TY - CHAP

T1 - Improved Weil and Tate pairings for elliptic and hyperelliptic curves

AU - Eisenträger, Kirsten

AU - Lauter, Kristin

AU - Montgomery, Peter L.

PY - 2004

Y1 - 2004

N2 - We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing on hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random choice of points. Our algorithm to evaluate the squared Weil pairing is about 20% more efficient than the standard Weil pairing. Our algorithm for the squared Tate pairing on elliptic curves matches the efficiency of the algorithm given by Barreto, Lynn, and Scott in the case of arbitrary base points where their denominator cancellation technique does not apply. Our algorithm for the squared Tate pairing for hyperelliptic curves is the first detailed implementation of the pairing for general hyperelliptic curves of genus 2, and saves an estimated 30% over the standard algorithm.

AB - We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing on hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random choice of points. Our algorithm to evaluate the squared Weil pairing is about 20% more efficient than the standard Weil pairing. Our algorithm for the squared Tate pairing on elliptic curves matches the efficiency of the algorithm given by Barreto, Lynn, and Scott in the case of arbitrary base points where their denominator cancellation technique does not apply. Our algorithm for the squared Tate pairing for hyperelliptic curves is the first detailed implementation of the pairing for general hyperelliptic curves of genus 2, and saves an estimated 30% over the standard algorithm.

UR - http://www.scopus.com/inward/record.url?scp=35048886487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35048886487&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-24847-7_12

DO - 10.1007/978-3-540-24847-7_12

M3 - Chapter

AN - SCOPUS:35048886487

SN - 3540221565

SN - 9783540221562

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

SP - 169

EP - 183

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

A2 - Buell, Duncan

PB - Springer Verlag

ER -