Equivalences between elliptic curves and real quadratic congruence function fields

DOI10.5802/jtnb.191zbMath0899.11054OpenAlexW2062451877MaRDI QIDQ1382095

Andreas Stein

Publication date: 25 March 1998

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1997__9_1_75_0

zbMATH Keywords

elliptic curvesdiscrete logarithm problemDiffie-Hellman key exchangereal quadratic congruence function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52)

Related Items (6)

Smooth ideals in hyperelliptic function fields ⋮ Key-exchange in real quadratic congruence function fields ⋮ Class group frequencies of real quadratic function fields: The degree 4 case ⋮ Cryptographic aspects of real hyperelliptic curves ⋮ The infrastructure of a global field of arbitrary unit rank ⋮ Real and imaginary quadratic representations of hyperelliptic function fields

Cites Work

• Algebraic function fields and codes
• A key-exchange protocol using real quadratic fields
• Key-exchange in real quadratic congruence function fields
• Lectures on the theory of algebraic functions of one variable
• New directions in cryptography
• Multiples of Points on Elliptic Curves and Continued Fractions
• Computing discrete logarithms in real quadratic congruence function fields of large genus
• On the Parallel Generation of the Residues for the Continued Fraction Factoring Algorithm
• On Gauss's Class Number Problems
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