Revisiting the Complex Multiplication Method for the Construction of Elliptic Curves

DOI10.1007/978-3-319-18275-9_12zbMath1368.11135OpenAlexW2275110487MaRDI QIDQ2790434

Elisavet Konstantinou, Aristides I. Kontogeorgis

Publication date: 4 March 2016

Published in: Computation, Cryptography, and Network Security (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-18275-9_12

zbMATH Keywords

complex multiplicationelliptic curve cryptographyShimura reciprocitycomputational class field theory

Mathematics Subject Classification ID

Cryptography (94A60) Complex multiplication and moduli of abelian varieties (11G15) Algebraic number theory computations (11Y40) Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Uses Software

• Magma

Cites Work

• Ramanujan's class invariants and their use in elliptic curve cryptography
• The Magma algebra system. I: The user language
• Writing representations over minimal fields
• Constructing class invariants
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