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A Small and Fast Software Implementation of Elliptic Curve Cryptosystems over GF(p) on a 16-Bit Microcomputer
Toshio HASEGAWA Junko NAKAJIMA Mitsuru MATSUI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1999/01/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
public key cryptography, elliptic curve cryptosystem, GF(p), 16-bit microcomputer, implementation,
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Recently the study and implementation of elliptic curve cryptosystems (ECC) have developed rapidly and its achievements have become a center of attraction. ECC has the advantage of high-speed processing in software even on restricted environments such as smart cards. In this paper, we concentrate on complete software implementation of ECC over a prime field on a 16-bit microcomputer M16C (10 MHz). We propose a new type of prime characteristic of base field suitable for small and fast implementation, and also improve basic elliptic arithmetic formulas. We report a small and fast software implementation of a cryptographic library which supports 160-bit elliptic curve DSA (ECDSA) signature generation, verification and SHA-1 on the processor. This library also includes general integer arithmetic routines for applicability to other cryptographic algorithms. We successfully implemented the library in 4 Kbyte code/data size including SHA-1, and confirmed a speed of 150 msec for generating an ECDSA signature and 630 msec for verifying an ECDSA signature on M16C.