10 search results - page 2 / 2 » On Quadratic Polynomials for the Number Field Sieve |
EUROCRYPT
2000
Springer
13 years 9 months ago
2000
Springer
The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard ove...
EUROCRYPT
2006
Springer
13 years 9 months ago
2006
Springer
Abstract. We introduce VSH, very smooth hash, a new S-bit hash function that is provably collision-resistant assuming the hardness of finding nontrivial modular square roots of ver...
FOCS
1998
IEEE
13 years 9 months ago
1998
IEEE
The properties of any system of k simultaneous equations in n variables over GF(q), are studied, with a particular emphasis on unsatisfiable systems. A general formula for the num...
DM
2008
13 years 5 months ago
2008
Let {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(x) (mod pn), where p is an odd prime and x is a rational p-integer. Such congruences are...
CORR
2010
Springer
13 years 5 months ago
2010
Springer
In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which ...