Efficient cryptographic schemes provably as secure as subset sum

Abstract

We show very efficient constructions for a pseudorandom generator and for a universal one-way hash function based on the intractability of the subset-sum problem for certain dimensions. (Pseudorandom 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 of our constructions can be implemented in NC using an optimal number of processors.