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

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). Disciplines Engineering | Science and Technology Studies Publication Details Bajard, J., Eynard, J., Merkiche, N. & Plantard, T. (2015). Babai round-off CVP method in RNS application to latice based cryptographic protocols. Proceedings of the 14th International Symposium on Integrated Circuits (ISIC) (pp. 440-443). United States: IEEE. This conference paper is available at Research Online: http://ro.uow.edu.au/eispapers/5192 Babaı̈ Round-Off CVP method in RNS Application to Lattice based cryptographic protocols Jean-Claude Bajard, Julien Eynard† Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, F-75005, Paris, France. CNRS, UMR 7606, LIP6, F-75005, Paris, France. {jean-claude.bajard,julien.eynard}@lip6.fr Nabil Merkiche DGA/MI, Rennes, France. [email protected] Thomas Plantard CCISR, Univ. of Wollongong, Australia. [email protected] 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).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). Keywords—Residue Number System; Base Conversions; Lattice; Closest Vector Problem