Identifying supersingular elliptic curves

DOI10.1112/S1461157012001106zbMath1307.11072arXiv1107.1140OpenAlexW2030002181MaRDI QIDQ5169642

Andrew V. Sutherland

Publication date: 11 July 2014

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

Full work available at URL: https://arxiv.org/abs/1107.1140

zbMATH Keywords

complexityisogenysupersingular elliptic curve

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Curves over finite and local fields (11G20) Elliptic curves over local fields (11G07)

Related Items (13)

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph ⋮ The Supersingular Isogeny Problem in Genus 2 and Beyond ⋮ On division polynomial PIT and supersingularity ⋮ Improved supersingularity testing of elliptic curves using Legendre form ⋮ On the hardness of the computational ring-LWR problem and its applications ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ On the distribution of Atkin and Elkies primes ⋮ Computing cardinalities of -curve reductions over finite fields ⋮ CSIDH: an efficient post-quantum commutative group action ⋮ Post-Quantum Constant-Round Group Key Exchange from Static Assumptions ⋮ Efficient Algorithms for Supersingular Isogeny Diffie-Hellman ⋮ Improved supersingularity testing of elliptic curves ⋮ On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

Uses Software

• Magma

Cites Work

• Unnamed Item
• Riemann's hypothesis and tests for primality
• Counting points on elliptic curves over finite fields
• Fast multiplication of large numbers
• Structure computation and discrete logarithms in finite abelian $p$-groups
• Computing Hilbert class polynomials with the Chinese remainder theorem
• A Note on Elliptic Curves Over Finite Fields
• Reducing elliptic curve logarithms to logarithms in a finite field
• Ramanujan graphs and Hecke operators
• Families of curves and weight distributions of codes

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