Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

DOI10.1112/S1461157000000723zbMath1055.94020MaRDI QIDQ4827599

Markus Maurer, Alfred J. Menezes, Edlyn Teske

Publication date: 18 November 2004

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

Full work available at URL: http://www.lms.ac.uk/jcm/5/lms2001-019/

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (6)

Fault-based attack on Montgomery's ladder algorithm ⋮ Algebraic curves and cryptography ⋮ Cryptographic implications of Hess' generalized GHS attack ⋮ Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem ⋮ Extractors for binary elliptic curves ⋮ Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields

Cites Work

• Discrete logarithms in \(\mathrm{GF}(p)\)
• Hyperelliptic cryptosystems
• Parallel collision search with cryptanalytic applications
• KANT V4
• Constructive and destructive facets of Weil descent on elliptic curves
• A general framework for subexponential discrete logarithm algorithms
• Computing in the Jacobian of a Hyperelliptic Curve
• An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.)
• Monte Carlo Methods for Index Computation (mod p)
• Real and imaginary quadratic representations of hyperelliptic function fields
• Constructing Isogenies between Elliptic Curves Over Finite Fields
• A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
• Reducing elliptic curve logarithms to logarithms in a finite field
• Improving the parallelized Pollard lambda search on anomalous binary curves

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