Hi,
In order to solve a system of 3 polynomials of order 3
with 3 variables x1, x2 and x3 in the set Z_{2^32} and
coeficients also in Z_{2^32} I used the Mathematica
5.1 function Reduce[...,{x1,x2,x3},Modulus->2^32]. It
is giving the solutions but it is not very fast. I
wanted to programe a procedure in C in order to get
more speed in the computation.I was trying to figure out what algorithms are used in the "Reduce" function of Mathematica (reading Wolfram web pages) but I couldn't find any specific information for the algorithms they are using for solving multivariate polynomials modulo 2^32. I found several papers that are dealing with solving univariate or multivariate polynomials in finite fields such as: 1. Lauder : http://www.maths.ox.ac.uk/~lauder/papers/LauderManyVarSept16.pdf 2. van de Woestijne : http://www.math.leidenuniv.nl/~cvdwoest/maths/ober.pdf and http://www.math.leidenuniv.nl/~cvdwoest/maths/issac2005.pdf 3. Barreto and Voloch: http://www.ma.utexas.edu/users/voloch/Preprints/roots.pdf 4. Ding, Gower and Schmidt: http://eprint.iacr.org/2006/038.pdf but the algorithms there are for soving polynomials over finite fields GF(p) or GF(p^n) which is different than just solving polynomials (univariate or multivariate) modulo 2^32. I will appreciate any hint or coment. Regards, Danilo Gligoroski --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]
