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Elliptic Curve Cryptosystems

Neal Koblitz
Mathematics of Computation
Vol. 48, No. 177 (Jan., 1987), pp. 203-209
DOI: 10.2307/2007884
Stable URL: http://www.jstor.org/stable/2007884
Page Count: 7
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Elliptic Curve Cryptosystems
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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 $\operatorname{GF}(2^n)$. 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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