A Lattice-Based Public-Key Cryptosystem

Abstract

Ajtai recently found a random class of lattices of integer points for which he could prove the following worst-case/average-case equivalence result: If there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice from the class, then there is also a probabilistic polynomial time algorithm which solves several problems related to the shortest lattice vector problem (SVP) in any n-dimensional lattice. Ajtai and Dwork then designed a public-key cryptosystem which is provably secure unless the worst case of a version of the SVP can be solved in probabilistic polynomial time. However, their cryptosystem suffers from massive data expansion because it encrypts data bit-by-bit. Here we present a public-key cryptosystem based on similar ideas, but with much less data expansion.