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MRHS Solver Based on Linear Algebra and Exhaustive Search
Algebraic cryptanalysis MRHS LowMC
2018/1/31
We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher's resis...
A Variant of Coppersmith's Algorithm with Improved Complexity and Efficient Exhaustive Search
Coppersmith's Method LLL
2014/3/11
Coppersmith described at Eurocrypt 96 a polynomial-time algorithm for finding small roots of univariate modular equations, based on lattice reduction. In this paper we describe the first improvement o...
Fast Exhaustive Search for Quadratic Systems in $\mathbb{F}_2$ on FPGAs --- Extended Version
multivariate quadratic polynomials solving systems of equations
2014/3/11
In 2010, Bouillaguet et al. proposed an efficient solver for polynomial systems over $\mathbb{F}_2$ that trades memory for speed. As a result, 48 quadratic equations in 48 variables can be solved on a...
Fast Exhaustive Search for Polynomial Systems in $F_2$
implementation multivariate polynomials system-solving parallelization Graphic Processing Units (GPUs)
2010/7/13
We analyze how fast we can solve general systems of multivariate equations of various low degrees over \GF{2}; this is a well known hard problem which is important both in itself and as part of many t...
Understanding Phase Shifting Equivalent Keys and Exhaustive Search
Phase Shifting Equivalent Keys Exhaustive Search specific ciphers
2009/6/3
Recent articles [6, 3, 5, 7] introduce the concept of phase shifting
equivalent keys in stream ciphers, and exploit this concept in order to
mount attacks on some speci c ciphers. The idea behind ph...