Improved efficiency of MP12

Abstract

MP12 (proposed by Micciancio and Peikert in Eurocrypt 2012) presented a chosen ciphertext secure public key encryption (PKE) scheme based on the learning with errors (LWE) problem. In this paper, we improve the efficiency of the scheme and give two sets of parameters. In both sets of parameters, the size of secret key is O(log q) times less than the scheme in MP12. Furthermore, in the second case of p = O(n), we can decrease the message expansion rate from O(log q) to O(1). The main ideas in our scheme are we can hide the message by the knapsack LWE assumption and embed the message into the error item.