Blum Blum Shub [SEP] named after
Blum Blum Shub
Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub that is derived from Michael O. Rabin's one-way function.
Blum Blum Shub takes the form
where "M" = "pq" is the product of two large primes "p" and "q". At each step of the algorithm, some output is derived from "x"; the output is commonly either the bit parity of "x" or
cipher). Again, the initial state must be kept secret.
Designs Number-theoretic designs.
- The Blum Blum Shub algorithm has a security proof based on the difficulty of the quadratic residuosity problem. Since the only known way to solve that problem is to factor the modulus, it is generally regarded that the difficulty of integer factorization provides a conditional security proof for the Blum Blum Shub algorithm. However the algorithm is very inefficient and therefore impractical unless extreme security is needed.
- The Blum–Micali algorithm has