Abstract
Cryptographically secure pseudo-random 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 (n 2 steps). Blum, Blum and Shub ask the open problem of outputting even two bits securely. We state a simple condition, the XOR-Condition, and show that any generator satisfying this condition can output logn bits on each multiplication. We also show that the logn least significant bits of RSA, Rabin’s Scheme, and the x 2 mod N generator satisfy this condition. As a corollary, we prove that all boolean predicates of these bits are secure. Furthermore, we strengthen the security of the x 2 mod N generator, which being a Trapdoor Generator, has several applications, by proving it as hard as Factoring.
Supported by NSF Grant MCS 82-04506, and by the IBM Doctoral Fellowship.
Supported by NSF Grant MCS 81-21431.
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7. References
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© 1985 Springer-Verlag Berlin Heidelberg
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Vazirani, U.V., Vazirani, V.V. (1985). Efficient and Secure Pseudo-Random Number Generation (Extended Abstract). In: Blakley, G.R., Chaum, D. (eds) Advances in Cryptology. CRYPTO 1984. Lecture Notes in Computer Science, vol 196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39568-7_17
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DOI: https://doi.org/10.1007/3-540-39568-7_17
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