Boolean ring cryptographic equation solving

DOI10.1007/978-3-030-81652-0_10zbMath1485.94110OpenAlexW3184415224MaRDI QIDQ832346

Sean Murphy, Christine Swart, Maura B. Paterson

Publication date: 25 March 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-81652-0_10

zbMATH Keywords

Gröbner basisBoolean ring\texttt{LPN} problem\texttt{MQ} problem\texttt{XL} algorithm

Mathematics Subject Classification ID

Cryptography (94A60) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Uses Software

• MutantXL

Cites Work

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• Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic
• Complexity of solving algebraic equations
• Cryptanalysis of the Matsumoto and Imai public key scheme of EUROCRYPT '98
• Analysing and exploiting the Mantin biases in RC4
• Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms
• A Polynomial-Time Key-Recovery Attack on MQQ Cryptosystems
• Practical Key-Recovery for All Possible Parameters of SFLASH
• A geometric view of cryptographic equation solving
• Algebraic Cryptanalysis of 58-Round SHA-1
• Cryptanalysis of MinRank
• Multivariate Public Key Cryptography
• Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography
• Geometric Ideas for Cryptographic Equation Solving in Even Characteristic
• Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
• Advances in Cryptology - CRYPTO 2003
• All in the XL Family: Theory and Practice
• The XL-Algorithm and a Conjecture from Commutative Algebra
• Comparison Between XL and Gröbner Basis Algorithms
• Noise-tolerant learning, the parity problem, and the statistical query model

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