We show very efficient constructions for a pseudo-random generator and for a universal one-way hash function based on the intractability of the subset sum problem for certain dimensions. (Pseudo-random generators can be used for private key encryption and universal one-way hash functions for signature schemes). The increase in efficiency in our construction is due to the fact that many bits can be generated/hashed with one application of the assumed one-way function. All our construction can be implemented in NC using an optimal number of processors. Part of this work done while both authors were at UC Berkeley and part when the second author was at the IBM Almaden Research Center. Research supported by NSF grant CCR 88 - 13632. A preliminary version of this paper appeared in Proc. of the 30th Symp. on Foundations of Computer Science, 1989. 1 Introduction Many cryptosystems are based on the intractability of such number theoretic problems such as factoring and discrete logarit...

A signature scheme is existentially unforgeable if, given any polynomial (in the security parameter) number of pairs (m 1 ; S(m 1 )); (m 2 ; S(m 2 )); : : : (m k ; S(m k )) where S(m) denotes the signature on the message m, it is computationally infeasible to generate a pair (m k+1 ; S(m k+1 )) for any message m k+1 = 2 fm 1 ; : : : m k g. We present an existentially unforgeable signature scheme that for a reasonable setting of parameters requires at most 6 times the amount of time needed to generate a signature using "plain" RSA (which is not existentially unforgeable). We point out applications where our scheme is desirable. Preliminary version appeared in Crypto'94 y IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120. Research supported by a BSF Grant 32-00032-1. E-mail: dwork@almaden.ibm.com. z Incumbent of the Morris and Rose Goldman Career Development Chair, Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Re...

Even, Goldreich and Micali showed at Crypto'89 that the existence of signature schemes secure against known message attacks implies the existence of schemes secure against adaptively chosen message attacks. Unfortunately, this transformation leads to a rather impractical scheme. We exhibit a similar security amplification, which takes the given scheme to a new signature scheme that is not even existentially forgeable under adaptively chosen message attacks. Additionally, however, our transformation will be practical: The complexity of the resulting scheme is twice that of the original scheme. The principles of both transformations carry over to block encryption systems. It is shown how they can be used to convert a block encryption system secure against known plaintext attacks to a system secure against chosen plaintext attacks. For both schemes it is shown that if the transformed scheme can be broken given a number, T , of encryptions of adaptively chosen plaintexts, then the...

We outline constructions for both pseudo-random generators and one-way hash functions. These constructions are based on the exact TSP (XTSP), a special variant of the well known traveling salesperson problem. We prove that these constructions are secure if the XTSP is infeasible. Our constructions are easy to implement, appear to be fast, but require a large amount of memory.