Fast Blum-Blum-Shub Sequence Generation Using Montgomery Multiplication

Blum Blum Shub on the GPU

Context. The cryptographically secure pseudo-random number generator Blum Blum Shub (BBS) is a simple algorithm with a strong security proof, however it requires very large numbers to be secure, which makes it computationally heavy. The Graphics Processing Unit (GPU) is a common vector processor originally dedicated to computer-game graphics, but has since been adapted to perform general-purpos...

Cryptographic Secure Pseudo-Random Bits Generation : The Blum-Blum-Shub Generator

Efficient and Secure Pseudo-Random Number Generation (Extended Abstract)

Cryptographically secure pseudorandom number generators known so far suffer from the handicap of being inefficient; the most efficient ones can generate only one bit on each modular multiplication (n2 steps). Hum, Blum and Shub ask the open problem of outputting even two bits securely. We state a simple condition, the XORCondition. and show that any generator satisfying this condition can outpu...

Nonquadratic Variation of the Blum-blum-shub Pseudorandom Number Generator

Cryptography is essential for secure online communications. Many different types of ciphers are implemented in modern-day cryptography, but they all have one common factor. All ciphers require a source of randomness, which makes them unpredictable. One such source of this randomness is a random number generator. This thesis focuses on Pseudorandom Number Generators (PRNG), specifically, a PRNG ...

Abstract geometrical computation with accumulations: Beyond the Blum, Shub and Smale model

geometrical computation with accumulations: Beyond the Blum, Shub and Smale model