Receiving</strong> state.
</t>
<t>
After the last <em><xref target="messages_full_element" format="title" /></em> message has been sent, the <em><xref target="messages_full_done" format="title" /></em> message
is sent to conclude the full synchronisation of the element sending peer.
</t>
</section>
<section anchor="messages_full_element_structure" numbered="true" toc="default">
<name>Structure</name>
<!-- MAYBE just refer to the "ELEMENT" section on structure and only
note the different MSG TYPE here? -->
<figure anchor="figure_full_element">
<artwork name="" type="" align="left" alt=""><![CDATA[
0 8 16 24 32 40 48 56
+-----+-----+-----+-----+-----+-----+-----+-----+
| MSG SIZE | MSG TYPE | E TYPE | PADDING |
+-----+-----+-----+-----+-----+-----+-----+-----+
| SIZE | AE TYPE | DATA
+-----+-----+-----+-----+
/ /
/ /
]]></artwork>
</figure>
<t>where:</t>
<dl>
<dt>MSG SIZE</dt>
<dd>
is a 16-bit unsigned integer in network byte order, which describes the message size in bytes with the header included.
</dd>
<dt>MSG TYPE</dt>
<dd>
is SETU_P2P_REQUEST_FULL_ELEMENT as registered in <xref target="gana" format="title" /> in network byte order.
</dd>
<dt>E TYPE</dt>
<dd>
is a 16-bit unsigned integer which defines the element type for
the application.
</dd>
<dt>PADDING</dt>
<dd>
is 16-bit always set to zero
</dd>
<dt>E SIZE</dt>
<dd>
is a 16-bit unsigned integer that signals the size of the elements data part.
</dd>
<dt>AE TYPE</dt>
<dd>
is a 16-bit unsigned integer that is needed to identify
the type of element that is in the data field
</dd>
<dt>DATA</dt>
<dd>
is a field with variable length that contains the data of the element.
</dd>
</dl>
</section>
</section>
</section>
<section anchor="performance" numbered="true" toc="default">
<name>Performance Considerations</name>
<section anchor="performance_formulas" numbered="true" toc="default">
<name>Formulas</name>
<section anchor="performance_formulas_operationmode" numbered="true" toc="default">
<name>Operation Mode</name>
<t>
The decision which <xref target="modeofoperation" format="title"/> is used is described by the following code.
More detailed explanations motivating the design can be found in the accompanying thesis in section 4.5.3.<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>
</t>
<t>
The function takes as input the average element size, the local set size, the remote set size, the set differences as estimated from the strata estimator for both the local and remote sets,
and the bandwidth/roundtrip tradeoff.
The function returns the exact <xref target="modeofoperation" format="title"/> that is predicted to be best as output: FULL_SYNC_REMOTE_SENDING_FIRST
if it is likely cheapest that the other peer transmits his elements first, FULL_SYNC_LOCAL_SENDING_FIRST
if it is likely cheapest that the elements are transmitted to the other peer directly, and
DIFFERENTIAL_SYNC if the differential synchronisation is likely cheapest.
</t>
<t>
The constant IBF_BUCKET_NUMBER_FACTOR is always 2 and IBF_MIN_SIZE is 37.
The method for deriving
this can be found in the IBF parameter study in <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> in section 4.5.2.
</t>
<figure anchor="performance_formulas_operationmode_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# CONSTANTS:
# IBF_BUCKET_NUMBER_FACTOR = 2: The amount the IBF gets increased if decoding fails
# RTT_MIN_FULL = 2: Minimal round trips used for full syncronisation (always 2 or 2.5)
# IBF_MIN_SIZE = 37: The minimal size of an IBF
# MAX_BUCKETS_PER_MESSAGE: Custom value depending on the underlying protocol
# INPUTS:
# avg_es: The average element size
# lss: The initial local set size
# rss: The remote set size
# lsd: the estimated local set difference calculated by the SE
# rsd: the estimated remote set difference calculated by the SE
# rtt: the tradeoff between round trips and bandwidth
# OUTPUT:
# FULL_SYNC_REMOTE_SENDING_FIRST, FULL_SYNC_LOCAL_SENDING_FIRST or DIFFERENTIAL_SYNC
FUNCTION decide_operation_mode(avg_es,
lss,
rss,
lsd
rsd,
rtt)
# If a set size is zero always do full sync
# TODO: check if these two conditions are
# actually meaningful, I suspect even without
# this check at the beginning the logic below
# should always yield the same result for these
# extreme cases, allowing us to omit this code.
IF (0 == rss)
RETURN FULL_SYNC_LOCAL_SENDING_FIRST
END IF
IF (0 == lss)
RETURN FULL_SYNC_REMOTE_SENDING_FIRST
END IF
# Estimate required transferred bytes when doing a full synchronisation
# and transmitting local set first.
estimated_total_diff = rsd + lsd
total_elements_local_send = rsd + lss
cost_local_full_sync = avg_es * total_elements_local_send
+ total_elements_local_send * sizeof(ELEMENT_MSG_HEADER)
+ sizeof(FULL_DONE_MSG_HEADER) * 2
+ RTT_MIN_FULL * rtt
# Estimate required transferred bytes when doing a full synchronisation
# and transmitting remote set first.
total_elements_remote_send = lsd + rss
cost_remote_full_sync = avg_es * total_elements_remote_send
+ total_elements_remote_send * sizeof(ELEMENT_MSG_HEADER)
+ sizeof(FULL_DONE_MSG_HEADER) * 2
+ (RTT_MIN_FULL + 0.5) * rtt
+ sizeof(REQUEST_FULL_MSG)
# Estimate required transferred bytes when doing a differential synchronisation
# Estimate messages required to transfer IBF
ibf_bucket_count = estimated_total_diff * IBF_BUCKET_NUMBER_FACTOR
IF (ibf_bucket_count <= IBF_MIN_SIZE)
ibf_bucket_count = IBF_MIN_SIZE
END IF
ibf_message_count = ceil (ibf_bucket_count / MAX_BUCKETS_PER_MESSAGE)
# Estimate average counter length with variable counter
estimated_counter_bits = MIN (2 * LOG2(lss / ibf_bucket_count),
LOG2(lss))
estimated_counter_bytes = estimated_counter_bits / 8
# Sum up all messages required to do differential synchronisation
ibf_bytes = sizeof(IBF_MESSAGE) * ibf_message_count
+ ibf_bucket_count * sizeof(IBF_KEY)
+ ibf_bucket_count * sizeof(IBF_KEYHASH)
+ ibf_bucket_count * estimated_counter_bytes
# Add 20% overhead to cover IBF retries due to decoding failures
total_ibf_bytes = ibf_bytes * 1.2
# Estimate other message sizes to be transfered in diff sync
# Note that we simplify by adding the header each time;
# if the implementation combines multiple INQUIRY/DEMAND/OFFER
# requests in one message, the bandwidth would be lower.
done_size = sizeof(DONE_HEADER)
element_size = (avg_es + sizeof(ELEMENT_MSG_HEADER))
* estimated_total_diff
inquery_size = (sizeof(IBF_KEY) + sizeof(INQUERY_MSG_HEADER))
* estimated_total_diff
demand_size = (sizeof(HASHCODE) + sizeof(DEMAND_MSG_HEADER))
* estimated_total_diff
offer_size = (sizeof(HASHCODE) + sizeof(OFFER_MSG_HEADER))
* estimated_total_diff
# Estimate total cost
diff_cost = element_size + done_size + inquery_size
+ demand_size + offer_size + total_ibf_bytes
+ DIFFERENTIAL_RTT_MEAN * rtt
# Decide for a optimal mode of operation
full_cost_min = MIN (cost_local_full_sync,
cost_remote_full_sync)
IF (full_cost_min < diff_cost)
IF (cost_remote_full_sync > cost_local_full_sync)
RETURN FULL_SYNC_LOCAL_SENDING_FIRST
ELSE
RETURN FULL_SYNC_REMOTE_SENDING_FIRST
END IF
ELSE
RETURN DIFFERENTIAL_SYNC
END IF
]]></artwork>
</figure>
</section>
<section anchor="performance_formula_ibf_parameters" numbered="true" toc="default">
<name>IBF Size</name>
<t>
The functions, described in this section, calculate a good initial size (initial_ibf_size)
and in case of decoding failure, a good next IBF size (get_next_ibf_size).
</t>
<t>
These algorithms are described and justified in more details in
<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> in the parameter study in
section 3.5.2, the max IBF counter in section 3.10 and the Improved IBF size in section 3.11.
</t>
<figure anchor="performance_formula_ibf_parameters_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# CONSTANTS:
# IBF_BUCKET_NUMBER_FACTOR = 2: The amount the IBF gets increased if decoding fails
# Inputs:
# sd: Estimated set difference
# Output:
# next_size: Size of the initial IBF
FUNCTION initial_ibf_size(sd)
# We do not go below 37, as 37 buckets should
# basically always be below one MTU, so there is
# little to be gained, while a smaller IBF would
# increase the chance of a decoding failure.
return MAX(37, IBF_BUCKET_NUMBER_FACTOR * sd);
FUNCTION END
# CONSTANTS:
# IBF_BUCKET_NUMBER_FACTOR = 2: The amount the IBF gets increased if decoding fails
# Inputs:
# de: Number of elements that have been successfully decoded
# lis: The number of buckets of the last IBF
# Output:
# number of buckets for the next IBF
FUNCTION get_next_ibf_size(de, lis)
next_size = IBF_BUCKET_NUMBER_FACTOR * (lis - de)
# The MAX operation here also ensures that the
# result is positive.
return MAX(37, next_size);
FUNCTION END
]]></artwork>
</figure>
</section>
<section anchor="performance_num_buck_hash" numbered="true" toc="default">
<name>Number of Buckets an Element is Hashed into</name>
<t>
The number of buckets an element is hashed to is hardcoded to 3. Reasoning and
justification can be found in
<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> in the
IBF parameter performance study in section 4.5.2.
</t>
</section>
</section>
<section anchor="performance_counter_variable_size" numbered="true" toc="default">
<name>Variable Counter Size</name>
<t>
The number of bits required to represent the counters of an IBF varies
due to different parameters as described in section 3.2 of
<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>.
Therefore, a packing algorithm has been implemented.
This algorithm encodes the IBF counters in their optimal bit-width
and thus minimizes the bandwidth needed to transmit the IBF.
</t>
<t>
A simple algorithm is used for the packing.
In a first step it is determined, which is the largest counter.
The the base 2 logarithm then determines how many bits are needed to store it.
In a second step for every counter of every bucket, the counter
is stored using this many bits. The resulting bit sequence is then simply concatenated.
</t>
<t>
Three individual functions are used for this purpose.
The first one is a function that iterates over each bucket of
the IBF to get the maximum counter in the IBF. The second function
packs the counters of the IBF, and the third function that unpacks the counters.
</t>
<figure anchor="performance_counter_variable_size_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# INPUTS:
# ibf: The IBF
# OUTPUTS:
# returns: Minimal amount of bits required to store the counter
FUNCTION ibf_get_max_counter(ibf)
max_counter=1 # convince static analysis that we never take log2(0)
FOR bucket IN ibf
IF bucket.counter > max_counter
max_counter = bucket.counter
END IF
END FOR
# next bigger discrete number of the binary logarithm of the max counter
RETURN CEILING( log2 ( max_counter ) )
# INPUTS:
# ibf: The IBF
# offset: The offset which defines the starting point from which bucket the
# pack operation starts
# count: The number of buckets in the array that will be packed
# OUTPUTS:
# returns: A byte array of packed counters to send over the network
# INPUTS:
# ibf: The IBF
# offset: The offset which defines the starting point from which bucket the
# pack operation starts
# count: The number of buckets in the array that will be packed
# OUTPUTS:
# returns: A byte array of packed counters to send over the network
FUNCTION pack_counter(ibf, offset, count)
counter_bytes = ibf_get_max_counter(ibf)
store_bits = 0
store = 0
byte_ctr = 0
buffer=[]
FOR bucket IN ibf[offset] to ibf[count]
counter = bucket.counter
byte_len = counter_bytes
WHILE byte_len + store_bits < 8
bit_to_shift = 0
IF store_bits > 0 OR byte_len > 8
bit_free = 8 - store_bits
bit_to_shift = byte_len - bit_free
store = store << bit_free
END IF
buffer[byte_ctr] = (( counter >> bit_to_shift) | store) & 0xFF
byte_ctr = byte_ctr + 1
byte_len -= 8 - store_bits
counter = counter & ((1 << byte_len) - 1)
store = 0
store_bits = 0
END WHILE
store = (store << byte_len) | counter
store_bits = store_bits + byte_len
byte_len = 0
END FOR
# Write the last partial packed byte to the buffer
IF store_bits > 0
buffer[byte_ctr] = store << (8 - store_bits)
byte_ctr = byte_ctr + 1
END IF
RETURN buffer
FUNCTION END
# INPUTS:
# ibf: The IBF
# offset: The offset which defines the starting point from which bucket
the packed operation starts
# count: The number of buckets in the array that will be packed
# cbl: The bit length of the counter can be found in the
ibf message in the ibf_counter_bit_length field
# pd: A byte array which contains the data packed with the pack_counter
function
# OUTPUTS:
# returns: Nothing because the unpacked counter is saved directly into the IBF
FUNCTION unpack_counter(ibf, offset, count, cbl, pd)
ibf_bucket_ctr = 0
store = 0
store_bits = 0
byte_ctr = 0
WHILE TRUE
byte_to_read = pd[byte_ctr]
bit_to_pack_left = 8
byte_ctr++
WHILE bit_to_pack_left >= 0
# Prevent packet from reading more than required
IF ibf_bucket_ctr > (count - 1)
RETURN
END IF
IF (store_bits + bit_to_pack_left) >= cbl
bit_use = cbl - store_bits
IF store_bits > 0
store = store << bit_use
END IF
bytes_to_shift = bit_to_pack_left - bit_use
counter_partial = byte_to_read >> bytes_to_shift
store = store | counter_partial
ibf.counter[ibf_bucket_ctr + offset] = store
byte_to_read = byte_to_read & (( 1 << bytes_to_shift ) - 1)
bit_to_pack_left -= bit_use
ibf_bucket_ctr++
store = 0
store_bits = 0
ELSE
store_bits = store_bits + bit_to_pack_left
IF 0 == store_bits
store = byte_to_read
ELSE
store = store << bit_to_pack_left
store = store | byte_to_read
END IF
BREAK
END IF
END WHILE
END WHILE
END FUNCTION
]]></artwork>
</figure>
</section>
<section anchor="performance_multi_se" numbered="true" toc="default">
<name>Multi Strata Estimators</name>
<t>
In order to improve the precision of the estimates not only one strata estimator
is transmitted for larger sets. One, two, four or eight strata estimators can be
transferred. Transmitting multiple strata estimators has the disadvantage that
additional bandwidth will be used, so despite the higher precision, it is not
always optimal to transmit eight strata estimators. Therefore, the following
rules are used, which are based on the average element size multiplied by the number
of elements in the set. This value is denoted as "b" in the table:
</t>
<dl>
<dt>SEs</dt>
<dd>Rule</dd>
<dt>1</dt>
<dd>b < 68kb</dd>
<dt>2</dt>
<dd>b > 68kb</dd>
<dt>4</dt>
<dd>b > 269kb</dd>
<dt>8</dt>
<dd>b > 1'077kb</dd>
</dl>
<t>
When creating multiple strata estimators, it is important to salt the keys for the IBFs in the strata
estimators differently, using the following bit rotation based salting method:
</t>
<figure anchor="performance_multi_se_salting_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# Inputs:
# value: Input value to salt (needs to be 64 bit unsigned)
# salt: Salt to salt value with; Should always be ascending and start at zero
i.e. SE1 = Salt 0; SE2 = Salt 1 etc.
# Output:
# Returns: Salted value
FUNCTION se_key_salting(value, salt)
s = (salt * 7) modulo 64
return (value >> s) | (value << (64 - s))
END FUNCTION
]]></artwork>
</figure>
<t>
Performance study and details about the reasoning for the used methods can be found in <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> in section
3.4.1 under the title "Added Support for Multiple Strata Estimators".
<xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>
</t>
</section>
</section>
<section anchor="security" numbered="true" toc="default">
<name>Security Considerations</name>
<t>
The security considerations in this document focus mainly on the security
goal of availability. The primary goal of the protocol is to prevent an attacker from
wasting computing and network resources of the attacked peer.
</t>
<t>
To prevent denial of service attacks, it is vital to check that peers can only
reconcile a set once in a predefined time span. This is a predefined value and needs
to be adapted per use basis. To enhance reliability and to allow
for legitimate failures, say due to network connectivity issues,
applications SHOULD define a threshold for
the maximum number of failed reconciliation attempts in a given time period.
</t>
<t>
It is important to close and purge connections after a given timeout
to prevent draining attacks.
</t>
<section anchor="security_generic_functions" numbered="true" toc="default">
<name>General Security Checks</name>
<t>
In this section general checks are described which should be applied to multiple states.
</t>
<section anchor="security_generic_input_validation" numbered="true" toc="default">
<name>Input validation</name>
<t>
The format of all received messages needs to be properly validated. This is important to prevent many
attacks on the code. The application data MUST be validated by the application using
the protocol not by the implementation of the protocol.
In case the format validation fails the set operation MUST be terminated.
</t>
</section>
<section anchor="security_generic_functions_check_byzantine_boundaries" numbered="true" toc="default">
<name>Byzantine Boundaries</name>
<t>
To restrict an attacker there should be an upper and lower bound defined and checked
at the beginning of the protocol, based
on prior knowledge, for the number of elements.
The lower byzantine bound can be, for example, the number of elements the
other peer had in his set at the last contact.
The upper byzantine bound can be a practical maximum e.g. the number
of e-voting votes, in Switzerland.
</t>
<figure anchor="security_generic_functions_missing_message_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# Input:
# rec: Number of elements in remote set
# rsd: Number of elements differ in remote set
# lec: Number of elements in local set
# lsd: Number of elements differ in local set
# UPPER_BOUND: Given byzantine upper bound
# LOWER_BOUND: Given byzantine lower bound
# Output:
# returns TRUE if parameters in byzantine bounds otherwise returns FALSE
FUNCTION check_byzantine_bounds (rec,rsd,lec,lsd)
IF (rec + rsd > UPPER_BOUND)
RETURN FALSE
IF END
IF (lec + lsd > UPPER_BOUND)
RETURN FALSE
IF END
IF (rec < LOWER_BOUND)
RETURN FALSE
IF END
RETURN TRUE
FUNCTION END
]]></artwork>
</figure>
<t>
For the byzantine upper bound checks to function
correctly, implementations must ensure that the
estimates of the set size difference added together
never exceed the set byzantine upper bound. This
could for example happen if the strata estimator
overestimates the set difference.
<!-- FIXME: if an implementation does this, then
the first two parts of the check are trivially
satisfied; so likely we should formulate this
not as a 'check' function to be _actually_
executed, but as a plausibility check which
is to be applied after the SE calculation to
the computed set size differences, resulting
in a hard cap on the set size difference estimate
that is then actually used. -->
</t>
</section>
<section anchor="security_generic_functions_check_valid_state" numbered="true" toc="default">
<name>Valid State</name>
<t>
To harden the protocol against attacks, controls were introduced in the improved
implementation that check for each message whether the message was received
in the correct state. This is central so that an attacker finds as little attack
surface as possible and makes it more difficult for the attacker to send the
protocol into an endless loop, for example.
</t>
</section>
<section anchor="security_generic_functions_mfc" numbered="true" toc="default">
<name>Message Flow Control</name>
<t>
For most messages received and sent there needs to be a check in place that checks
that a message is not received multiple times. This is solved with a global store (message)
and the following code
</t>
<t>
The sequence in which messages are received and sent is arranged in a chain.
The messages are dependent on each other. There are dependencies that are
mandatory, e.g. for a sent "Demand" message, an "Element" message must
always be received. But there are also messages for which a response is
not mandatory, e.g. the <em><xref target="messages_inquiry" format="title" /></em> message is only followed by an
"Offer" message, if the corresponding element is in the set. Due to this
fact, checks can be installed to verify compliance with the following chain.
</t>
<figure anchor="security_generic_functions_mfc_chain">
<artwork name="" type="" align="left" alt=""><![CDATA[
Chain for elements +---------+ +---------+ +---------+ +---------+
NOT in IBF decoding | INQUIRY | ---> | OFFER | ===> | DEMAND | ===> | ELEMENT |
peers set +---------+ +---------+ +---------+ +---------+
Chain for elements +---------+ +---------+ +---------+
in IBF decoding | OFFER | ---> | DEMAND | ===> | ELEMENT |
peers set +---------+ +---------+ +---------+
--->: Answer not mandatory
===>: Always answer needed.
]]></artwork>
</figure>
<t>
A possible implementation of the check in pseudocode could look as follows:
</t>
<figure anchor="security_generic_functions_mfc_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# ValidStates:
# The following message states are used to track the message flow.
# - NOT_INITIALIZED: Fresh initialized value
# - SENT: Element has been sent
# - EXPECTED: Element is expected
# - RECEIVED: Element is received
# Function to initialize new store
# Output:
# Returns empty store
FUNCTION initialize_store()
RETURN {}
FUNCTION END
# Function to initialize a store element
# Output:
# Returns an empty element for the store
FUNCTION initialize_element()
RETURN {
INQUIRY: NOT_INITIALIZED,
OFFER: NOT_INITIALIZED,
DEMAND: NOT_INITIALIZED,
ELEMENT: NOT_INITIALIZED
}
FUNCTION END
# Function called every time a new message is transmitted to other peer
# Input:
# store: Store created by the initialize_store() function
# mt: The message that was sent type e.g. INQUIRY or DEMAND
# hash: The hash of the element which is sent
# Output:
# Returns TRUE if the message flow was followed, otherwise FALSE
FUNCTION send(store, mt, hash)
IF NOT hash IS IN store
store_element = initialize_element()
ELSE
store_element = store.get(hash)
END IF
CASE based ON mt
CASE INQUIRY
IF store_element.INQUIRY == NOT_INITIALIZED
store_element.INQUIRY = SENT
ELSE
RETURN FALSE
END IF
CASE OFFER
IF store_element.OFFER == NOT_INITIALIZED
store_element.OFFER = SENT
store_element.DEMAND = EXPECTED
ELSE
RETURN FALSE
END IF
CASE DEMAND
IF store_element.DEMAND == NOT_INITIALIZED AND
(store_element.INQUIRY == SENT OR
store_element.INQUIRY == NOT_INITIALIZED)
store_element.DEMAND = SENT
store_element.ELEMENT = EXPECTED
ELSE
RETURN FALSE
END IF
CASE ELEMENT
IF store_element.ELEMENT == NOT_INITIALIZED AND
store_element.OFFER == SENT
store_element.ELEMENT = SENT
ELSE
RETURN FALSE
END IF
DEFAULT
RETURN FALSE
CASE END
ADD OR UPDATE KEY hash IN store WITH store_element
RETURN TRUE
FUNCTION END
# Function called every time a new message is received from the other peer
# Input:
# store: Store created by the initialize_store() function
# mt: The message that was received type e.g. INQUIRY or DEMAND
# hash: The hash of the element which is received
# Output:
# Returns TRUE if the message flow was followed, otherwise FALSE
FUNCTION receive (store, mt, hash)
IF NOT hash IS IN store
store_element = initialize_element()
ELSE
store_element = store.get(hash)
END IF
CASE based on mt
CASE INQUIRY
IF store_element.INQUIRY == NOT_INITIALIZED
store_element.INQUIRY = RECEIVED
ELSE
RETURN FALSE
END IF
CASE OFFER
IF store_element.OFFER == NOT_INITIALIZED
store_element.OFFER = RECEIVED
ELSE
RETURN FALSE
END IF
CASE DEMAND
IF store_element.DEMAND == EXPECTED AND
store_element.OFFER == SENT
store_element.DEMAND = RECEIVED
ELSE
RETURN FALSE
END IF
CASE ELEMENT
IF store_element.ELEMENT == EXPECTED AND
store_element.DEMAND == SENT
store_element.ELEMENT = RECEIVED
ELSE
RETURN FALSE
END IF
DEFAULT
RETURN FALSE
CASE END
ADD OR UPDATE KEY hash IN store WITH store_element
RETURN TRUE
FUNCTION END
# Function called when the union operation is finished to ensure that all demands have
# been fulfilled
# Input:
# store: Store created by the initialize_store() function
# Output:
# Returns TRUE if all demands have been fulfilled otherwise FALSE
FUNCTION check_if_synchronisation_is_complete(store):
FOR element in store.getAll()
IF element.ELEMENT == EXPECTED OR
element.DEMAND == EXPECTED
RETURN FALSE
IF END
FOR END
RETURN TRUE
FUNCTION END
]]></artwork>
</figure>
<t>
This is based on <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>, section 5.3 (Message Control Flow).
</t>
</section>
<section anchor="security_generic_functions_active_passive_switches" numbered="true" toc="default">
<name>Limit Active/Passive Decoding changes</name>
<t>
To prevent an attacker from sending a peer into an endless loop between active and passive decoding, a
limitation for active/passive roll switches is required.
Otherwise, an attacker could
force the victim to waste unlimited amount of resources by just transmitting
IBFs that do not decode.
This can be implemented by
a simple counter which terminates the operation after a predefined number of switches.
The maximum number of switches needs to be defined in such a way that it is
very improbable that more switches are required in a legitimate interaction,
and hence the malicious behavior of the other peer is assured.
</t>
<t>
The question after how many active/passive switches it can be assumed that the other peer is not honest,
depends on the various tuning parameters of the algorithm.
Section 5.4 of <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>
demonstrates that the probability of decoding failure is less than
15% for each round. The probability that there will be n legitimate
active/passive changes is thus less than 0.15^{round number}.
Which means that after about 30 active/passive switches it can be said with a certainty of 2^80 that one of the peers
is not following the protocol.
Hence, participants MUST impose a maximum of 30 active/passive changes.
</t>
</section>
<section anchor="security_generic_functions_full_plausibility_check" numbered="true" toc="default">
<name>Full Synchronisation Plausibility Check</name>
<t>
An attacker can try to use up a peer's bandwidth by pretending that the peer
needs full synchronisation, even if the set difference is very small and the attacker
only has a few (or even zero) elements that are not already synchronised.
In such a case, it would be ideal if the plausibility could already be checked
during full synchronisation as to whether the other peer was honest or not with
regard to the estimation of the set size difference and thus the choice of mode
of operation.
</t>
<t>
In order to calculate this plausibility, section 5.5 of <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/> describes a formula, which depicts the probability with which one
can calculate the corresponding plausibility based on the number of
new and repeated elements after each received element.
</t>
<t>
Besides this approach from probability theory, there is an additional check
that can be made. After the entire set has been transferred to the other peer,
no known elements may be returned by the second peer, since the second peer
should only return the elements that are missing from the initial peer's set.
</t>
<t>
This two approaches are implemented in the following pseudocode:
</t>
<figure anchor="security_generic_functions_full_plausibility_check_code">
<artwork name="" type="" align="left" alt=""><![CDATA[
# Input:
# SECURITY_LEVEL: The security level used e.g. 2^80
# state: The statemachine state
# rs: Estimated remote set difference
# lis: Number of elements in set
# rd: Number of duplicated elements received
# rf: Number of fresh elements received
# Output:
# Returns TRUE if full synchronisation is plausible and FALSE otherwise
FUNCTION full_sync_plausibility_check (state,rs,lis,rd,rf)
security_level_lb = -1 * SECURITY_LEVEL
# Make sure that no element is received double when
# all elements already are transmitted to the oder side.
IF ( (FULL_SENDING == state) && (rd > 0) )
RETURN FALSE
END IF
# Probabilistic algorithm to check for plausible
# element distribution
IF (FULL_RECEIVING == state)
# Prevent division by 0
IF (0 <= rs)
rs = 1
END IF
# Formula to verify plausibility
base = 1 - (rs / (lis + rs))
exponent = rd - rf * lis / rs
value = exponent * (LOG2(base)/LOG2(2))
IF ((value < security_level_lb) || (value > SECURITY_LEVEL)
RETURN FALSE
END IF
END IF
RETURN TRUE
END FUNCTION
]]></artwork>
</figure>
</section>
</section>
<section anchor="security_states" numbered="true" toc="default">
<name>States</name>
<t>
In this section the security considerations for each valid message
in all states is described, if any other message
is received the peer MUST terminate the operation.
</t>
<section anchor="security_states_expecting_ibf" numbered="true" toc="default">
<name>Expecting IBF</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_request_full" format="title" /></dt>
<dd>
<t>
It needs to be checked that the full synchronisation mode with receiving peer
sending first is plausible according to the algorithm deciding which operation mode
is applicable as described in <xref target="performance_formulas_operationmode" format="default"/>.
</t>
</dd>
<dt><xref target="messages_ibf" format="title" /></dt>
<dd>
<t>
It needs to be checked that the differential synchronisation mode is plausible according
to the algorithm deciding which operation mode
is applicable as described in <xref target="performance_formulas_operationmode" format="default"/>.
</t>
</dd>
<dt><xref target="messages_send_full" format="title" /></dt>
<dd>
<t>
It needs to be checked that the full synchronisation mode with initiating peer
sending first is plausible according to the algorithm deciding which operation mode
is applicable as described in <xref target="performance_formulas_operationmode" format="default"/>.
</t>
</dd>
</dl>
</section>
<section anchor="security_states_full_sending" numbered="true" toc="default">
<name>Full Sending</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_full_element" format="title" /></dt>
<dd>
<t>
When receiving full elements there needs to be checked, that every
element is a valid element, that no element has been received more than once and
not more or less elements are received, as the other peer has committed
to in the beginning of the operation. The plausibility should also be checked
with an algorithm as described in <xref target="security_generic_functions_full_plausibility_check" format="default"/>.
</t>
</dd>
<dt><xref target="messages_full_done" format="title" /></dt>
<dd>
<t>
When receiving the <em><xref target="messages_full_done" format="title" /></em> message, it is important to check that
not less elements are received as the other peer has committed to
send. If the sets differ, a resynchronisation is required. The number of possible
resynchronisation MUST be limited, to prevent resource exhaustion attacks.
</t>
</dd>
</dl>
</section>
<section anchor="security_states_expecting_ibf_last" numbered="true" toc="default">
<name>Expecting IBF Last</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_ibf" format="title" /></dt>
<dd>
<t>
No special safety measures are necessary in this state.
The maximum of <xref target="messages_ibf" format="title" /> messages should be limited to a reasonable amount.
</t>
</dd>
</dl>
</section>
<section anchor="security_states_active_decoding" numbered="true" toc="default">
<name>Active Decoding</name>
<t>
In the <strong>Active Decoding</strong> state it is important to prevent an attacker from
generating and passing an unlimited amount of IBFs, that do not decode or
even worse, generate an IBF constructed to send the peers in an endless loop.
To prevent an endless loop in decoding, a loop detection should be implemented.
The simplest solution would be to prevent decoding of more than a given amount of elements.
A more robust solution is to implement a algorithm that detects a loop by
analyzing past partially decoded IBFs. This can be achieved
by saving the hash of all prior partly decoded IBFs hashes in a hashmap and check
for every inserted hash, if it is already in the hashmap.
</t>
<t>
If the IBF decodes more or less elements than are plausible, the
operation MUST be terminated. The upper and lower threshold
for the decoded elements can be calculated with the peers set sizes
and the other peer committed set sizes from the <strong>Expecting IBF</strong>
state.
</t>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_offer" format="title" /></dt>
<dd>
<t>
If an offer for an element, that never has been requested by
an inquiry or if an offer is received twice, the operation MUST be terminated.
This requirement can be fulfilled by saving lists that keep track of the state of
all sent inquiries and offers. When answering offers these lists MUST be checked.
The sending and receiving of <xref target="messages_offer" format="title" /> messages should
always be protected with an <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</t>
</dd>
<dt><xref target="messages_elements" format="title" /></dt>
<dd>
<t>
If an element that never has been requested by
a demand or is received double, the operation MUST be terminated.
The sending and receiving of <xref target="messages_elements" format="title" /> messages should
always be protected with an <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</t>
</dd>
<dt><xref target="messages_demand" format="title" /></dt>
<dd>
<t>
For every received demand an offer has to be sent in advance. If a demand
for an element is received, that never has been offered or the offer already has
been answered with a demand, the operation MUST be terminated. It is required to implement
a list which keeps track of the state of all sent offers and received demands.
The sending and receiving of <em><xref target="messages_demand" format="title" /></em> messages should
always be protected with an <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</t>
</dd>
<dt><xref target="messages_done" format="title" /></dt>
<dd>
<t>
The <em><xref target="messages_done" format="title" /></em> message is only received, if the IBF has been finished
decoding and all offers have been sent. If the <em><xref target="messages_done" format="title" /></em> message is received before
the decoding of the IBF is finished or all open offers and demands
have been answered, the operation MUST be terminated. If
the sets differ, a resynchronisation is required. The number of possible
resynchronisation MUST be limited to prevent resource exhaustion attacks.
</t>
<t>
When a <em><xref target="messages_done" format="title" /></em> message is received the
"check_if_synchronisation_is_complete()" function from the <xref target="security_generic_functions_mfc" format="title" />
is required to ensure that all demands have been satisfied successfully.
</t>
</dd>
</dl>
</section>
<section anchor="security_states_finish_closing" numbered="true" toc="default">
<name>Finish Closing</name>
<t>
In the <strong>Finish Closing</strong> state the protocol waits for
all sent demands to be fulfilled.
</t>
<t>
In case not all sent demands have been answered in time,
the operation has failed and MUST be terminated.
</t>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_elements" format="title" /></dt>
<dd>
When receiving <xref target="messages_elements" format="title" /> messages it is important
to always check the <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</dd>
</dl>
</section>
<section anchor="security_states_finished" numbered="true" toc="default">
<name>Finished</name>
<t>
In this state the connection is terminated, so no security considerations are needed.
</t>
</section>
<section anchor="security_states_expect_se" numbered="true" toc="default">
<name>Expect SE</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_se" format="title" /></dt>
<dd>
<t>
In case the strata estimator does not decode, the
operation MUST be terminated to prevent to get to an unresolvable state.
The set difference calculated from the strata estimator needs to be plausible,
which means within the byzantine boundaries described in section <xref target="security_generic_functions_check_byzantine_boundaries" format="title" />.
</t>
<t>
In case of compressed strata estimators the unpacking algorithm needs to
be protected against unpacking memory corruption (memory overflow).
</t>
</dd>
</dl>
</section>
<section anchor="security_states_full_receiving" numbered="true" toc="default">
<name>Full Receiving</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_full_element" format="title" /></dt>
<dd>
<t>
When receiving full elements there needs to be checked, that every
element is a valid element, no element has been received more than once and
not more or less elements are received, as the other peer has committed
to in the beginning of the operation. The plausibility should also be checked
with an algorithm as described in <xref target="security_generic_functions_full_plausibility_check" format="default"/>.
</t>
</dd>
<dt><xref target="messages_full_done" format="title" /></dt>
<dd>
<t>
When the <em><xref target="messages_full_done" format="title" /></em> message is received from the remote peer, all
elements, that the remote peer has committed to, need to be received,
otherwise the operation MUST be terminated. After receiving the
<em><xref target="messages_full_done" format="title" /></em> message, future elements MUST NOT be accepted. If
the sets differ, a resynchronisation is required. The number of possible
resynchronisation MUST be limited to prevent resource exhaustion attacks.
</t>
</dd>
</dl>
</section>
<section anchor="security_states_passive_decoding" numbered="true" toc="default">
<name>Passive Decoding</name>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_ibf" format="title" /></dt>
<dd>
<t>
In case an <xref target="messages_ibf" format="title" /> message is received by the peer a active/passive role switch
is initiated by the active decoding remote peer. In this moment the peer MUST
wait for all open offers and demands to be fulfilled, to prevent
retransmission before switching into active decoding operation mode.
A switch into active decoding mode MUST only be permitted for
a predefined number of times as described in <xref target="security_generic_functions_active_passive_switches" format="default"/>
</t>
</dd>
<dt><xref target="messages_inquiry" format="title" /></dt>
<dd>
<t>
A check needs to be in place that prevents receiving an inquiry
for an element multiple times or more inquiries than are plausible.
The sending and receiving of <em><xref target="messages_inquiry" format="title" /></em> messages should
always be protected with an <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</t>
</dd>
<dt><xref target="messages_demand" format="title" /></dt>
<dd>
Same action as described for <em><xref target="messages_demand" format="title" /></em> message in section
<xref target="security_states_active_decoding" format="title"/>.
</dd>
<dt><xref target="messages_offer" format="title" /></dt>
<dd>
Same action as described for <em><xref target="messages_offer" format="title" /></em> message in section
<xref target="security_states_active_decoding" format="title"/>.
</dd>
<dt><xref target="messages_done" format="title" /></dt>
<dd>
Same action as described for <em><xref target="messages_done" format="title" /></em> message in section
<xref target="security_states_active_decoding" format="title"/>.
</dd>
<dt><xref target="messages_elements" format="title" /></dt>
<dd>
Same action as described for <em><xref target="messages_elements" format="title" /></em> message in section
<xref target="security_states_active_decoding" format="title"/>.
</dd>
</dl>
</section>
<section anchor="security_states_finish_waiting" numbered="true" toc="default">
<name>Finish Waiting</name>
<t>
In the <strong>Finish Waiting</strong> state the protocol waits for
all sent demands to be fulfilled.
</t>
<t>
In case not all sent demands have been answered in time, the operation
has failed and MUST be terminated.
</t>
<t>Security considerations for received messages:</t>
<dl>
<dt><xref target="messages_elements" format="title" /></dt>
<dd>
When receiving <xref target="messages_elements" format="title" /> messages it is important
to always check the <xref target="security_generic_functions_mfc" format="title" />
to secure the protocol against missing, doubled, not in order or unexpected messages.
</dd>
</dl>
</section>
</section>
</section>
<section anchor="constants" numbered="true" toc="default">
<name>Constants</name>
<t>
The following table contains constants used by the protocol. The constants marked with a * are
validated through experiments in <xref target="byzantine_fault_tolerant_set_reconciliation" format="default"/>.
</t>
<figure anchor="figure_constants">
<artwork name="" type="" align="left" alt=""><![CDATA[
Name | Value | Description
----------------------------+------------+--------------------------
SE_STRATA_COUNT | 32 | Number of IBFs in a strata estimator
IBF_HASH_NUM* | 3 | Number of times an element is hashed to an
IBF (from section 4.5.2)
IBF_FACTOR* | 2 | The factor by which the size of the IBF is
increased in case of decoding failure or
initially from the set difference.
(from section 4.5.2)
MAX_BUCKETS_PER_MESSAGE | 1120 | Maximum bucket of an IBF that are
transmitted in single message
IBF_MIN_SIZE* | 37 | Minimal number of buckets in an IBF
(from section 3.8)
DIFFERENTIAL_RTT_MEAN* | 3.65145 | The average RTT that is needed for a
differential synchronisation
SECURITY_LEVEL* | 2^80 | Security level for probabilistic security
algorithms (from section 5.8)
PROBABILITY_FOR_NEW_ROUND* | 0.15 | The probability for a IBF decoding failure
in the differential synchronisation mode
(from section 5.4)
DIFFERENTIAL_RTT_MEAN* | 3.65145 | The average RTT that is needed for a
differential synchronisation.
(from section 4.5.3)
MAX_IBF_SIZE | 1048576 | Maximal number of buckets in an IBF
AVG_BYTE_SIZE_SE* | 4221 | Average byte size of a single strata
estimator (from section 3.4.3)
VALID_NUMBER_SE* | [1,2,4,8] | Valid number of SE in (from section 3.4)
]]></artwork>
</figure>
</section>
<section anchor="gana" numbered="true" toc="default">
<name>GANA Considerations</name>
<t>
GANA is requested to amend the "GNUnet Message Type" <xref target="GANA" format="default"/> registry
as follows:
</t>
<figure anchor="figure_purposenums">
<artwork name="" type="" align="left" alt=""><![CDATA[
Type | Name | References | Description
--------+----------------------------+------------+--------------------------
559 | SETU_P2P_REQUEST_FULL | [This.I-D] | Request the full set of the other
peer
710 | SETU_P2P_SEND_FULL | [This.I-D] | Signals to send the full set to the
other peer
560 | SETU_P2P_DEMAND | [This.I-D] | Demand the whole element from the
other peer, given only the hash
code.
561 | SETU_P2P_INQUIRY | [This.I-D] | Tell the other peer to send a list
of hashes that match an IBF key.
562 | SETU_P2P_OFFER | [This.I-D] | Tell the other peer which hashes
match a given IBF key.
563 | SETU_P2P_OPERATION_REQUEST | [This.I-D] | Request a set union operation from
a remote peer.
564 | SETU_P2P_SE | [This.I-D] | Strata Estimator uncompressed
565 | SETU_P2P_IBF | [This.I-D] | Invertible Bloom Filter slices.
566 | SETU_P2P_ELEMENTS | [This.I-D] | Actual set elements.
567 | SETU_P2P_IBF_LAST | [This.I-D] | Invertible Bloom Filter Last Slice.
568 | SETU_P2P_DONE | [This.I-D] | Set operation is done.
569 | SETU_P2P_SEC | [This.I-D] | Strata Estimator compressed
570 | SETU_P2P_FULL_DONE | [This.I-D] | All elements in full synchronisation
mode have been sent is done.
571 | SETU_P2P_FULL_ELEMENT | [This.I-D] | Send an actual element in full
synchronisation mode.
]]></artwork>
</figure>
</section>
<!-- gana -->
<section anchor="contributors" numbered="true" toc="default">
<name>Contributors</name>
<t>
The GNUnet implementation of the byzantine fault tolerant set reconciliation
protocol was originally implemented by Florian Dold.
</t>
</section>
</middle>
<back>
<references>
<name>Normative References</name>
&RFC5869;
&RFC2119;
&RFC3385;
&RFC1951;
<reference anchor="byzantine_fault_tolerant_set_reconciliation" target="https://summermatter.net/byzantine-fault-tolerant-set-reconciliation-summermatter.pdf">
<front>
<title>Byzantine Fault Tolerant Set Reconciliation</title>
<author initials="E." surname="Summermatter" fullname="Elias Summermatter">
<organization>University of Applied Sciences Bern</organization>
</author>
<date year="2021"/>
</front>
</reference>
<reference anchor="GANA" target="https://gana.gnunet.org/">
<front>
<title>GNUnet Assigned Numbers Authority (GANA)</title>
<author>
<organization>GNUnet e.V.</organization>
</author>
<date month="April" year="2020"/>
</front>
</reference>
<reference anchor="CryptographicallySecureVoting" target="https://git.gnunet.org/bibliography.git/plain/docs/ba_dold_voting_24aug2014.pdf">
<front>
<title>Cryptographically Secure, Distributed Electronic Voting</title>
<author initials="F." surname="Dold" fullname="Florian Dold">
<organization>Technische Universität München</organization>
</author>
</front>
</reference>
<reference anchor="ByzantineSetUnionConsensusUsingEfficientSetReconciliation" target="https://doi.org/10.1186/s13635-017-0066-3">
<front>
<title>Byzantine set-union consensus using efficient set reconciliation</title>
<author initials="F." surname="Dold" fullname="Florian Dold">
<organization>Technische Universität München</organization>
</author>
<author initials="C." surname="Grothoff" fullname="Christian Grothoff">
<organization>Inria, Domaine de Voluceau Rocquencourt</organization>
</author>
</front>
</reference>
<reference anchor="Eppstein" target="https://doi.org/10.1145/2018436.2018462">
<front>
<title>What’s the Difference? Efficient Set Reconciliation without Prior Context</title>
<author initials="D." surname="Eppstein" fullname="David Eppstein">
<organization>U.C. Irvine</organization>
</author>
<author initials="M." surname="Goodrich" fullname="Michael T. Goodrich">
<organization>U.C. Irvine</organization>
</author>
<author initials="F." surname="Uyeda" fullname="Frank Uyeda">
<organization>U.C. San Diego</organization>
</author>
<author initials="G." surname="Varghese" fullname="George Varghese">
<organization>U.C. San Diego</organization>
</author>
</front>
</reference>
<reference anchor="GNS" target="https://doi.org/10.1007/978-3-319-12280-9_9">
<front>
<title>A Censorship-Resistant, Privacy-Enhancing and Fully Decentralized Name System</title>
<author initials="M." surname="Wachs" fullname="Matthias Wachs">
<organization>Technische Universitaet Muenchen</organization>
</author>
<author initials="M." surname="Schanzenbach" fullname="Martin Schanzenbach">
<organization>Technische Universitaet Muenchen</organization>
</author>
<author initials="C." surname="Grothoff"
fullname="Christian Grothoff">
<organization>Technische Universitaet Muenchen</organization>
</author>
<date year="2014"/>
</front>
</reference>
</references>
<section anchor="test_vectors" numbered="true" toc="default">
<name>Test Vectors</name>
<section anchor="test_vectors_map_function" numbered="true" toc="default">
<name>Map Function</name>
<t>
INPUTS:
</t>
<figure anchor="test_vectors_map_function_inputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
k: 3
ibf_size: 300
key1: 0xFFFFFFFFFFFFFFFF (64-bit)
key2: 0x0000000000000000 (64-bit)
key3: 0x00000000FFFFFFFF (64-bit)
key4: 0xC662B6298512A22D (64-bit)
key5: 0xF20fA7C0AA0585BE (64-bit)
]]></artwork>
</figure>
<t>
OUTPUT:
</t>
<figure anchor="test_vectors_map_function_outputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
key1: ["122","157","192"]
key2: ["85","243","126"]
key3: ["208","101","222"]
key4: ["239","269","56"]
key5: ["150","104","33"]
]]></artwork>
</figure>
</section>
<section anchor="test_vectors_id_function" numbered="true" toc="default">
<name>ID Calculation Function</name>
<t>
INPUTS:
</t>
<figure anchor="test_vectors_id_function_inputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
element 1: 0xFFFFFFFFFFFFFFFF (64-bit)
element 2: 0x0000000000000000 (64-bit)
element 3: 0x00000000FFFFFFFF (64-bit)
element 4: 0xC662B6298512A22D (64-bit)
element 5: 0xF20fA7C0AA0585BE (64-bit)
]]></artwork>
</figure>
<t>
OUTPUT:
</t>
<figure anchor="test_vectors_id_function_outputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
element 1: 0x5AFB177B
element 2: 0x64AB557C
element 3: 0xCB5DB740
element 4: 0x8C6A2BB2
element 5: 0x7EC42981
]]></artwork>
</figure>
</section>
<section anchor="test_counter_compression_function" numbered="true" toc="default">
<name>Counter Compression Function</name>
<t>
INPUTS:
</t>
<figure anchor="test_counter_compression_function_inputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
counter serie 1: [1,8,10,6,2] (min bytes 4)
counter serie 2: [26,17,19,15,2,8] (min bytes 5)
counter serie 3: [4,2,0,1,3] (min bytes 3)
]]></artwork>
</figure>
<t>
OUTPUT:
</t>
<figure anchor="test_counter_compression_function_outputs">
<artwork name="" type="" align="left" alt=""><![CDATA[
counter serie 1: 0x18A62
counter serie 2: 0x3519BC48
counter serie 3: 0x440B
]]></artwork>
</figure>
</section>
</section>
</back>
</rfc>
|