On Constructing Parameterized Families of Pairing-Friendly Elliptic Curves with $$\rho =1$$

DOI10.1007/978-3-319-54705-3_25zbMath1404.94123OpenAlexW2592899897MaRDI QIDQ2980869

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Publication date: 5 May 2017

Published in: Information Security and Cryptology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-54705-3_25

zbMATH Keywords

elliptic curvescyclotomic polynomialspairing based cryptographyparameterized families

Mathematics Subject Classification ID

Cryptography (94A60) Elliptic curves (14H52) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Uses Software

• ECPP

Cites Work

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• Technical history of discrete logarithms in small characteristic finite fields. The road from subexponential to quasi-polynomial complexity
• The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm
• A taxonomy of pairing-friendly elliptic curves
• Ordinary Abelian varieties having small embedding degree
• Breaking ‘128-bit Secure’ Supersingular Binary Curves
• Elliptic Curves and Primality Proving
• Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
• 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
• Breaking Pairing-Based Cryptosystems Using η T Pairing over GF(397)
• On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves

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