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CORR
1998
Springer
105views Education» more  CORR 1998»
13 years 5 months ago
Solving Degenerate Sparse Polynomial Systems Faster
Abstract. Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in...
J. Maurice Rojas
EUROCRYPT
2006
Springer
13 years 9 months ago
Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects
The Isomorphism of Polynomials (IP) [28], which is the main concern of this paper, originally corresponds to the problem of recovering the secret key of a C scheme [26]. Besides, t...
Jean-Charles Faugère, Ludovic Perret
CANS
2011
Springer
258views Cryptology» more  CANS 2011»
12 years 5 months ago
Fast Computation on Encrypted Polynomials and Applications
In this paper, we explore fast algorithms for computing on encrypted polynomials. More specifically, we describe efficient algorithms for computing the Discrete Fourier Transform,...
Payman Mohassel
JC
2000
138views more  JC 2000»
13 years 5 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
ASIACRYPT
2004
Springer
13 years 10 months ago
The XL-Algorithm and a Conjecture from Commutative Algebra
The “XL-algorithm” is a computational method to solve overdetermined systems of polynomial equations which is based on a generalization of the well-known method of linearizatio...
Claus Diem