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A public-key cryptosystem invented by Pascal Paillier in 1999.
13
votes
Division in paillier cryptosystem
Paillier encryption is built on the bijeective mapping from $(x,y)\in \mathbb{Z}_n \times \mathbb{Z}_n^*$ to:
$E_{g,n}(x,y)=g^x y^n \bmod{n^2}$. … ], n];
m = RandomInteger[{1, n - 1}];
s = RandomInteger[{1, n - 1}];
si = PowerMod[s, -1, n];
c = PowerMod[Enc[m], si, n^2];
Dec[c] == Mod[m*si, n]
This answer is the result of a crash course in Paillier …
0
votes
Accepted
ZKIP for Paillier public key correctness
First, the awkwardness of ZKPs and distributed key generation in Paillier is the reason many protocols use exponential Elgamal for protocols like mental poker. … I don't know of a ZKP for well-formed keys in Paillier. This is just an initial thought. …