Cryptology ePrint Archive: Report 2002/147

Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

Tanja Lange

Abstract: We investigate formulae to double and add in the ideal class group of a hyperelliptic genus 2 curve avoiding inversions. To that aim we introduce a further coordinate in the representation of a class in which we collect the common denominator of the usual 4 coordinates. The analysis shows that this is practical and advantageous whenever inversions are expensive compared to multiplications like for example on smart cards.

Category / Keywords: public-key cryptography / hyperelliptic curve cryptosystems, elliptic curve cryptosystems, projective coordinates, implementation, number theory, arithmetic, explicit formulae

Date: received 23 Sep 2002, last revised 22 May 2003

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

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

Note: An updated, enlarged, and corrected paper has been submitted and can be found on the author's homepage http://www.ruhr-uni-bochum.de/itsc/tanja

Version: 20030522:215636 (All versions of this report)

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