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
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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 -