RNS Arithmetic Approach in Lattice-based Cryptography Accelerating the Rounding-off Core ProcedureReport as inadecuate




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1 PEQUAN - Performance et Qualité des Algorithmes Numériques LIP6 - Laboratoire d-Informatique de Paris 6 2 DGA.MI - DGA Maîtrise de l-information 3 University of Wollongong

Abstract : —Residue Number Systems RNS are naturally considered as an interesting candidate to provide efficient arithmetic for implementations of cryptosystems such as RSA, ECC El-liptic Curve Cryptography, pairings, etc. More recently, RNS have been used to accelerate fully homomorphic encryption as lattice-based cryptogaphy. In this paper, we present an RNS algorithm resolving the Closest Vector Problem CVP. This algorithm is particularly efficient for a certain class of lattice basis. It provides a full RNS Babai round-off procedure without any costly conversion into alternative positional number system such as Mixed Radix System MRS. An optimized Cox-Rower architecture adapted to the proposed algorithm is also presented. The main modifications reside in the Rower unit whose feature is to use only one multiplier. This allows to free two out of three multipliers from the Rower unit by reusing the same one with an overhead of 3 more cycles per inner reduction. An analysis of feasibility of implementation within FPGA is also given.

Keywords : FPGA Hardware Implementation Index Terms—Residue Number System Lattices CVP Round-off





Author: Jean-Claude Bajard - Julien Eynard - Nabil Merkiche - Thomas Plantard -

Source: https://hal.archives-ouvertes.fr/



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