## Supersingular curves in cryptography (2001)

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Citations: | 87 - 8 self |

### BibTeX

@INPROCEEDINGS{Galbraith01supersingularcurves,

author = {Steven D. Galbraith},

title = {Supersingular curves in cryptography},

booktitle = {},

year = {2001},

pages = {495--513},

publisher = {Springer-Verlag}

}

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### Abstract

Frey and Rück gave a method to map the discrete logarithm problem in the divisor class group of a curve over ¢¡ into a finite field discrete logarithm problem in some extension. The discrete logarithm problem in the divisor class group can therefore be solved as long ¥ as is small. In the elliptic curve case it is known that for supersingular curves one ¥§¦© ¨ has. In this paper curves of higher genus are studied. Bounds on the possible values ¥ for in the case of supersingular curves are given. Ways to ensure that a curve is not supersingular are also given. 1.