Reif J.H. and Tygar J.D., "Efficient Parallel Pseudo-Random Number Generation", presented at Crypto 85.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is that the reductions from oneway functions to cryptographic generators is sequential i.e. even if the oneway function is easy to compute in parallel the resulting cryptographic generator will require large parallel time. For a discussion of parallel cryptography we refer to Reif and Tygar [8]. We have proved that there is a sequence of uniform NC 0 circuits which are P complete to invert. An interesting open question is whether inverting every uniform family of NC 0 permutations is in P. Acknowledgment: I would like to thank Mike Sipser and David Barrington for fruitful ....

Reif J.H. and Tygar J.D., "Efficient Parallel Pseudo-Random Number Generation", presented at Crypto 85.

....and Kompella [1] gave a randomized Boolean circuit algorithm for GCD that requires O(log 2 n) depth, but exp(O( p n log n) gates. Adelman and Kompella ask whether or not GCD is in DSPACE( p n) which still seems to be an open question. See [1] It is interesting to note that Reif and Tygar [10] have shown that if MI w.r.t. a prime p is in P NC, then randomized NC is contained in DSPACE(n ffl ) for any ffl 0. The parallel complexity of MI is also open. As a corollary to Theorem 1 we have Corollary 1 Integer coprimality is in polylog space. Proof : This follows from Theorem 1 and ....

J. Reif and J. Tygar. Efficient parallel pseudo-random number generation. In CRYPTO 85, 1985.

....efficiently by parallel evaluation. 2.6. Some presumed PT perfect generators Various generators proposed recently have been proved to be PT perfect, under some yet unproven complexity assumption. See for instance Yao (1982) Blum and Micali (1984) Blum et al. 1986) Alexi et al. 1988) Reif and Tygar (1988), Micali and Schnorr (1988) All of these are in fact based on presumed one way functions. In the next sections, we examine in more detail two of these generators. 3. THE BBS GENERATOR 3.1. Definition Blum, Blum and Schub (1986) have proposed the following generator. Let N = pq be a n bit Blum ....

Reif, J. H. and Tygar, J. D. (1988). Efficient Parallel Pseudorandom Number Generation. SIAM J. Computing , 17, 2, 404--411.

....Blum et al. 13] proposed a way of constructing in parallel several cryptographic primitives based on problems that are hard to learn. We extend their result by showing that hard to learn problems can be used to obtain synthesizers and thus pseudo random functions. A different line of work [1, 4, 47, 48, 49, 50, 54], more relevant to derandomization and saving random bits, is to construct bit generators such that their output is indistinguishable from a truly random source to an observer of restricted computational power (e.g. generators against polynomialsize constant depth circuits) Most of these ....

J. H. Reif and J. D. Tygar, Efficient parallel pseudorandom number generation, SIAM J. Comput., vol. 17(2), 1988, pp. 404-411.

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J.H. REIF AND J.D. TYGAR, Efficient Parallel Pseudo-Random Number Generation, CRYPTO'85, Santa Barbara, CA, Aug. 1985.

....6, we describe a protocol that preserves the integrity of the data against an active adversary, and Section 7 concludes with a survey of related work and a brief discussion. 2. Background 2.1. Terminology We use two notions of cryptographic security in this paper. One notion, of bit security, [3, 19], implies that given ciphertext, no processor with randomized polynomial resources can derive information about any given bit in the corresponding cleartext with certainty greater than 1 2 e for any e 0. Given the current limits of complexity theory, we do not have a way of proving bit security ....

J. Reif and J. D. Tygar. Efficient parallel pseudo-random number generation. In Advances in Cryptology: CRYPTO-85, pages 433-446. Springer-Verlag, August, 1985. To appear in SIAM J. on Computing.

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Reif, J. H., Tygar, J. D., Efficient parallel pseudorandom number generation. In SIAM J. Comput., Vol 17, No. 2, April 1988.

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J.H. Reif and J.D. Tygar. Efficient parallel pseudorandom number generation. SIAM J. Computing, 17(2):404--411, April 1988.

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