Improved Weil and Tate pairings for elliptic and hyperelliptic curves

Kirsten Eisentraeger; Kristin Lauter; Peter L.  Montgomery

Paper 2003/242

Improved Weil and Tate pairings for elliptic and hyperelliptic curves

Kirsten Eisentraeger, Kristin Lauter, and Peter L. Montgomery

Abstract

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.

Note: version revised for publication, references added

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. to appear in the proceedings of ANTS-6 (Algorithmic Number Theory Symposium)
Keywords: pairing-based cryptography
Contact author(s): klauter @ microsoft com
History: 2004-03-04: last of 2 revisions; 2003-11-23: received; See all versions
Short URL: https://ia.cr/2003/242
License: CC BY

BibTeX

@misc{cryptoeprint:2003/242,
      author = {Kirsten Eisentraeger and Kristin Lauter and Peter L.  Montgomery},
      title = {Improved Weil and Tate pairings for elliptic and hyperelliptic curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/242},
      year = {2003},
      url = {https://eprint.iacr.org/2003/242}
}