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Systems of set constraints are a natural formalism for many problems in program analysis. Set constraints are also a generalization of tree automata. We present an algorithm for solving systems of set...
An Excursion from Enumerative Geometry to Solving Systems of Polynomial Equations with Macaulay 2
To solve the polynomial equations mathematics geometry cross theory
2014/12/29
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics ha...
An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)
public-key cryptography
2014/3/6
We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using Gentry's technique. Initially, a private-key cryptosystem is built over $\mathbb{Z}_n$ ($n$ being an ...
An efficient FHE based on the hardness of solving systems of non-linear multivariate equations
FHE homomorphic cryptosystem
2014/3/13
We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using the Gentry's technique. The security relies on the difficulty of solving systems of non-linear equati...
Solving Systems of Transcendental Equations Involving the Heun Functions
Root-Finding Algorithm M¨1ller Algorithm TwoDimensional M¨1ller Algorithm Regge-Wheeler Equation Quasinormal Modes Teukolsky Master Equation
2013/1/30
The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functi...
Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations
amplitude faster quantum algorithm equations
2010/11/8
We present two new quantum algorithms. Our first algorithm is a generalization of amplitude amplification to the case when parts of the quantum algorithm that is being amplified stop at different time...
Reproducing kernel method for solving systems of linear equations
Exact solution system of linear equations
2010/9/17
A new method for finding the exact solutions of systems of linear equations is presented. Advantage of this method is the simplicity of the procedure. There are no additional constraint conditions. Th...
Obtaining and solving systems of equations in key variables only for the small variants of Obtaining and solving systems of equations in key variables only for the small variants of
Algebraic attack meet-in-the-middle attack AES
2009/6/9
This work is devoted to attacking the small scale variants of the
Advanced Encryption Standard (AES) via systems that contain only
the initial key variables. To this end, we introduce a system of eq...
Solving Systems of Differential Equations of Addition
Differential Cryptanalysis Addition Optimal bound Asymptotic Complexity
2009/4/1
The difficulty of solving an arbitrary system of such equations { named differential equations of addition (DEA) { is an important consideration in the evaluation of the security of many ciphers again...
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...
A new technique for solving systems of nonlinear equations
Systems of non-linear equations Gauss-Seidel method
2010/9/14
The aim of this paper is to construct a new method for solving systems of nonlinear equations. The new method is based on the idea of Gauss-Seidel method, which is a known method for solving systems o...