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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

Abstract : Recently, the Residue Number System and the Cox-Rower architec-ture have been used to compute efficiently Elliptic Curve Cryptography over FPGA. In this paper, we are rewriting the conditions of Kawamura-s theorem for the base extension without error in order to define the maximal range of the set from which the moduli can be chosen to build a base. At the same time, we give a procedure to compute correctly the truncation function of the Cox mod-ule. We also present a modified ALU of the Rower architecture using a second level of Montgomery Representation. Such architecture allows us to select the moduli with the new upper bound defined with the condition. This modification makes the Cox-Rower architecture suitable to compute 521 bits ECC with radix downto 16 bits compared to 18 with the classical Cox-Rower architecture. We validate our results through FPGA implementation of a scalar multiplication at classical cryptography security levels NIST curves. Our implementation uses 35% less LUTs compared to the state of the art generic implementation of ECC using RNS for the same performance 5. We also slightly improve the computa-tion time latency and our implementation shows best ratio throughput-area for RNS computation supporting any curve independently of the chosen base.

Keywords : Elliptic Curve Cryptography Hardware Implementation High Speed Residue Number System FPGA





Author: Jean-Claude Bajard - Nabil Merkiche -

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



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