diff options
Diffstat (limited to 'gp-scripts')
-rw-r--r-- | gp-scripts/firstPrice | 91 | ||||
-rw-r--r-- | gp-scripts/smc.gp | 35 |
2 files changed, 126 insertions, 0 deletions
diff --git a/gp-scripts/firstPrice b/gp-scripts/firstPrice new file mode 100644 index 0000000..d936e36 --- /dev/null +++ b/gp-scripts/firstPrice | |||
@@ -0,0 +1,91 @@ | |||
1 | \\ From: "How to obtain full privacy in auctions" (2006) by Felix Brandt pages 19-20 | ||
2 | |||
3 | |||
4 | \\\\\\\\\\\\ | ||
5 | \\ Adapt the following values to your needs | ||
6 | \\\\\\\\\\\\ | ||
7 | |||
8 | \\ amount of bidders | ||
9 | n = 2^3 | ||
10 | \\ amount of possible prices | ||
11 | k = 2^7 | ||
12 | \\ randomize bids (change to something static, if you like) | ||
13 | bid = vector(n,i,random(k)+1) | ||
14 | \\bid = vector(n,i,n-i+1) \\ first bidder wins | ||
15 | \\bid = vector(n,i,i) \\ last bidder wins | ||
16 | \\bid = vector(n,i,(i+1)%2) \\ second bidder wins (with ties) | ||
17 | |||
18 | \\ prime finite field setup (result may be ambiguous if your prime is too small, 4*n*k seems to work fine) | ||
19 | q = prime(4*n*k) | ||
20 | |||
21 | \\\\\\\\\\\\ | ||
22 | \\ SETUP | ||
23 | \\\\\\\\\\\\ | ||
24 | |||
25 | \\ p not needed? wat? | ||
26 | \\p = 47 | ||
27 | |||
28 | \\ get generator / primitive element for Z_q | ||
29 | var = 'x \\ copy pasta from internet | ||
30 | pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element | ||
31 | 1/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong | ||
32 | g = Mod(eval(Str(pe)), q) \\ dirty hack to convert t_FFELEM to t_INT | ||
33 | |||
34 | \\\\\\\\\\\\ | ||
35 | \\ PROLOG | ||
36 | \\\\\\\\\\\\ | ||
37 | |||
38 | \\ private keys of agents | ||
39 | x = vector(n,i,random(q)) | ||
40 | \\ public keyshares of agents | ||
41 | yshares = vector(n,i,g^x[i]) | ||
42 | \\ shared public key | ||
43 | y = prod(X=1,n,yshares[X]) | ||
44 | |||
45 | \\ first index level = owning agent id (additive share) | ||
46 | \\ second index level = agent id, price id | ||
47 | m = vector(n,i,matrix(n,k,a,b,random(q))) | ||
48 | |||
49 | \\ index = owning agent id, price id | ||
50 | r = matrix(n,k,i,j,random(q)) | ||
51 | \\ bid matrix | ||
52 | b = matrix(n,k,i,j,g^(bid[i]==j)) | ||
53 | |||
54 | \\\\\\\\\\\\ | ||
55 | \\ ROUND1 | ||
56 | \\\\\\\\\\\\ | ||
57 | |||
58 | \\ encrypted bids | ||
59 | alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j]) | ||
60 | beta = matrix(n,k,i,j, g^r[i,j]) | ||
61 | |||
62 | \\\\\\\\\\\\ | ||
63 | \\ ROUND2 | ||
64 | \\\\\\\\\\\\ | ||
65 | |||
66 | \\ multiplicative shares | ||
67 | \\ first index level = owning agent id (multiplicative share) | ||
68 | \\ second index level = agent id, price id | ||
69 | Gamma = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j+1,k,alpha[h,d])) * prod(d=1,j-1,alpha[i,d]) * prod(h=1,i-1,alpha[h,j]) )^m[a][i,j] )) | ||
70 | Delta = vector(n,a,matrix(n,k,i,j, ( prod(h=1,n,prod(d=j+1,k, beta[h,d])) * prod(d=1,j-1, beta[i,d]) * prod(h=1,i-1, beta[h,j]) )^m[a][i,j] )) | ||
71 | |||
72 | \\\\\\\\\\\\ | ||
73 | \\ ROUND3 | ||
74 | \\\\\\\\\\\\ | ||
75 | |||
76 | \\ multiplicative shares (decryption) | ||
77 | \\ first index level = owning agent id (multiplicative share) | ||
78 | \\ second index level = agent id, price id | ||
79 | Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j])^x[a] )) | ||
80 | |||
81 | \\\\\\\\\\\\ | ||
82 | \\ EPILOG | ||
83 | \\\\\\\\\\\\ | ||
84 | |||
85 | \\ winner matrix | ||
86 | v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) ) | ||
87 | |||
88 | vi = lift(v) | ||
89 | |||
90 | print("bids are: ", bid) | ||
91 | for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) )) | ||
diff --git a/gp-scripts/smc.gp b/gp-scripts/smc.gp new file mode 100644 index 0000000..2b7e188 --- /dev/null +++ b/gp-scripts/smc.gp | |||
@@ -0,0 +1,35 @@ | |||
1 | /* search for a random prime with the specified amount of bits */ | ||
2 | \\ randomprime(bits:small=127)= | ||
3 | \\ { | ||
4 | \\ local(r:int=4); | ||
5 | \\ while(!isprime(r), | ||
6 | \\ r = bitor(2^(bits-1) + random(2^(bits-1)-1), 1); | ||
7 | \\ ); | ||
8 | \\ r; | ||
9 | \\ } | ||
10 | |||
11 | smc_hextodec(s:str) = | ||
12 | { | ||
13 | local(v:vecsmall = Vecsmall(s), ret:int = 0); | ||
14 | for(i = 1, #v, | ||
15 | ret = (ret<<4) + if(v[i]<=57 && v[i]>=48, v[i]-48, v[i]<=70 && v[i]>=65, v[i]-55, v[i]<=102 && v[i]>=97, v[i]-87, error("invalid input format")) | ||
16 | ); | ||
17 | ret; | ||
18 | } | ||
19 | |||
20 | smc_genbid(k:small, bid:small, g)= | ||
21 | { | ||
22 | vector(k,j,g^(bid==j)); | ||
23 | } | ||
24 | |||
25 | smc_genalpha(k:small, b:vec, r:vec, y)= | ||
26 | { | ||
27 | vector(k, j, b[j]*y^r[j]); | ||
28 | } | ||
29 | |||
30 | smc_genbeta(k:small, r:vec, g)= | ||
31 | { | ||
32 | vector(k, j, g^r[j]); | ||
33 | } | ||
34 | |||
35 | |||