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On Secure and Fast Elliptic Curve Cryptosystems over Fp
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1994/04/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
public-key, elliptic curves,
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From a practical point of view, a cryptosystem should require a small key size and less running time. For this purpose, we often select its definition field in such a way that the arithmetic can be implemented fast. But it often brings attacks which depend on the definition field. In this paper, we investigate the definition field Fp on which elliptic curve cryptosystems can be implemented fast, while maintaining the security. The expected running time on a general construction of many elliptic curves with a given number of rational points is also discussed.