99 lines
2.7 KiB
Plaintext
99 lines
2.7 KiB
Plaintext
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\\ 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
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\\ amount of bidders
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n = 2^3
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\\ amount of possible prices
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k = 2^7
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\\ randomize bids (change to something static, if you like)
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bid = vector(n,i,random(k)+1)
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\\bid = vector(n,i,n-i+1) \\ first bidder wins
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\\bid = vector(n,i,i) \\ last bidder wins
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\\bid = vector(n,i,(i+1)%2) \\ second bidder wins (with ties)
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\\ prime finite field setup (result may be ambiguous if your prime is too small, 4*n*k seems to work fine)
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q = prime(4*n*k)
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\\ SETUP
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\\ p not needed? wat?
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\\p = 47
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\\ get generator / primitive element for Z_q
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var = 'x \\ copy pasta from internet
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pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element
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1/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong
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g = Mod(eval(Str(pe)), q) \\ dirty hack to convert t_FFELEM to t_INT
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\\ setup static matrices
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U = matrix(k,k,i,j,Mod(i<=j,q))
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L = matrix(k,k,i,j,Mod(i>=j,q))
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Id = matrix(k,k,i,j,Mod(i==j,q))
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\\ PROLOG
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\\ private keys of agents
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x = vector(n,i,random(q))
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\\ public keyshares of agents
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yshares = vector(n,i,g^x[i])
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\\ shared public key
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y = prod(X=1,n,yshares[X])
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\\ what is m?
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\\ first index level = agent id (additive share)
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\\ second index level = agent id, price id
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m = vector(n,i,matrix(n,k,a,b,random(q)))
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\\ what is r?
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\\ index = agent id, price id
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r = matrix(n,k,i,j,random(q))
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\\ bid matrix
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b = matrix(n,k,i,j,g^(bid[i]==j))
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\\ ROUND1
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\\ encrypted bids
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alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j])
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beta = matrix(n,k,i,j, g^r[i,j])
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\\ ROUND2
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\\ multiplicative shares
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\\ first index level = agent id (multiplicative share)
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\\ second index level = agent id, price id
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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] ))
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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] ))
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\\ ROUND3
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\\ multiplicative shares (decryption)
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\\ first index level = agent id (multiplicative share)
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\\ second index level = agent id, price id
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Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j])^x[a] ))
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\\ EPILOG
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\\ winner matrix
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v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) )
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vi = lift(v)
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print("bids are: ", bid)
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for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) ))
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