The XL-Algorithm and a Conjecture from Commutative Algebra

DOI10.1007/978-3-540-30539-2_23zbMath1094.94029OpenAlexW94701028MaRDI QIDQ5465821

Claus Diem

Publication date: 12 August 2005

Published in: Advances in Cryptology - ASIACRYPT 2004 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-30539-2_23

zbMATH Keywords

algebraic attacksCryptanalysisextended linearizationoverdetermined systems of polynomial equationsFröberg's Conjecture

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Cryptography (94A60) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Related Items (14)

SoK: how (not) to design and implement post-quantum cryptography ⋮ Boolean ring cryptographic equation solving ⋮ An algorithm for solving over-determined multivariate quadratic systems over finite fields ⋮ From 5-Pass $$\mathcal {MQ}$$-Based Identification to $$\mathcal {MQ}$$-Based Signatures ⋮ FUTURE: a lightweight block cipher using an optimal diffusion matrix ⋮ On the relation between the MXL family of algorithms and Gröbner basis algorithms ⋮ Worst-case subexponential attacks on PRGs of constant degree or constant locality ⋮ Probabilistic analysis on Macaulay matrices over finite fields and complexity of constructing Gröbner bases ⋮ Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$ ⋮ Analysis of Multivariate Hash Functions ⋮ On the termination of the general XL algorithm and ordinary multinomials ⋮ Loiss: A Byte-Oriented Stream Cipher ⋮ QUAD: A Practical Stream Cipher with Provable Security ⋮ Kipnis-Shamir Attack on HFE Revisited

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