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Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography

Published online by Cambridge University Press:  20 November 2018

Neal Koblitz
Neal Koblitz*
Affiliation:
Dept. of Mathematics GN-50 Univ. of Washington Seattle, WA 98195 USA
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Abstract

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We find conditions under which the numerator of the zeta-function of the curve y2+y = xd over Fp, where d — 2g +1 is a prime, d ≠ p, is irreducible over Q. This leads to the generalized Mersenne problem of "almost primality" of the number of points on the jacobian of such a curve over an extension of Fp, which has application to public key cryptography.

Keywords

11L0511G2011G2511T7112E05.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 229 - 235
Copyright
Copyright © Canadian Mathematical Society 1991

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