On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

DOI10.1112/S1461157015000017zbMath1400.11164arXiv1404.0399OpenAlexW2162354153MaRDI QIDQ5252488

Andrew V. Sutherland, Igor E. Shparlinski

Publication date: 2 June 2015

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

Full work available at URL: https://arxiv.org/abs/1404.0399

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Estimates on character sums (11L40) Elliptic curves over local fields (11G07)

Related Items (4)

From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Computing cardinalities of -curve reductions over finite fields ⋮ Cycles in the Supersingular ℓ-Isogeny Graph and Corresponding Endomorphisms

Cites Work

• On the distribution of Atkin and Elkies primes
• An explicit height bound for the classical modular polynomial
• Counting points on elliptic curves over finite fields
• Counting points on hyperelliptic curves in average polynomial time
• Fast multiplication of large numbers
• Galois properties of points of finite order of elliptic curves
• Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
• Mathematics of Public Key Cryptography
• Pseudoprime Reductions of Elliptic Curves
• Almost prime values of the order of elliptic curves over finite fields
• Faster Integer Multiplication
• Choosing the correct elliptic curve in the CM method
• Frobenius fields for elliptic curves
• The Arithmetic of Elliptic Curves
• Probabilistic Algorithms in Finite Fields
• Identifying supersingular elliptic curves
• Modular polynomials via isogeny volcanoes

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