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25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24-October 26
ISBN: 0-8186-0591-X
U.V. Vazirani, University of California
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/sup 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/sup 2/ mod N generator satisfy boolean predicates of these bits are secure. Furthermore, we strengthen the security of the x/sup 2/ mod N generator, which being a Trapdoor Generator, has several applications, by proving it as hard as Factoring.
U.V. Vazirani, V.V. Vazirani, "Efficient And Secure Pseudo-Random Number Generation," focs, pp.458-463, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
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