# Blum-Micali algorithm

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The * Blum-Micali algorithm* is a cryptographically secure pseudorandom number generator. The algorithm gets its security from the difficulty of computing discrete logarithms.

^{[1]}

Let be an odd prime, and let be a primitive root modulo . Let be a seed, and let

.

The th output of the algorithm is 1 if . Otherwise the output is 0.

In order for this generator to be secure, the prime number needs to be large enough so that computing discrete logarithms modulo is infeasible.^{[1]} To be more precise, if this generator is not secure then there is an algorithm that computes the discrete logarithm faster than is currently thought to be possible.^{[2]}

## References Edit

- ↑
^{1.0}^{1.1}Bruce Schneier,*Applied Cryptography: Protocols, Algorithms, and Source Code in C*, pages 416-417, Wiley; 2nd edition (October 18, 1996), ISBN 0471117099 - ↑ Manuel Blum and Silvio Micali,
*How to Generate Cryptographically Strong Sequences of Pseudorandom Bits,*SIAM Journal on Computing 13, no. 4 (1984): 850-864.