Obstacles to the torsion-subgroup attack on the decision Diffie-Hellman Problem

DOI10.1090/S0025-5718-04-01637-0zbMath1064.94013OpenAlexW2066290790MaRDI QIDQ4813622

Neal Koblitz, Alfred J. Menezes

Publication date: 13 August 2004

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01637-0

zbMATH Keywords

elliptic curvepolynomial time algorithmdecision Diffie-Hellman problem

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Cites Work

• Modular curves and the Eisenstein ideal
• Points of small height on elliptic curves
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Separating decision Diffie-Hellman from computational Diffie-Hellman in cryptographic groups
• Bounds for the torsion of elliptic curves over number fields
• Analysis of the Xedni calculus attack
• Counting points of small height on elliptic curves
• A public key cryptosystem and a signature scheme based on discrete logarithms
• Universal Bounds on the Torsion of Elliptic Curves
• Sur le nombre de points de torsion rationnels sur une courbe elliptique
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