The Blum–Micali algorithm is a cryptographically secure pseudorandom number generator.
The algorithm gets its security from the difficulty of computing discrete logarithms.
be an odd prime, and let
be a primitive root modulo
This is equivalent to using one bit of
can be used if solving the discrete log problem is infeasible even for exponents with as few as
[2] In order for this generator to be secure, the prime number
needs to be large enough so that computing discrete logarithms modulo
[1] To be more precise, any method that predicts the numbers generated will lead to an algorithm that solves the discrete logarithm problem for that prime.
[3] There is a paper discussing possible examples of the quantum permanent compromise attack to the Blum–Micali construction.
This attacks illustrate how a previous attack to the Blum–Micali generator can be extended to the whole Blum–Micali construction, including the Blum Blum Shub and Kaliski generators.
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