An Efficient and Parallel R-LWE Cryptoprocessor

Abstract

Lattice-based cryptography (LBC) is a promising and efficient public key cryptography scheme whose theoretical foundation usually lies in Learning with Error (LWE) problem and its variant such as Ring-LWE (R-LWE) is the most studied cryptosystem which allows for more efficient implementation while maintaining the hardness of an original problem. Polynomial multiplication is the bottleneck of R-LWE, that can either be done using Number Theoretic Transform (NTT) or schoolbook polynomial multiplication (SPM) algorithm. The use of SPM is wider and possible for all parameters of R-LWE schemes. This brief proposes an efficient and parallel strategy for SPM in R-LWE; by successfully reducing its time complexity from $n^{2}$ to $n^{2}/4$ (making it $1.8\times $ faster and $1.4\times $ hardware efficient). Furthermore, by adjusting the bit width for the error terms, the polynomial multiplication and addition blocks are reused for both encryption and decryption modules resulting in 14% reduced area and $1.7\times $ better throughput in comparison to state-of-art SPM based R-LWE designs.