On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves

DOI10.1090/S0025-5718-2011-02543-3zbMath1329.11063MaRDI QIDQ5389447

Florian Luca, Jorge Jiménez-Urroz, Igor E. Shparlinski

Publication date: 26 April 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

elliptic curvespairing based cryptographyembedding degreeMNT curves

Mathematics Subject Classification ID

Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50) Elliptic curves over local fields (11G07)

Related Items (6)

On the near prime-order MNT curves ⋮ On consecutive integers divisible by the number of their divisors ⋮ Heuristics on pairing-friendly abelian varieties ⋮ Elliptic curves withj= 0,1728 and low embedding degree ⋮ Heuristics of the Cocks-Pinch method ⋮ On Constructing Parameterized Families of Pairing-Friendly Elliptic Curves with $$\rho =1$$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Das asymptotische Verhalten von Summen über multiplikative Funktionen
• Elliptic curves with low embedding degree
• On the embedding degree of reductions of an elliptic curve
• The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm
• MOV attack in various subgroups on elliptic curves
• Short signatures from the Weil pairing
• Separating decision Diffie-Hellman from computational Diffie-Hellman in cryptographic groups
• A taxonomy of pairing-friendly elliptic curves
• The distribution of integers with a divisor in a given interval
• A note on Mertens' formula for arithmetic progressions
• On finite fields for pairing based cryptography
• Computing Hilbert class polynomials with the Chinese remainder theorem
• A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
• On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6
• Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
• Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
• Reducing elliptic curve logarithms to logarithms in a finite field
• Identity-Based Encryption from the Weil Pairing
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Advances in Elliptic Curve Cryptography

This page was built for publication: On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves