Faster computation of the Tate pairing

DOI10.1016/j.jnt.2010.05.013zbMath1222.14069arXiv0904.0854OpenAlexW2122825463MaRDI QIDQ2430985

Christophe Ritzenthaler, Christophe Arène, Michael Naehrig, Tanja Lange

Publication date: 8 April 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.0854

zbMATH Keywords

Weierstrass formpairingsEdwards curvesMiller functionsdoubling and addition formulas.

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

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Identity-based undetachable digital signature for mobile agents in electronic commerce ⋮ Formal Proof of the Group Law for Edwards Elliptic Curves ⋮ Further refinements of Miller's algorithm on Edwards curves ⋮ On the near prime-order MNT curves ⋮ Pairing Computation on Edwards Curves with High-Degree Twists ⋮ Twisted Hessian Curves ⋮ Improved Sieving on Algebraic Curves ⋮ On Near Prime-Order Elliptic Curves with Small Embedding Degrees ⋮ A complete set of addition laws for incomplete Edwards curves ⋮ Unnamed Item ⋮ Parallelizing pairings on Hessian elliptic curves ⋮ The pairing computation on Edwards curves ⋮ An optimal Tate pairing computation using Jacobi quartic elliptic curves ⋮ Efficient Self-pairing on Ordinary Elliptic Curves ⋮ Elliptic curves in Huff’s model ⋮ Huff’s Model for Elliptic Curves ⋮ An Analysis of Affine Coordinates for Pairing Computation ⋮ A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties ⋮ Deterministic Encoding into Twisted Edwards Curves ⋮ A short-list of pairing-friendly curves resistant to special TNFS at the 128-bit security level ⋮ Efficient Pairing Computation on Ordinary Elliptic Curves of Embedding Degree 1 and 2

Uses Software

• SageMath
• EFD

Cites Work

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