Fast parallel absolute irreducibility testing
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Theoretical Computer Science - Algebraic and numerical algorithm
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Journal of Symbolic Computation
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Information and Computation
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
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Let f(X,Y)@?Z[X,Y] be an irreducible polynomial over Q. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of f, or more precisely, of f modulo some prime integer p. The same idea of choosing a p satisfying some prescribed properties together with LLL is used to provide a new strategy for absolute factorization of f(X,Y). We present our approach in the bivariate case but the techniques extend to the multivariate case. Maple computations show that it is efficient and promising as we are able to construct the algebraic extension containing one absolute factor of a polynomial of degree up to 400.