Cryptographic Primitives Based on Hard Learning Problems

Modern cryptography has had considerable impact on the development of computational learning theory. Virtually every intractability result in Valiant’s model [13] (which is representation-independent in the sense that it does not rely on an artificial syntactic restriction on the learning algorithm’s hypotheses) has at its heart a cryptographic construction [4, 9, 1, 10]. In this paper, we give results in the reverse direction by showing how to construct several cryptographic primitives based on certain assumptions on the difficulty of learning. In doing so, we develop further a line of thought introduced by Impagliazzo and Levin [6].