92 lines
2.6 KiB
Plaintext
92 lines
2.6 KiB
Plaintext
|
\\ From: "Fully private auctions in a constant number of rounds" (2003) by Felix Brandt pages 9-10
|
||
|
|
|
||
|
|
|
||
|
|
\\\\\\\\\\\\
|
||
|
|
\\ 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
|
||
|
|
|
||
|
|
\\\\\\\\\\\\
|
||
|
|
\\ 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) ))
|