25th Annual Symposium onFoundations of Computer Science, 1984. (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
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.
V. Vazirani and U. Vazirani, "Efficient And Secure Pseudo-Random Number Generation," 25th Annual Symposium onFoundations of Computer Science, 1984.(FOCS), Singer Island, FL, 1984, pp. 458-463.