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path: root/gp-scripts/firstPrice.gp
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 ``` ``````\\ From: "How to obtain full privacy in auctions" (2006) by Felix Brandt pages 19-20 \\\\\\\\\\\\ \\ Adapt the following values to your needs \\\\\\\\\\\\ \\ amount of bidders n = 3 \\ amount of possible prices k = 2^2 \\ randomize bids (change to something static, if you like) bid = vector(n,i,random(k)+1) \\bid = vector(n,i,n-i+1) \\ first bidder wins \\bid = vector(n,i,i) \\ last bidder wins \\bid = vector(n,i,(i+1)%2) \\ second bidder wins (with ties) \\\\\\\\\\\\ \\ SETUP \\\\\\\\\\\\ read(group) read(zkp) \\\\\\\\\\\\ \\ PROLOG \\\\\\\\\\\\ \\ private keys of agents x = vector(n,i,random(q)) \\ first index level = owning agent id (additive share) \\ second index level = agent id, price id m = vector(n,i,matrix(n,k,a,b,random(q))) \\ zkp proofs1 = vector(n,i,zkp1_proof(G, x[i])) \\ public keyshares of agents yshares = vector(n,i,proofs1[i]) \\yshares = vector(n,i,G^x[i]) \\ for performance evaluations we need to check the proofs for every bidder \\ i := checking bidder (0 == seller) \\ h := bidder to check { for(i=0,n, for(h=1,n, if(1 != zkp1_check(proofs1[h]), error("zkp1 failure in round0") ) ) ) } \\ shared public key y = prod(X=1,n,yshares[X]) \\\\\\\\\\\\ \\ ROUND1 \\\\\\\\\\\\ \\ bid matrix b = matrix(n,k,i,j,G^(bid[i]==j)) \\ zkp proofs3 = matrix(n,k,i,j, zkp3_proof(G,y,G^(bid[i]==j))) \\ index = owning agent id, price id r = matrix(n,k,i,j,proofs3[i,j]) \\r = matrix(n,k,i,j,random(q)) \\ encrypted bids Alpha = matrix(n,k,i,j, proofs3[i,j]) Beta = matrix(n,k,i,j, proofs3[i,j]) \\Alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j]) \\Beta = matrix(n,k,i,j, G^r[i,j]) proofs2 = vector(n,i, zkp2_proof(y,G,sum(j=1,k, r[i,j]))) \\ i := checking bidder (0 == seller) \\ h := bidder to check \\ j := price index to check { for(i=0,n, for(h=1,n, for(j=1,k, if(1 != zkp3_check(proofs3[h,j]), error("zkp3 failure in round1") ) ); if((prod(j=1,k,Alpha[h,j])/G) != proofs2[h], error("alpha product doesn't match") ); if(prod(j=1,k,Beta[h,j]) != proofs2[h], error("beta product doesn't match") ); if(1 != zkp2_check(proofs2[h]), error("zkp2 failure in round1") ) ) ) } \\\\\\\\\\\\ \\ ROUND2 \\\\\\\\\\\\ \\ multiplicative shares \\ first index level = owning agent id (multiplicative share) \\ second index level = agent id, price id 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]) )) 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]) )) \\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] )) \\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] )) \\ random masking and zkp proofs2 = vector(n,a,matrix(n,k,i,j, zkp2_proof(Gamma[a][i,j], Delta[a][i,j], random(q)) )) \\ for performance evaluations we need to check the proofs for every bidder \\ i := checking bidder (0 == seller) \\ h := bidder to check \\ t := target bidder (creator of the proof) \\ j := price { for(t=1,n, for(h=1,n, for(j=1,k, for(i=0,n, if(1 != zkp2_check(proofs2[t][h,j]), error("zkp2 failure in round2") ) ); \\ use masked values generated during the zkp Gamma[t][h,j] = proofs2[t][h,j]; Delta[t][h,j] = proofs2[t][h,j]; ) ) ) } \\\\\\\\\\\\ \\ ROUND3 \\\\\\\\\\\\ \\ multiplicative shares (decryption) \\ first index level = owning agent id (multiplicative share) \\ second index level = agent id, price id Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j]) )) \\Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j])^x[a] )) proofs2 = vector(n,a,matrix(n,k,i,j, zkp2_proof(Phi[a][i,j], G, x[a]) )) \\ for performance evaluations we need to check the proofs for every bidder \\ i := checking bidder (0 == seller) \\ h := bidder to check \\ t := target bidder (creator of the proof) \\ j := price { for(t=1,n, for(h=1,n, for(j=1,k, for(i=0,n, if(1 != zkp2_check(proofs2[t][h,j]), error("zkp2 failure in round2") ) ); \\ use masked values generated during the zkp Phi[t][h,j] = proofs2[t][h,j]; ) ) ) } \\\\\\\\\\\\ \\ EPILOG \\\\\\\\\\\\ \\ winner matrix v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) ) vi = lift(v) print("bids are: ", bid) for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) )) ; 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