Last Fall Degree, HFE, and Weil Descent Attacks on ECDLP

DOI10.1007/978-3-662-47989-6_28zbMath1375.94135OpenAlexW2266246005MaRDI QIDQ3457129

Sze Ling Yeo, Michiel Kosters, Ming-Deh A. Huang

Publication date: 10 December 2015

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-47989-6_28

zbMATH Keywords

solving equationsfirst fall degreeWeil descentelliptic curve discrete logarithm problem (ECDLP)last fall degreeHidden Field Equation (HFE) public key systems

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16)

Related Items (12)

Stronger bounds on the cost of computing Gröbner bases for HFE systems ⋮ On index calculus algorithms for subfield curves ⋮ On the security of biquadratic \(C^\ast\) public-key cryptosystems and its generalizations ⋮ Solving degree, last fall degree, and related invariants ⋮ Quasi-subfield polynomials and the elliptic curve discrete logarithm problem ⋮ On the last fall degree of zero-dimensional Weil descent systems ⋮ On product decomposition ⋮ Worst-case subexponential attacks on PRGs of constant degree or constant locality ⋮ Recent progress on the elliptic curve discrete logarithm problem ⋮ On the first fall degree of summation polynomials ⋮ Complexity bounds on Semaev's naive index calculus method for ECDLP ⋮ On the last fall degree of Weil descent polynomial systems

Cites Work

• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Constructive and destructive facets of Weil descent on elliptic curves
• Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms
• On the discrete logarithm problem in elliptic curves
• Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
• On Polynomial Systems Arising from a Weil Descent
• Inverting HFE Systems Is Quasi-Polynomial for All Fields
• Inverting HFE Is Quasipolynomial
• Factoring polynomials over finite fields: A survey

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