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 ```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 ``` ``````\\ 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 = 4 \\ amount of possible prices k = 2^4 \\ 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) \\ 2048bit prime: \\q = 31905233907400964621684499856844075173802000556075101303613351426740101897961025481077892281365444367883091980681462491724119317344478120131982416132058173572772607966572720945691237876256074322291459510766147107539260048324345382562673904236506104922357079761457605045674628331006193183908801308817507027556440703972646885207099302085383887085776295396030033300833460743425162726394704256227108175491673135830378272029374848904772902525385997099641162537271298634032011458617811670193865244028195169383991286227040469186123958053863978710424421008752927011390777187889943940479064193231486057910586526439884046593027 \\ 3072bit prime: q = 5175054779340588353586849786144680366505563673837334790820581054294754700842534366479020240016540005621125885927641963390708863183739793208880756653713659686139600715884857385144475261507869935694699816011948585170171332029002674283854825650901258017026965486602158722052719421343475066067509485302858041368266332080773331946039572497794442067057597327877030322029413318847025776818839927761556478107499002213648377029201340152459685610920194363099878398871001275336711869213616313858200583491913270052111910410231060407633125816386053759634073500319223989240814564691163285769745840521560940666058800931070258886096469889796899266014106833050284032035948051974659796051419431527095503586817863043771919051402039741075037010264761045992285666560487072740505566408086913711094879155498223636912657852688296081316652278801546924079650897913388978423388839346058027184069633227966507908979049369500450630036982661231208087459099 \\\\\\\\\\\\ \\ 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 g = Mod(2, 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]) \\ 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))) \\ index = owning 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 = 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]) )^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 = 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])^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) )) ``````