Improved Weil and Tate pairings for elliptic and hyperelliptic curves

2003/11/21 by Kirsten Eisentraeger, Kristin Lauter, Eisentraeger, Kirsten +3
Computer Science · Mathematics · #11T71 #14G50 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11T71 #msc:14G50

paper · pdf · doi:10.48550/arxiv.math/0311391

15 pages, new version revised for publication in ANTS-6, references added

openalex publication_date 2003/11/21 · arxiv created 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the 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.

Citations

• Identity-Based Encryption from the Weil Pairing
• Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

Related

• Refinements of Miller's Algorithm over Weierstrass Curves Revisited
• Faster computation of the Tate pairing
• Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
• Further Refinements of Miller Algorithm on Edwards curves
• Pairings on Generalized Huff Curves