Programmable RNS lattice-based parallel cryptographic decryption

Abstract

Should quantum computing become viable, current public-key cryptographic schemes will no longer be valid. Since cryptosystems take many years to mature, research on postquantum cryptography is now more important than ever. Herein, lattice-based cryptography is focused on, as an alternative postquantum cryptosystem, to improve its efficiency. We put together several theoretical developments so as to produce an efficient implementation that solves the Closest Vector Problem (CVP) on Goldreich-Goldwasser-Halevi (GGH)-like cryptosystems based on the Residue Number System (RNS). We were able to produce speed-ups of up to 5.9 and 11.2 on the GTX 780 Ti and i7 4770K devices, respectively, when compared to a single-core optimized implementation. Finally, we show that the proposed implementation is a competitive alternative to the Rivest-Shamir-Adleman (RSA).

RNS Approach in Lattice-Based Cryptography

“…As a matter of example, some practical results provided in [16] are indicated hereafter. The RNS/MRS approach was implemented on multi-core CPU and GPU and was compared with a classical multi-precision computation.…”

“…The performances of implementations on CPU or GPU have been investigated in [16]. In order to output the same value in both M and M 0 , Bex meth2 must be exact.…”

Mixed Radix Conversion based RSA Encryption System

“…Hence, should quantum computing become viable, currentlyin-use cryptosystems will be broken. As such, research on efficient post-quantum public-key cryptosystems is most valuable [4].…”