TY - CHAP

T1 - Aspects of hyperelliptic curves over large prime fields in software implementations

AU - Avanzi, Roberto Maria

PY - 2004

Y1 - 2004

N2 - Department of Electrical Engineering and Information Sciences Ruhr University of Bochum, Universitätsstraβe 150, D-44780 Bochum, Germany We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups, we developed an ad-hoc arithmetic library, designed to remove most of the overheads that penalize implementations of curve-based cryptography over prime fields. These overheads get worse for smaller fields, and thus for larger genera for a fixed group size. We also use techniques for delaying modular reductions to reduce the amount of modular reductions in the formulae for the group operations. The result is that the performance of hyperelliptic curves of genus 2 over prime fields is much closer to the performance of elliptic curves than previously thought. For groups of 192 and 256 bits the difference is about 14% and 15% respectively.

AB - Department of Electrical Engineering and Information Sciences Ruhr University of Bochum, Universitätsstraβe 150, D-44780 Bochum, Germany We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups, we developed an ad-hoc arithmetic library, designed to remove most of the overheads that penalize implementations of curve-based cryptography over prime fields. These overheads get worse for smaller fields, and thus for larger genera for a fixed group size. We also use techniques for delaying modular reductions to reduce the amount of modular reductions in the formulae for the group operations. The result is that the performance of hyperelliptic curves of genus 2 over prime fields is much closer to the performance of elliptic curves than previously thought. For groups of 192 and 256 bits the difference is about 14% and 15% respectively.

KW - Cryptography

KW - Efficient implementation

KW - Elliptic and hyperelliptic curves

KW - Lazy and incomplete modular reduction

KW - Prime field arithmetic

UR - http://www.scopus.com/inward/record.url?scp=35048858891&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-28632-5_11

DO - 10.1007/978-3-540-28632-5_11

M3 - Chapter

AN - SCOPUS:35048858891

SN - 3540226664

SN - 9783540226666

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 148

EP - 162

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Joye, Marc

A2 - Quisquater, Jean-Jacques

PB - Springer Verlag

ER -