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» On solving sparse algebraic equations over finite fields
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DCC
2008
IEEE
14 years 9 months ago
On solving sparse algebraic equations over finite fields
A system of algebraic equations over a finite field is called sparse if each equation depends on a small number of variables. Finding efficiently solutions to the system is an unde...
Igor Semaev
MOC
2002
70views more  MOC 2002»
13 years 9 months ago
Solving norm equations in relative number fields using S-units
Abstract. In this paper, we are interested in solving the so-called norm equation NL/K(x) = a, where L/K is a given arbitrary extension of number fields and a a given algebraic num...
Denis Simon
ICISC
2000
126views Cryptology» more  ICISC 2000»
13 years 10 months ago
Cryptographic Applications of Sparse Polynomials over Finite Rings
Abstract. This paper gives new examples that exploit the idea of using sparse polynomials with restricted coefficients over a finite ring for designing fast, reliable cryptosystems...
William D. Banks, Daniel Lieman, Igor Shparlinski,...
MOC
1998
97views more  MOC 1998»
13 years 9 months ago
Euclid's algorithm and the Lanczos method over finite fields
Abstract. This paper shows that there is a close relationship between the Euclidean algorithm for polynomials and the Lanczos method for solving sparse linear systems, especially w...
Jeremy Teitelbaum
ALGORITHMICA
1999
123views more  ALGORITHMICA 1999»
13 years 9 months ago
Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields
We describe a coarse-grain parallel software system for the homogeneous solution of linear systems. Our solutions are symbolic, i.e., exact rather than numerical approximations. O...
Erich Kaltofen, A. Lobo