Alexandre Paillier on Reels

Vincent PAILLIER

SOLVED:The Paillier cryptosystem is a public key cryptosystem described in 1999 by P. Paillier, used in some electronic voting systems. A public key (n, g) and a corresponding private key (p, q) are created by randomly selecting primes p and q so that gcd(p q, λ)=1, where λ=(p-1)(q-1), and a nonzero element g of 𝐙n^2 with gcd((g^λ n^2-1) / n, n)=1 . To encrypt a message m ∈𝐙n a random nonzero element r of 𝐙n is first selected, and then used to find c=g^m r^n n^2 Show that the Paillier cryptos