Montgomery Multiplier Design for ECDSA Signature Generation Processor

Masato TAMURA  Makoto IKEDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.12   pp.2444-2452
Publication Date: 2016/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.2444
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
ECDSA,  pipelined Montgomery multiplier,  optimization,  

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This paper presents the optimal implementation methods for 256-bit elliptic curve digital signature algorithm (ECDSA) signature generation processors with high speed Montgomery multipliers. We have explored the radix of the data path of the Montgomery multiplier from 2-bit to 256-bit operation and proposed the use of pipelined Montgomery multipliers for signature generation speed, area, and energy optimization. The key factor in the design optimization is how to perform modular multiplication. The high radix Montgomery multiplier is known to be an efficient implementation for high-speed modular multiplication. We have implemented ECDSA signature generation processors with high radix Montgomery multipliers using 65-nm SOTB CMOS technology. Post-layout results show that the fastest ECDSA signature generation time of 63.5µs with radix-256-bit, a two-module four-streams pipeline architecture, and an area of 0.365mm2 (which is the smallest) with a radix-16-bit zero-pipeline architecture, and the smallest signature generation energy of 9.51µJ with radix-256-bit zero-pipeline architecture.