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authorMarkus Teich <markus.teich@stusta.mhn.de>2016-06-08 15:40:22 +0200
committerMarkus Teich <markus.teich@stusta.mhn.de>2016-06-08 15:40:22 +0200
commitd4360a4f8b7d29aedf6f9af0a878a9060d434ea2 (patch)
tree40836708043afa8fb7c1a320e86e652fec44dd14 /gp-scripts
parent8cf93a6c188d6a726bce46aa987c11611cf2baac (diff)
downloadlibbrandt-d4360a4f8b7d29aedf6f9af0a878a9060d434ea2.tar.gz
libbrandt-d4360a4f8b7d29aedf6f9af0a878a9060d434ea2.zip
fix typos and types
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1\\ From: "Fully private auctions in a constant number of rounds" (2003) by Felix Brandt pages 9-10
2
3
4\\\\\\\\\\\\
5\\ Adapt the following values to your needs
6\\\\\\\\\\\\
7
8\\ amount of bidders
9n = 2^3
10\\ amount of possible prices
11k = 2^7
12\\ randomize bids (change to something static, if you like)
13bid = 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)
19q = 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
29var = 'x \\ copy pasta from internet
30pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element
311/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong
32g = 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
39x = vector(n,i,random(q))
40\\ public keyshares of agents
41yshares = vector(n,i,g^x[i])
42\\ shared public key
43y = prod(X=1,n,yshares[X])
44
45\\ first index level = owning agent id (additive share)
46\\ second index level = agent id, price id
47m = vector(n,i,matrix(n,k,a,b,random(q)))
48
49\\ index = owning agent id, price id
50r = matrix(n,k,i,j,random(q))
51\\ bid matrix
52b = matrix(n,k,i,j,g^(bid[i]==j))
53
54\\\\\\\\\\\\
55\\ ROUND1
56\\\\\\\\\\\\
57
58\\ encrypted bids
59alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j])
60beta = 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
69Gamma = 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] ))
70Delta = 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
79Phi = 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
86v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) )
87
88vi = lift(v)
89
90print("bids are: ", bid)
91for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) ))