97 lines
4.1 KiB
Plaintext
97 lines
4.1 KiB
Plaintext
\\ 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 = 4
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\\ amount of possible prices
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k = 2^4
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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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\\ 2048bit prime:
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\\q = 31905233907400964621684499856844075173802000556075101303613351426740101897961025481077892281365444367883091980681462491724119317344478120131982416132058173572772607966572720945691237876256074322291459510766147107539260048324345382562673904236506104922357079761457605045674628331006193183908801308817507027556440703972646885207099302085383887085776295396030033300833460743425162726394704256227108175491673135830378272029374848904772902525385997099641162537271298634032011458617811670193865244028195169383991286227040469186123958053863978710424421008752927011390777187889943940479064193231486057910586526439884046593027
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\\ 3072bit prime:
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q = 5175054779340588353586849786144680366505563673837334790820581054294754700842534366479020240016540005621125885927641963390708863183739793208880756653713659686139600715884857385144475261507869935694699816011948585170171332029002674283854825650901258017026965486602158722052719421343475066067509485302858041368266332080773331946039572497794442067057597327877030322029413318847025776818839927761556478107499002213648377029201340152459685610920194363099878398871001275336711869213616313858200583491913270052111910410231060407633125816386053759634073500319223989240814564691163285769745840521560940666058800931070258886096469889796899266014106833050284032035948051974659796051419431527095503586817863043771919051402039741075037010264761045992285666560487072740505566408086913711094879155498223636912657852688296081316652278801546924079650897913388978423388839346058027184069633227966507908979049369500450630036982661231208087459099
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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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g = Mod(2, 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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\\ first index level = owning 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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\\ index = owning 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 = owning 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 = owning 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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