GOLDWASSER-MICALI ENCRYPTION SCHEME
The Goldwasser-Micali encryption scheme (see public key cryptography) is the first encryption scheme that achieved semanticsecurity against a passive adversary under the assumption that solving the quadratic residuosityproblem is hard. The scheme encrypts 1 bit of information, and the resulting ciphertext is typically 1024 bits long.
In the Goldwasser-Micali encryption scheme, a public key is a number n, that is a product of two primes numbers, say p and q. Let Y be a quadratic nonresidue modulo n (see quadratic residue and modular arithmetic), whose Jacobi Symbol is 1. The decryption key is formed by the prime factors of n.
The Goldwasser-Micali encryption scheme encrypts a bit b as follows. One picks an integer \( r\, (1<r<n-1) \)