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EUROCRYPT
2000
Springer
13 years 8 months ago
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard ove...
Nicolas Courtois, Alexander Klimov, Jacques Patari...
FSE
2006
Springer
109views Cryptology» more  FSE 2006»
13 years 8 months ago
Computing the Algebraic Immunity Efficiently
The purpose of algebraic attacks on stream and block ciphers is to recover the secret key by solving an overdefined system of multivariate algebraic equations. They become very eff...
Frédéric Didier, Jean-Pierre Tillich
IMA
2009
Springer
111views Cryptology» more  IMA 2009»
13 years 11 months ago
Geometric Ideas for Cryptographic Equation Solving in Even Characteristic
Abstract. The GeometricXL algorithm is a geometrically invariant version of the XL algorithm that uses polynomials of a much smaller degree than either a standard Groebner basis al...
Sean Murphy, Maura B. Paterson
JC
2000
138views more  JC 2000»
13 years 4 months ago
Multivariate Polynomials, Duality, and Structured Matrices
We rst review thebasic properties of the well knownclasses of Toeplitz, Hankel, Vandermonde, and other related structured matrices and reexamine their correlation to operations wi...
Bernard Mourrain, Victor Y. Pan