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 -