On Cycles of Pairing-Friendly Elliptic Curves

DOI10.1137/18M1173708zbMath1411.14035arXiv1803.02067OpenAlexW2963284730MaRDI QIDQ5742695

Matthew Weidner, Alessandro Chiesa, Lynn Chua

Publication date: 8 May 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02067

zbMATH Keywords

elliptic curvescryptographyWeil pairing

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Elliptic curves (14H52) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (5)

Plumo: an ultralight blockchain client ⋮ A survey of elliptic curves for proof systems ⋮ Revisiting cycles of pairing-friendly elliptic curves ⋮ \textsc{Fractal}: post-quantum and transparent recursive proofs from holography ⋮ A short-list of pairing-friendly curves resistant to special TNFS at the 128-bit security level

Uses Software

• Magma
• SageMath
• zk-SNARK

Cites Work

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• Building curves with arbitrary small MOV degree over finite prime fields
• The discrete logarithm problem on elliptic curves of trace one
• The Magma algebra system. I: The user language
• A one round protocol for tripartite Diffie-Hellman
• A taxonomy of pairing-friendly elliptic curves
• Elliptic aliquot cycles of fixed length
• Elliptic curves suitable for pairing based cryptography
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Scalable Zero Knowledge via Cycles of Elliptic Curves
• Amicable pairs and aliquot cycles on average
• High-Speed High-Security Signatures
• On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6
• Twisted Edwards Curves
• The Arithmetic of Elliptic Curves
• A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
• Reducing elliptic curve logarithms to logarithms in a finite field
• Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝
• An asymptotic for the average number of amicable pairs for elliptic curves
• Identity-Based Encryption from the Weil Pairing
• Amicable Pairs and Aliquot Cycles for Elliptic Curves
• Accelerating the CM method
• Faster Addition and Doubling on Elliptic Curves
• A normal form for elliptic curves
• Pairing-Friendly Elliptic Curves of Prime Order
• Algorithmic Number Theory

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