A Fast Elliptic Curve Cryptosystem LSI Embedding Word-Based Montgomery Multiplier

Jumpei UCHIDA
Nozomu TOGAWA
Masao YANAGISAWA
Tatsuo OHTSUKI

Publication
IEICE TRANSACTIONS on Electronics   Vol.E89-C    No.3    pp.243-249
Publication Date: 2006/03/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e89-c.3.243
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design Technology in the Sub-100 nm Era)
Category: System LSIs and Microprocessors
Keyword: 
elliptic curve cryptosystem,  Montgmery multiplier,  public-key cryptosystem,  LSI design,  

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Summary: 
Elliptic curve cryptosystems are expected to be a next standard of public-key cryptosystems. A security level of elliptic curve cryptosystems depends on a difficulty of a discrete logarithm problem on elliptic curves. The security level of a elliptic curve cryptosystem which has a public-key of 160-bit is equivalent to that of a RSA system which has a public-key of 1024-bit. We propose an elliptic curve cryptosystem LSI architecture embedding word-based Montgomery multipliers. A Montgomery multiplication is an efficient method for a finite field multiplication. We can design a scalable architecture for an elliptic curve cryptosystem by selecting structure of word-based Montgomery multipliers. Experimental results demonstrate effectiveness and efficiency of the proposed architecture. In the hardware evaluation using 0.18 µm CMOS library, the high-speed design using 126 Kgates with 208-bit multipliers achieved operation times of 3.6 ms for a 160-bit point multiplication.