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| -rw-r--r-- | firstPrice.gp | 98 |
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diff --git a/firstPrice.gp b/firstPrice.gp new file mode 100644 index 0000000..6935ab6 --- /dev/null +++ b/firstPrice.gp @@ -0,0 +1,98 @@ +\\ 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 = 2^3 +\\ amount of possible prices +k = 2^7 +\\ 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) + +\\ prime finite field setup (result may be ambiguous if your prime is too small, 4*n*k seems to work fine) +q = prime(4*n*k) + +\\\\\\\\\\\\ +\\ SETUP +\\\\\\\\\\\\ + +\\ p not needed? wat? +\\p = 47 + +\\ get generator / primitive element for Z_q +var = 'x \\ copy pasta from internet +pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element +1/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong +g = Mod(eval(Str(pe)), q) \\ dirty hack to convert t_FFELEM to t_INT + +\\ setup static matrices +U = matrix(k,k,i,j,Mod(i<=j,q)) +L = matrix(k,k,i,j,Mod(i>=j,q)) +Id = matrix(k,k,i,j,Mod(i==j,q)) + +\\\\\\\\\\\\ +\\ PROLOG +\\\\\\\\\\\\ + +\\ private keys of agents +x = vector(n,i,random(q)) +\\ public keyshares of agents +yshares = vector(n,i,g^x[i]) +\\ shared public key +y = prod(X=1,n,yshares[X]) + +\\ what is m? +\\ first index level = agent id (additive share) +\\ second index level = agent id, price id +m = vector(n,i,matrix(n,k,a,b,random(q))) + +\\ what is r? +\\ index = agent id, price id +r = matrix(n,k,i,j,random(q)) +\\ bid matrix +b = matrix(n,k,i,j,g^(bid[i]==j)) + +\\\\\\\\\\\\ +\\ ROUND1 +\\\\\\\\\\\\ + +\\ encrypted bids +alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j]) +beta = matrix(n,k,i,j, g^r[i,j]) + +\\\\\\\\\\\\ +\\ ROUND2 +\\\\\\\\\\\\ + +\\ multiplicative shares +\\ first index level = 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]) )^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] )) + +\\\\\\\\\\\\ +\\ ROUND3 +\\\\\\\\\\\\ + +\\ multiplicative shares (decryption) +\\ first index level = 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])^x[a] )) + +\\\\\\\\\\\\ +\\ 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) )) |