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COCOA
2011
Springer
9 years 3 months ago
The Complexity of Testing Monomials in Multivariate Polynomials
The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economi...
Zhixiang Chen, Bin Fu
EUROCRYPT
2011
Springer
9 years 7 months ago
Homomorphic Signatures for Polynomial Functions
We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an...
Dan Boneh, David Mandell Freeman
JSC
2010
103views more  JSC 2010»
10 years 2 months ago
Bounds on absolute positiveness of multivariate polynomials
We propose a general framework for obtaining bounds on absolute positiveness of multivariate polynomials. We show that a known bound by Hong is a nearly optimal bound within this ...
Prashant Batra, Vikram Sharma
ECCC
1998
105views more  ECCC 1998»
10 years 3 months ago
Pseudorandom generators without the XOR Lemma
Impagliazzo and Wigderson IW97] have recently shown that if there exists a decision problem solvable in time 2O(n) and having circuit complexity 2 (n) (for all but nitely many n) ...
Madhu Sudan, Luca Trevisan, Salil P. Vadhan
CCCG
2008
10 years 5 months ago
Polynomial irreducibility testing through Minkowski summand computation
In this paper, we address the problem of deciding absolute irreducibility of multivariate polynomials. Our work has been motivated by a recent work due to Gao et. al. [1, 2, 3] wh...
Deepanjan Kesh, Shashank K. Mehta
STOC
1993
ACM
121views Algorithms» more  STOC 1993»
10 years 8 months ago
On the generation of multivariate polynomials which are hard to factor
In this paper we consider the di culty of factoring multivariate polynomials F(x y z :::) modulo n. We consider in particular the case in which F is a product of two randomly chose...
Adi Shamir
STACS
2009
Springer
10 years 8 months ago
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials ...
Mahdi Cheraghchi, Amin Shokrollahi
FSE
2003
Springer
152views Cryptology» more  FSE 2003»
10 years 9 months ago
Block Ciphers and Systems of Quadratic Equations
Abstract. In this paper we compare systems of multivariate polynomials, which completely define the block ciphers Khazad, Misty1, Kasumi, Camellia, Rijndael and Serpent in the vie...
Alex Biryukov, Christophe De Cannière
ISSAC
2004
Springer
118views Mathematics» more  ISSAC 2004»
10 years 9 months ago
The approximate GCD of inexact polynomials
This paper presents an algorithm and its implementation for computing the approximate GCD (greatest common divisor) of multivariate polynomials whose coefficients may be inexact. ...
Zhonggang Zeng, Barry H. Dayton
ISSAC
2004
Springer
135views Mathematics» more  ISSAC 2004»
10 years 9 months ago
The truncated fourier transform and applications
In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminati...
Joris van der Hoeven
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