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Solving Multivariate Polynomial Systems and an Invariant from Commutative Algebra
post-quantum cryptography multivariate cryptography Groebner basis
2017/6/22
The security of several post-quantum cryptosystems is based on the assumption that solving a system of multivariate (quadratic) polynomial equations p1=⋯=pm=0p1=⋯=pm=0 over a finite field ...
SBIM(Q) - a Multivariate Polynomial Trapdoor Function over the Field of Rational Numbers
trap-door function bi-permutations quasigroup transformations
2016/1/7
In this paper we define a trapdoor function called SBIM(Q) by using multivariate polynomials over the field of rational numbers Q. The public key consists of 2n multivariate polynomials with 3n variab...
Computation of the Smith Form for Multivariate Polynomial Matrices Using Maple
Smith Form Unimodular Equivalence Quillen-Suslin Theorem Maple
2013/1/30
In this paper we show how the transformations associated with the reduction to the Smith form of some classes of multivariate polynomial matrices are computed. Using a Maple implementation of a constr...
Multivariate polynomial interpolation and sampling in Paley-Wiener spaces
Multivariate polynomial interpolation sampling Paley-Wiener spaces
2010/12/3
In this paper, an equivalence between existence of particular exponential Riesz bases
for multivariate bandlimited functions and existence of certain polynomial interpolants for these bandlimited fun...
Short Signatures, Provable Security, Generic Attacks and Computational Security of Multivariate Polynomial Schemes such as HFE, Quartz and Sflash
Generic signature schemes short signatures provable security
2009/3/27
The object of this paper is the concrete security of recent
multivariate signature schemes. A major challenge is to reconcile some
”tricky” ad-hoc constructions that allow to make short signatures, ...
A New Efficient Algorithm for Solving Systems of Multivariate Polynomial Equations
multivariate cryptography cryptography algebraic attack
2009/3/4
The security of many recently proposed cryptosystems is based on the difficulty of solving
large systems of quadratic multivariate polynomial equations. The classical algorithm for solving such
a sy...
Zhuang-Zi: A New Algorithm for Solving Multivariate Polynomial Equations over a Finite Field
multivariate polynomials Hidden Field Equation Berlekamp algorithm
2008/10/24
We present the Zhuang-Zi algorithm, a new method for solv-
ing multivariate polynomial equations over a ¯nite ¯eld. We describe the
algorithm and present examples, some of which cannot be...
