Elliptic curve cryptosystems
Author:
Neal Koblitz
Journal:
Math. Comp. 48 (1987), 203209
MSC:
Primary 94A60; Secondary 11T71, 11Y16, 68P25
MathSciNet review:
866109
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Abstract: We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over . We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point.
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 S. Lang & J. Tate, eds., The Collected Papers of Emil Artin, AddisonWesley, Reading, Mass., 1965. MR 0176888 (31:1159)
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 S. Lang & H. Trotter, "Primitive points on elliptic curves," Bull. Amer. Math. Soc., v. 83, 1977, pp. 289292. MR 0427273 (55:308)
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 H. W. Lenstra, Jr., "Factoring integers with elliptic curves." (Preprint.)
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 V. S. Miller, "Use of elliptic curves in cryptography," Abstracts for Crypto '85.
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 M. R. P. Murty, "On Artin's conjecture," J. Number Theory, v. 16, 1983, pp. 147168. MR 698163 (86f:11087)
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 A. M. Odlyzko, "Discrete logarithms and their cryptographic significance," Advances in Cryptology: Proceedings of Eurocrypt 84, SpringerVerlag, New York, 1985, pp. 224314. MR 825593 (87g:11022)
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 D. Shanks, Solved and Unsolved Problems in Number Theory, 3rd ed., Chelsea, New York, 1985. MR 798284 (86j:11001)
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 H. Trotter, personal correspondence and unpublished tables, October 29, 1985.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708661095
PII:
S 00255718(1987)08661095
Article copyright:
© Copyright 1987
American Mathematical Society
