Encyclopedia of Cryptography and Security

2005 Edition
| Editors: Henk C. A. van Tilborg


  • Kazue Sako
Reference work entry
DOI: https://doi.org/10.1007/0-387-23483-7_177

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 \( r\, (1<r<n-1) \)

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  1. [1]
    Goldwasser, S. and S. Micali (1984). “Probabilistic encryption.” Journal of Computer and System Sciences, 28, 270–299.zbMATHMathSciNetCrossRefGoogle Scholar

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© International Federation for Information Processing 2005

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  • Kazue Sako

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