commit 19f871a71e034f89ba2502be08a4c12622a9fa82
parent 9479b663fda654482588626d3fe10c1f8415909c
Author: Mikolai Gütschow <mikolai.guetschow@tu-dresden.de>
Date: Wed, 29 Apr 2026 14:19:36 +0200
protocol: add recoup protocol
Diffstat:
2 files changed, 510 insertions(+), 248 deletions(-)
diff --git a/draft-guetschow-taler-protocol.md b/draft-guetschow-taler-protocol.md
@@ -68,7 +68,7 @@ Use at your own risk!
- `a * b (mod N)` / `a ** b (mod N)` denotes the multiplication / exponentiation of multiple precision integers a and b, modulo N
- `for`, `if`, variable assignment `=`, and conditional operators are to be interpreted like their Python/Julia equivalents
- `data.key` denotes the property `key` on the object `data`
-- `0..n` denotes the exclusive range of integer numbers from `0` to `n-1`
+- `0..n` denotes the exclusive range of integer numbers from `0` to `n`, i.e., `0, 1, 2, ..., n-1`
- `⟨dataᵢ⟩` within a context of `i = 0..n` denotes `n` objects `dataᵢ`, represented in memory as a continuous array
- `⟨dataᵢ.key⟩` within a context of `i = 0..n` denotes an array of the `n` properties `key` of all `n` objects `dataᵢ`
@@ -334,11 +334,11 @@ and `Convert-Point-Ed25519-Curve25519(p)` which implements the birational map of
pub' = Convert-Point-Ed25519-Curve25519(pub)
shared' = X25519(priv, pub')
shared = SHA-512(shared')
+~~~
{::comment}
see GNUNET_CRYPTO_eddsa_ecdh
{:/}
-~~~
~~~
ECDH-GetPub(priv) -> pub
@@ -801,8 +801,6 @@ Persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
// TODO: explain CoinSelection
-// TODO: maybe introduce symbol for pub/priv
-
~~~
(M3) deposit check (merchant)
@@ -911,11 +909,12 @@ Check Ed25519-Verify(exchange.pub, msg, sig)
The wallet obtains `n` new coins `⟨coinᵢ⟩` of denominations `⟨denomᵢ⟩`
in exchange for one old `coin` of denomination `denom` from the exchange.
-There are two reasons why a wallet needs to do this:
+There are three reasons why a wallet needs to do this:
1. Obtaining unlinkable change after using only a part of the coin's value during a payment (cf. {{payment}}) or deposit (cf. {{deposit}}),
i.e. where `contribution <= denom.value`
-2. Renewing a coin before it deposit-expires.
+2. Obtaining unlinkable change after a successful refund (cf. {{refund}})
+3. Renewing a coin before it deposit-expires
The sum of the refresh fee of `denom` and the new denominations' values and withdrawal fees (defined by the exchange)
must be smaller or equal to the residual value of the old `coin`.
@@ -1133,11 +1132,13 @@ for i in 0..n:
### Link {#link}
-// todo: add introductory text
+Coins ⟨coinᵧᵢ⟩ obtained via the refresh protocol (cf. {{refresh}}) can be regenerated
+with the knowledge of the old coin's private key `coin.priv` using the link protocol,
+integrated in the coin history endpoint.
~~~
wallet exchange
-Knows coin Knows refresh_record for coin
+Knows coin Knows refresh_record for coin.pub
| |
+----------------------+ |
| (W1) history request | |
@@ -1225,7 +1226,145 @@ if ⟨blind_sigᵢ⟩ returned:
## Refund {#refund}
-// todo
+A wallet can request a refund for an order from the merchant after it has been completed successfully
+(cf. {{payment}}) and before the merchant has been paid out by the exchange (i.e., before `contract.wire_deadline`).
+The merchant needs to approve the refund via its business logic,
+and is free to decide the total amount of the refund
+as well as which coins' deposit operations (cf. {{deposit}}) are (potentially partly) invalidated.
+After the exchange has accepted the refund request,
+the coins obtain their (partial) value back.
+The wallet should proceed to refresh (cf. {{refresh}}) the coins before spending them again
+to obtain unlinkability.
+
+In case the wallet itself has used deposit to its own payto,
+it can act as the merchant in the protocol below.
+
+// todo: if proves practical, similar strucuture could be used for pay/deposit
+(interaction) between wallet, merchant and exchange
+
+~~~
+ wallet merchant exchange
+Knows order.id Knows merchant.priv Knows deposit_record
+Knows contract | for coinᵢ.pub
+ | | |
++---------------------+ | |
+| (W1) refund request | | |
++---------------------+ | |
+ | | |
+ |- /orders/{order.id}/refund ->| |
+ | (h_contract) | |
+ | | |
+ | +------------------------+ |
+ | | (M1) refund processing | |
+ | +------------------------+ |
+ | | |
+ | |- /coins/{coinᵢ.pub}/refund ->|
+ | | (valueᵢ, h_contract, id, |
+ | | merchant.pub, sigᵢ) |
+ | | |
+ | | +-------------------+
+ | | | (E1) refund check |
+ | | +-------------------+
+ | | |
+ | |<--- (exchange.pub, sigᵢ) ----|
+ | | |
+ | +--------------------------+ |
+ | | (M2) refund confirmation | |
+ | +--------------------------+ |
+ | | |
+ |<-----(value, ⟨refundᵢ⟩,------| |
+ | merchant.pub) | | // todo: why merchant.pub if no sig transmitted?
+ | | |
++-----------------------+ | |
+| (W2) refund reception | | |
++-----------------------+ | |
+ | | |
+~~~
+
+where (for RSA, without age-restriction)
+
+{::comment}
+
+⟨ᵧₖᵢ⟩
+{:/}
+
+~~~
+(W1) refund request (wallet)
+
+h_contract = SHA-512(canonicalJSON(contract))
+~~~
+
+{::comment}
+
+⟨ᵧₖᵢ⟩
+{:/}
+
+~~~
+(M1) refund processing (merchant)
+
+Check h_contract known and refund possible
+time = now()
+⟨coinᵢ⟩ = Lookup by h_contract
+id = ?
+for i in 0..n:
+ denomᵢ = Lookup by coinᵢ.h_denom
+ valueᵢ = refund amount // todo: split wisely
+ msgᵢ = Gen-Msg(MERCHANT_REFUND,
+ ( h_contract | coinᵢ.pub | id | valueᵢ | denomᵢ.fee_refund ))
+ sigᵢ = Ed25519-Sign(merchant.priv, msgᵢ)
+~~~
+
+{::comment}
+
+⟨ᵧₖᵢ⟩
+{:/}
+
+~~~
+(E1) refund check and confirmation (exchange)
+
+deposit_record = Lookup by h_contract // todo: needs to be persisted before with order.id and used coins!
+Check coinᵢ.pub part of deposit_record
+denomᵢ = Lookup by coinᵢ.pub
+msgᵢ = Gen-Msg(MERCHANT_REFUND,
+ ( h_contract | coinᵢ.pub | id | valueᵢ | denomᵢ.fee_refund ))
+Check Ed25519-Verify(merchant.pub, msgᵢ, sigᵢ)
+Check valueᵢ >= denomᵢ.fee_refund
+Check refund possible (prior to wire transfer deadline)
+remove/update scheduled wire transfer
+mark coin part as unspent
+msgᵢ = Gen-Msg(MERCHANT_REFUND_OK, SHA-512(order.id)) // todo: hashing string without terminating \0
+sigᵢ = Ed25519-Sign(exchange.priv, msgᵢ)
+~~~
+
+{::comment}
+
+⟨ᵧₖᵢ⟩
+{:/}
+
+~~~
+(M2) refund confirmation (merchant)
+
+for i in 0..n:
+ msgᵢ = Gen-Msg(MERCHANT_REFUND_OK, SHA-512(order.id)) // todo: hashing string without terminating \0
+ Check Ed25519-Verify(exchange.pub, msgᵢ, sigᵢ)
+ update business logic
+ refundᵢ = (valueᵢ, sigᵢ, id, coinᵢ.pub, time)
+value = sum ⟨valueᵢ⟩
+~~~
+
+{::comment}
+
+⟨ᵧₖᵢ⟩
+{:/}
+
+~~~
+(W2) refund reception (wallet)
+
+for i in 0..n:
+ (valueᵢ, sigᵢ, id, coinᵢ.pub, time) = refundᵢ
+update persistent transaction information
+refresh ⟨coinᵢ⟩
+~~~
## Recoup {#recoup}
diff --git a/draft-guetschow-taler-protocol.xml b/draft-guetschow-taler-protocol.xml
@@ -24,7 +24,7 @@
<email>mikolai.guetschow@tu-dresden.de</email>
</address>
</author>
- <date year="2026" month="April" day="08"/>
+ <date year="2026" month="April" day="29"/>
<workgroup>independent</workgroup>
<keyword>taler</keyword>
<keyword>cryptography</keyword>
@@ -82,7 +82,7 @@ Use at your own risk!</t>
<t><tt>data.key</tt> denotes the property <tt>key</tt> on the object <tt>data</tt></t>
</li>
<li>
- <t><tt>0..n</tt> denotes the exclusive range of integer numbers from <tt>0</tt> to <tt>n-1</tt></t>
+ <t><tt>0..n</tt> denotes the exclusive range of integer numbers from <tt>0</tt> to <tt>n</tt>, i.e., <tt>0, 1, 2, ..., n-1</tt></t>
</li>
<li>
<t><tt>⟨dataᵢ⟩</tt> within a context of <tt>i = 0..n</tt> denotes <tt>n</tt> objects <tt>dataᵢ</tt>, represented in memory as a continuous array</t>
@@ -322,10 +322,6 @@ and <tt>Convert-Point-Ed25519-Curve25519(p)</tt> which implements the birational
pub' = Convert-Point-Ed25519-Curve25519(pub)
shared' = X25519(priv, pub')
shared = SHA-512(shared')
-
-{::comment}
-see GNUNET_CRYPTO_eddsa_ecdh
-{:/}
]]></artwork>
<artwork><![CDATA[
ECDH-GetPub(priv) -> pub
@@ -759,7 +755,6 @@ for i in 0..n:
Persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
]]></artwork>
<t>// TODO: explain CoinSelection</t>
- <t>// TODO: maybe introduce symbol for pub/priv</t>
<artwork><![CDATA[
(M3) deposit check (merchant)
@@ -861,13 +856,16 @@ Check Ed25519-Verify(exchange.pub, msg, sig)
<name>Refresh</name>
<t>The wallet obtains <tt>n</tt> new coins <tt>⟨coinᵢ⟩</tt> of denominations <tt>⟨denomᵢ⟩</tt>
in exchange for one old <tt>coin</tt> of denomination <tt>denom</tt> from the exchange.
-There are two reasons why a wallet needs to do this:</t>
+There are three reasons why a wallet needs to do this:</t>
<ol spacing="normal" type="1"><li>
<t>Obtaining unlinkable change after using only a part of the coin's value during a payment (cf. <xref target="payment"/>) or deposit (cf. <xref target="deposit"/>),
i.e. where <tt>contribution <= denom.value</tt></t>
</li>
<li>
- <t>Renewing a coin before it deposit-expires.</t>
+ <t>Obtaining unlinkable change after a successful refund (cf. <xref target="refund"/>)</t>
+ </li>
+ <li>
+ <t>Renewing a coin before it deposit-expires</t>
</li>
</ol>
<t>The sum of the refresh fee of <tt>denom</tt> and the new denominations' values and withdrawal fees (defined by the exchange)
@@ -1040,7 +1038,7 @@ for i in 0..n:
<t>// todo: add introductory text</t>
<artwork><![CDATA[
wallet exchange
-Knows coin Knows refresh_record for coin
+Knows coin Knows refresh_record for coin.pub
| |
+----------------------+ |
| (W1) history request | |
@@ -1109,7 +1107,110 @@ if ⟨blind_sigᵢ⟩ returned:
</section>
<section anchor="refund">
<name>Refund</name>
- <t>// todo</t>
+ <t>A wallet can request a refund for an order after it has been completed successfully
+(cf. <xref target="payment"/>) and before the deadline for the wire transfer from the exchange
+to the merchant's bank account has passed.
+The merchant needs to approve the refund via its business logic,
+and is free to decide the total amount of the refund
+as well as which coins' deposit operations (cf. <xref target="deposit"/>) are (potentially partly) invalidated.
+After the exchange has accepted the refund request,
+the coins obtain their (partial) value back.
+The wallet should proceed to refresh (cf. <xref target="refresh"/>) the coins before spending them again
+to obtain unlinkability.</t>
+ <t>// todo: if proves practical, similar strucuture could be used for pay/deposit
+(interaction) between wallet, merchant and exchange</t>
+ <artwork><![CDATA[
+ wallet merchant exchange
+Knows order.id Knows merchant.priv Knows deposit_record
+Knows contract | for coinᵢ.pub
+ | | |
++---------------------+ | |
+| (W1) refund request | | |
++---------------------+ | |
+ | | |
+ |- /orders/{order.id}/refund ->| |
+ | (h_contract) | |
+ | | |
+ | +------------------------+ |
+ | | (M1) refund processing | |
+ | +------------------------+ |
+ | | |
+ | |- /coins/{coinᵢ.pub}/refund ->|
+ | | (valueᵢ, h_contract, id, |
+ | | merchant.pub, sigᵢ) |
+ | | |
+ | | +-------------------+
+ | | | (E1) refund check |
+ | | +-------------------+
+ | | |
+ | |<--- (exchange.pub, sigᵢ) ----|
+ | | |
+ | +--------------------------+ |
+ | | (M2) refund confirmation | |
+ | +--------------------------+ |
+ | | |
+ |<-----(value, ⟨refundᵢ⟩,------| |
+ | merchant.pub) | | // todo: why merchant.pub if no sig transmitted?
+ | | |
++-----------------------+ | |
+| (W2) refund reception | | |
++-----------------------+ | |
+ | | |
+]]></artwork>
+ <t>where (for RSA, without age-restriction)</t>
+ <artwork><![CDATA[
+(W1) refund request (wallet)
+
+h_contract = SHA-512(canonicalJSON(contract))
+]]></artwork>
+ <artwork><![CDATA[
+(M1) refund processing (merchant)
+
+Check h_contract known and refund possible
+time = now()
+⟨coinᵢ⟩ = Lookup by h_contract
+id = ?
+for i in 0..n:
+ denomᵢ = Lookup by coinᵢ.h_denom
+ valueᵢ = refund amount // todo: split wisely
+ msgᵢ = Gen-Msg(MERCHANT_REFUND,
+ ( h_contract | coinᵢ.pub | id | valueᵢ | denomᵢ.fee_refund ))
+ sigᵢ = Ed25519-Sign(merchant.priv, msgᵢ)
+]]></artwork>
+ <artwork><![CDATA[
+(E1) refund check and confirmation (exchange)
+
+deposit_record = Lookup by h_contract // todo: needs to be persisted before with order.id and used coins!
+Check coinᵢ.pub part of deposit_record
+denomᵢ = Lookup by coinᵢ.pub
+msgᵢ = Gen-Msg(MERCHANT_REFUND,
+ ( h_contract | coinᵢ.pub | id | valueᵢ | denomᵢ.fee_refund ))
+Check Ed25519-Verify(merchant.pub, msgᵢ, sigᵢ)
+Check valueᵢ >= denomᵢ.fee_refund
+Check refund possible (prior to wire transfer deadline)
+remove/update scheduled wire transfer
+mark coin part as unspent
+msgᵢ = Gen-Msg(MERCHANT_REFUND_OK, SHA-512(order.id)) // todo: hashing string without terminating \0
+sigᵢ = Ed25519-Sign(exchange.priv, msgᵢ)
+]]></artwork>
+ <artwork><![CDATA[
+(M2) refund confirmation (merchant)
+
+for i in 0..n:
+ msgᵢ = Gen-Msg(MERCHANT_REFUND_OK, SHA-512(order.id)) // todo: hashing string without terminating \0
+ Check Ed25519-Verify(exchange.pub, msgᵢ, sigᵢ)
+ update business logic
+ refundᵢ = (valueᵢ, sigᵢ, id, coinᵢ.pub, time)
+value = sum ⟨valueᵢ⟩
+]]></artwork>
+ <artwork><![CDATA[
+(W2) refund reception (wallet)
+
+for i in 0..n:
+ (valueᵢ, sigᵢ, id, coinᵢ.pub, time) = refundᵢ
+update persistent state about transaction
+refresh ⟨coinᵢ⟩
+]]></artwork>
</section>
<section anchor="recoup">
<name>Recoup</name>
@@ -1238,7 +1339,7 @@ if ⟨blind_sigᵢ⟩ returned:
<refcontent>National Institute of Standards and Technology (U.S.)</refcontent>
</reference>
</references>
- <?line 1250?>
+ <?line 1385?>
<section anchor="change-log">
<name>Change log</name>
@@ -1251,233 +1352,255 @@ Education and Research (BMBF) within the project Concrete Contracts.</t>
</section>
</back>
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