One way functions and pseudorandom generators
- 360 Downloads
Pseudorandom generators transform in polynomial time a short random “seed” into a long “pseudorandom” string. This string cannot be random in the classical sense of , but testing that requires an unrealistic amount of time (say, exhaustive search for the seed). Such pseudorandom generators were first discovered in  assuming that the function (a x modb) is one-way, i.e., easy to compute, but hard to invert on a noticeable fraction of instances. In  this assumption was generalized to the existence of any one-way permutation. The permutation requirement is sufficient but still very strong. It is unlikely to be proven necessary, unless something crucial, like P=NP, is discovered. Below, among other observations, a weaker assumption about one-way functions is proposed, which is not only sufficient, but also necessary for the existence of pseudorandom generators.
KeywordsPolynomial Time Hamiltonian Cycle Probabilistic Algorithm Pseudorandom Generator Bell System Technical Journal
Unable to display preview. Download preview PDF.
- L. Blum, M. Blum andM. Shub, A Simple Secure Pseudo-Random Number Generator,Advances in Cryptology (ed. D. Chaum, R. L. Rivest and A. T. Sherman), Plenum Press, 1983, 61–78.Google Scholar
- S. Goldwasser,Probabilistic Encryption: Theory and Applications, Ph. D. Dissert, University of California at Berkeley (1984), Section 4.2.3.Google Scholar
- A. N. Kolmogorov, Three Approaches to the Concept of the Amount of Information,Probl. Inf. Transm. (1965), 1/1.Google Scholar
- L. Levin, Average Case Complete Problems,SIAM J. Comput. (1986), 285–286.Google Scholar
- L. Levin, Randomness Conservation Inequalities,Information and Control 61 (1984), section 1.3; In less detail in Theorem 2 of Universal Sequential Search Problems,Probl. Inf. Transm. 9 (1973).Google Scholar
- C. Rackoff, Personal communication, (1985).Google Scholar
- A. C. Yao, Theory and Applications of Trapdoor Functions,Proc. 23rd IEEE Symp. on Foundations of Computer Science (1982), 80–91.Google Scholar