Babaï round-off CVP method in RNS: Application to lattice based cryptographic protocols

Abstract

Lattice based cryptography is claimed as a serious candidate for post quantum cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if lattice based cryptography has made theoretical progresses, its chances to be adopted in practice are still low due to the cost of the computation. If some approaches like RSA and ECC have been strongly optimized-in particular their core arithmetic operations, the modular multiplication and/or the modular exponentiation-lattice based cryptography has not been arithmetically improved. This paper proposes to fill the gap with a new approach using Residue Number Systems, RNS, for one of the core arithmetic operation of lattice based cryptography: namely solving the Closest Vector Problem (CVP).

RNS Approach in Lattice-Based Cryptography

“…no multiple of M 0 should appear in the residues of the output in base M), the base M 0 has to be large enough to completely represent the result. In further parts, different approaches and their consequences will be discussed [4,5].…”

“…The approach depicted in this part was first described in [4]. The performances of implementations on CPU or GPU have been investigated in [16].…”

“…To overcome this issue, another approach, which was introduced in [4], is possible, where b q M 0 is reduced inside the base M 0 by using a small Montgomery reduction based on an extra modulus Q m. Algorithm 4 depicts this new modular reduction.…”

Single Base Modular Multiplication for Efficient Hardware RNS Implementations of ECC

“…[10,32]) and very recently lattice based cryptography (e.g. [5]). In this paper, we only deal with hardware implementations of ECC.…”

Programmable RNS lattice-based parallel cryptographic decryption

“…Recently, GGH has got many improvements [9]- [11] to make it competitive under secure parameters. This article deals with efficient implementation of GGH decryption function, via an arithmetical approach as suggested in [12].…”