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Solving Quadratic Equations with XL on Parallel Architectures - extended version
block Wiedemann sparse solver multivariate quadratic systems
2016/5/3
Solving a system of multivariate quadratic equations (MQ) is an NP-complete problem whose complexity estimates are relevant to many cryptographic scenarios. In some cases it is required in the best kn...
Unreval XL and its variants
Multivariate Cryptography Algebraic Cryptanalysis eXtended Linearization XL MutantXL Unbalanced Oil and Vinegar Signature Scheme
2010/11/26
Systems of non-linear multivariate equations are at the heart of many cryptographic algorithms, in particular in the public key setting. This paper investigates some algorithms to solve such systems. ...
Higher Order Correlation Attacks, XL Algorithm and Cryptanalysis of Toyocrypt
Algebraic cryptanalysis multivariate equations overdefined equations
2009/4/14
Many stream ciphers are built of a linear sequence generator
and a non-linear output function f. There is an abundant literature on
(fast) correlation attacks, that use linear approximations of f to...
Relation between XL algorithm and Gr¨obner Bases Algorithms
Algebraic attacks Gr¨obner bases algorithm F4 XL algorithm
2009/3/26
We clarify a relation between the XL algorithm and Gr¨obner
bases algorithms. The XL algorithm was proposed to be a more efficient
algorithm to solve a system of equations with a special assumptio w...