International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Kirsten Eisenträger

Publications

Year
Venue
Title
2018
EUROCRYPT
2003
EPRINT
Improved Weil and Tate pairings for elliptic and hyperelliptic curves
Kirsten Eisenträger Kristin E. Lauter Peter L. Montgomery
We present algorithms for computing the {\it squared} Weil and Tate pairings on an elliptic curve and the {\it squared} Tate pairing for 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 pairings save about 20-30\% over the usual pairings.
2002
EPRINT
An Efficient Procedure to Double and Add Points on an Elliptic Curve
Kirsten Eisenträger Kristin E. Lauter Peter L. Montgomery
We present an algorithm that speeds exponentiation on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general exponentiation methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P + Q from given points P, Q on the curve. We give applications to simultaneous multiple exponentiation and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.