Cryptology ePrint Archive: Report 2002/121

Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae

Tanja Lange

Abstract: We extend the explicit formulae for arithmetic on genus two curves of Takahashi and Miyamoto,Doi,Matsuo,Chao,and Tsuji to fields of even characteristic and to arbitrary equation of the curve and slightly improve them. These formulae can be evaluated faster than the more general Cantor algorithm and allow to obtain faster arithmetic on a hyperelliptic genus 2 curve than on elliptic curves. We give timings for implementations using various libraries for the field arithmetic.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, implementation, number theory, hyperellitptic curve cryptosystem, arithmetic, explicit formulae

Date: received 16 Aug 2002, last revised 15 Dec 2003

Contact author: lange at itsc ruhr-uni-bochum de

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: Corrected NTL timings and mistake on p.4. More recent version at

Version: 20031215:223305 (All versions of this report)

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