A framework for deterministic primality proving using elliptic curves with complex multiplication

DOI10.1090/mcom/3001zbMath1345.11088arXiv1404.0107OpenAlexW1644390545MaRDI QIDQ2792372

Alexander Abatzoglou, Angela Wong, Andrew V. Sutherland, Alice Silverberg

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1404.0107

zbMATH Keywords

elliptic curvesclass numbercomplex multiplicationprimality

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Primality (11Y11)

Related Items (2)

An elliptic curve analogue to the Fermat numbers ⋮ Some remarks on primality proving and elliptic curves

Uses Software

• SageMath
• ECPP
• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Even faster integer multiplication
• Deterministic primality tests based on tori and elliptic curves
• Elliptic curve primality tests for Fermat and related primes
• Point counting on reductions of CM elliptic curves
• Primality testing through algebraic groups
• Probabilistic algorithm for testing primality
• Riemann's hypothesis and tests for primality
• Counting points on \(\text{CM}\) elliptic curves
• Primality testing with Gaussian periods
• An elliptic curve test for Mersenne primes
• PRIMES is in P
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• Fast multiplication of large numbers
• Deterministic elliptic curve primality proving for a special sequence of numbers
• Primality tests for 2^{𝑝}±2^{(𝑝+1)/2}+1 using elliptic curves
• Elliptic Curves and Primality Proving
• Primality testing using elliptic curves
• Implementing the asymptotically fast version of the elliptic curve primality proving algorithm
• Faster Integer Multiplication
• The Arithmetic of Elliptic Curves
• Very Short Primality Proofs
• Primality Tests Using Algebraic Groups

This page was built for publication: A framework for deterministic primality proving using elliptic curves with complex multiplication