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Solving underdefined systems of multivariate quadratic equations
 Proceedings of Public Key Cryptography 2002, LNCS 2274
, 2002
"... Abstract. The security of several recent digital signature schemes is based on the difficulty of solving large systems of quadratic multivariate polynomial equations over a finite field F. This problem, sometimes called MQ, is known to be NPhard. When the number m of equations is equal to the numbe ..."
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Cited by 15 (0 self)
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schemes Flash and Sflash submitted to Nessie call for primitives or the UOV scheme published at Eurocrypt 1999. Little is known about the security of such underdefined systems. In this paper, three new and different methods are presented for solving underdefined multivariate systems of quadratic equations
Algorithms to solve massively underdefined systems of multivariate quadratic equations
"... Abstract. It is well known that the problem to solve a set of randomly chosen multivariate quadratic equations over a finite field is NPhard. However, when the number of variables is much larger than the number of equations, it is not necessarily difficult to solve equations. In fact, when n ≥ m(m ..."
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Abstract. It is well known that the problem to solve a set of randomly chosen multivariate quadratic equations over a finite field is NPhard. However, when the number of variables is much larger than the number of equations, it is not necessarily difficult to solve equations. In fact, when n ≥ m
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 403 (48 self)
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This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPT’2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 182 (20 self)
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The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms
Sparse Reconstruction by Separable Approximation
, 2007
"... Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing ..."
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Cited by 364 (37 self)
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Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing
Algorithms
"... to solve massively underdefined systems of multivariate quadratic equations ..."
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to solve massively underdefined systems of multivariate quadratic equations
Algebraic Attacks on Stream Ciphers with Linear Feedback
, 2003
"... A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC'0 ..."
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Cited by 261 (21 self)
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A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC
Multivariate Quadratic Polynomials
, 2005
"... Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door ..."
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Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door
Asymptotic Acceleration of Solving Multivariate Polynomial Systems of Equations
"... We propose new Las Vegas randomized algorithms for the solution of a multivariate generic or sparse polynomial system of equations. The algorithms use ¢¡¤£¦¥¤§©¨������������� � arithmetic operations to approximate all real roots of the system as well as all roots lying in a � fixeddimensional box ..."
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Cited by 22 (12 self)
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We propose new Las Vegas randomized algorithms for the solution of a multivariate generic or sparse polynomial system of equations. The algorithms use ¢¡¤£¦¥¤§©¨������������� � arithmetic operations to approximate all real roots of the system as well as all roots lying in a � fixeddimensional box
On building hash functions from multivariate quadratic equations
 of Lecture Notes in Computer Science
, 2007
"... Abstract. Recent advances in hash functions cryptanalysis provide a strong impetus to explore new designs. This paper describes a new hash function mqhash that depends for its security on the difficulty of solving randomly drawn systems of multivariate equations over a finite field. While provably ..."
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Cited by 8 (1 self)
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Abstract. Recent advances in hash functions cryptanalysis provide a strong impetus to explore new designs. This paper describes a new hash function mqhash that depends for its security on the difficulty of solving randomly drawn systems of multivariate equations over a finite field. While provably
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