On the distribution of Atkin and Elkies primes

DOI10.1007/s10208-013-9181-9zbMath1312.11048arXiv1112.3390OpenAlexW3099013557MaRDI QIDQ404278

Igor E. Shparlinski, Andrew V. Sutherland

Publication date: 4 September 2014

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3390

zbMATH Keywords

elliptic curvecharacter sumAtkin primeElkies prime

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Estimates on character sums (11L40) Elliptic curves over local fields (11G07)

Related Items (5)

Finding elliptic curves with a subgroup of prescribed size ⋮ Computing cardinalities of -curve reductions over finite fields ⋮ Explicit isogenies in quadratic time in any characteristic ⋮ On the product of small Elkies primes ⋮ On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On quadratic fields generated by polynomials
• Factoring integers with elliptic curves
• Probabilistic algorithm for testing primality
• Elliptic curve implementation of zero-knowledge blobs
• PRIMES is in P
• Counting points on elliptic curves over finite fields
• Fast multiplication of large numbers
• Mathematics of Public Key Cryptography
• Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm
• Computing Hilbert class polynomials with the Chinese remainder theorem
• Proving primality in essentially quartic random time
• Fast algorithms for computing isogenies between elliptic curves
• The Arithmetic of Elliptic Curves
• Subtleties in the Distribution of the Numbers of Points on Elliptic Curves Over a Finite Prime Field
• Identifying supersingular elliptic curves
• On the product of small Elkies primes
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Modular polynomials via isogeny volcanoes

This page was built for publication: On the distribution of Atkin and Elkies primes