Cryptology ePrint Archive: Report 2004/241

A Comparison of Point Counting methods for Hyperelliptic Curves over Prime Fields and Fields of Characteristic 2

Colm O hEigeartaigh

Abstract: Computing the order of the Jacobian of a hyperelliptic curve remains a hard problem. It is usually essential to calculate the order of the Jacobian to prevent certain sub-exponential attacks on the cryptosystem. This paper reports on the viability of implementations of various point-counting techniques. We also report on the scalability of the algorithms as the fields grow larger.

Category / Keywords: Hyperelliptic Curve Cryptography, lattices, point counting, Jacobian

Date: received 17 Sep 2004, last revised 27 Sep 2004

Contact author: coheigeartaigh at computing dcu ie

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Note: Faulty submission title

Version: 20040927:122629 (All versions of this report)

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