Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University

Shafi Goldwasser
Silvio Micali
This leads to the Goldwasser-Micali probabilistic encryption algorithm:
Init: Alice starts by selecting two large distinct prime numbers p and q.
She then computes n = pq and selects a pseudosquare y. n and y will be
public, p and q private.
Algorithm 1.7 ( Goldwasser-Micali probabilistic encryption )
1: Represent message m in binary (m = m 1 m 2 ...m t ).
2: FOR i =1TO t DO
3:
∗
Pick x ∈ R Z n
4: c i ← y m i
x 2 mod n
5: RETURN c = c 1 c 2 ...c t