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| 1 | \\ From: "How to obtain full privacy in auctions" (2006) by Felix Brandt pages 19-20 | ||
| 2 | |||
| 3 | |||
| 4 | \\\\\\\\\\\\ | ||
| 5 | \\ Adapt the following values to your needs | ||
| 6 | \\\\\\\\\\\\ | ||
| 7 | |||
| 8 | \\ amount of bidders | ||
| 9 | n = 4 | ||
| 10 | \\ amount of possible prices | ||
| 11 | k = 2^4 | ||
| 12 | \\ randomize bids (change to something static, if you like) | ||
| 13 | bid = vector(n,i,random(k)+1) | ||
| 14 | \\bid = vector(n,i,n-i+1) \\ first bidder wins | ||
| 15 | \\bid = vector(n,i,i) \\ last bidder wins | ||
| 16 | \\bid = vector(n,i,(i+1)%2) \\ second bidder wins (with ties) | ||
| 17 | |||
| 18 | \\ prime finite field setup (result may be ambiguous if your prime is too small, 4*n*k seems to work fine) | ||
| 19 | \\q = prime(4*n*k) | ||
| 20 | \\ 2048bit prime: | ||
| 21 | \\q = 31905233907400964621684499856844075173802000556075101303613351426740101897961025481077892281365444367883091980681462491724119317344478120131982416132058173572772607966572720945691237876256074322291459510766147107539260048324345382562673904236506104922357079761457605045674628331006193183908801308817507027556440703972646885207099302085383887085776295396030033300833460743425162726394704256227108175491673135830378272029374848904772902525385997099641162537271298634032011458617811670193865244028195169383991286227040469186123958053863978710424421008752927011390777187889943940479064193231486057910586526439884046593027 | ||
| 22 | \\ 3072bit prime: | ||
| 23 | q = 5175054779340588353586849786144680366505563673837334790820581054294754700842534366479020240016540005621125885927641963390708863183739793208880756653713659686139600715884857385144475261507869935694699816011948585170171332029002674283854825650901258017026965486602158722052719421343475066067509485302858041368266332080773331946039572497794442067057597327877030322029413318847025776818839927761556478107499002213648377029201340152459685610920194363099878398871001275336711869213616313858200583491913270052111910410231060407633125816386053759634073500319223989240814564691163285769745840521560940666058800931070258886096469889796899266014106833050284032035948051974659796051419431527095503586817863043771919051402039741075037010264761045992285666560487072740505566408086913711094879155498223636912657852688296081316652278801546924079650897913388978423388839346058027184069633227966507908979049369500450630036982661231208087459099 | ||
| 24 | |||
| 25 | \\\\\\\\\\\\ | ||
| 26 | \\ SETUP | ||
| 27 | \\\\\\\\\\\\ | ||
| 28 | |||
| 29 | \\ p not needed? wat? | ||
| 30 | \\p = 47 | ||
| 31 | |||
| 32 | \\ get generator / primitive element for Z_q | ||
| 33 | \\ var = 'x \\ copy pasta from internet | ||
| 34 | \\ pe=ffgen(minpoly(ffprimroot(ffgen(ffinit(q,1))),var),var) \\ get primitive element | ||
| 35 | \\ 1/(fforder(pe) == q-1) \\ error out, if ord(pe) is wrong | ||
| 36 | \\ g = Mod(eval(Str(pe)), q) \\ dirty hack to convert t_FFELEM to t_INT | ||
| 37 | g = Mod(2, q) | ||
| 38 | |||
| 39 | \\\\\\\\\\\\ | ||
| 40 | \\ PROLOG | ||
| 41 | \\\\\\\\\\\\ | ||
| 42 | |||
| 43 | \\ private keys of agents | ||
| 44 | x = vector(n,i,random(q)) | ||
| 45 | \\ public keyshares of agents | ||
| 46 | yshares = vector(n,i,g^x[i]) | ||
| 47 | \\ shared public key | ||
| 48 | y = prod(X=1,n,yshares[X]) | ||
| 49 | |||
| 50 | \\ first index level = owning agent id (additive share) | ||
| 51 | \\ second index level = agent id, price id | ||
| 52 | m = vector(n,i,matrix(n,k,a,b,random(q))) | ||
| 53 | |||
| 54 | \\ index = owning agent id, price id | ||
| 55 | r = matrix(n,k,i,j,random(q)) | ||
| 56 | \\ bid matrix | ||
| 57 | b = matrix(n,k,i,j,g^(bid[i]==j)) | ||
| 58 | |||
| 59 | \\\\\\\\\\\\ | ||
| 60 | \\ ROUND1 | ||
| 61 | \\\\\\\\\\\\ | ||
| 62 | |||
| 63 | \\ encrypted bids | ||
| 64 | alpha = matrix(n,k,i,j, b[i,j]*y^r[i,j]) | ||
| 65 | beta = matrix(n,k,i,j, g^r[i,j]) | ||
| 66 | |||
| 67 | \\\\\\\\\\\\ | ||
| 68 | \\ ROUND2 | ||
| 69 | \\\\\\\\\\\\ | ||
| 70 | |||
| 71 | \\ multiplicative shares | ||
| 72 | \\ first index level = owning agent id (multiplicative share) | ||
| 73 | \\ second index level = agent id, price id | ||
| 74 | 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] )) | ||
| 75 | 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] )) | ||
| 76 | |||
| 77 | \\\\\\\\\\\\ | ||
| 78 | \\ ROUND3 | ||
| 79 | \\\\\\\\\\\\ | ||
| 80 | |||
| 81 | \\ multiplicative shares (decryption) | ||
| 82 | \\ first index level = owning agent id (multiplicative share) | ||
| 83 | \\ second index level = agent id, price id | ||
| 84 | Phi = vector(n,a,matrix(n,k,i,j, prod(h=1,n,Delta[h][i,j])^x[a] )) | ||
| 85 | |||
| 86 | \\\\\\\\\\\\ | ||
| 87 | \\ EPILOG | ||
| 88 | \\\\\\\\\\\\ | ||
| 89 | |||
| 90 | \\ winner matrix | ||
| 91 | v = matrix(n,k,a,j, prod(i=1,n,Gamma[i][a,j]) / prod(i=1,n,Phi[i][a,j]) ) | ||
| 92 | vi = lift(v) | ||
| 93 | |||
| 94 | print("bids are: ", bid) | ||
| 95 | for(X=1,n, if(vecmin(vi[X,])==1, print("And the winner is ", X) )) | ||