Choosing the correct elliptic curve in the CM method
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Publication:3584790
DOI10.1090/S0025-5718-09-02266-2zbMath1213.11127OpenAlexW2048406250MaRDI QIDQ3584790
Publication date: 30 August 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-09-02266-2
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Curves over finite and local fields (11G20) Complex multiplication and moduli of abelian varieties (11G15) Elliptic curves over local fields (11G07)
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From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture ⋮ Efficient hash maps to \(\mathbb{G}_2\) on BLS curves ⋮ Finding elliptic curves with a subgroup of prescribed size ⋮ Isolated elliptic curves and the MOV attack ⋮ Constructing pairing-friendly hyperelliptic curves using Weil restriction ⋮ Accelerating the CM method ⋮ Ramanujan's class invariants and their use in elliptic curve cryptography ⋮ Optimised Versions of the Ate and Twisted Ate Pairings ⋮ Computing Hilbert class polynomials with the Chinese remainder theorem ⋮ Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings ⋮ Point counting on reductions of CM elliptic curves ⋮ On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average ⋮ Generalized class polynomials
Uses Software
Cites Work
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