\\ From: "How to obtain full privacy in auctions" (2006) by Felix Brandt pages 19-20
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\\ 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)
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\\ SETUP
\\\\\\\\\\\\
read(group);
read(zkp);
fp_priv(bids:vec, k:int) =
{
local(n:int = length(bids));
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\\ PROLOG
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\\ 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][4]);
\\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]);
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\\ ROUND1
\\\\\\\\\\\\
\\ bid matrix
b = matrix(n,k,i,j,G^(bids[i]==j));
\\ zkp
proofs3 = matrix(n,k,i,j, zkp3_proof(G,y,G^(bids[i]==j)));
\\ index = owning agent id, price id
r = matrix(n,k,i,j,proofs3[i,j][13]);
\\r = matrix(n,k,i,j,random(q))
\\ encrypted bids
Alpha = matrix(n,k,i,j, proofs3[i,j][3]);
Beta = matrix(n,k,i,j, proofs3[i,j][4]);
\\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][6],
error("alpha product doesn't match")
);
if(prod(j=1,k,Beta[h,j]) != proofs2[h][7],
error("beta product doesn't match")
);
if(1 != zkp2_check(proofs2[h]),
error("zkp2 failure in round1")
)
)
);
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\\ ROUND2
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\\ 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][6];
Delta[t][h,j] = proofs2[t][h,j][7];
)
)
);
\\\\\\\\\\\\
\\ 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][6];
)
)
);
\\\\\\\\\\\\
\\ 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: ", bids);
for(X=1,n,
if(vecmin(vi[X,])==1,
print("And the winner is ", X)
)
);
}
;