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A method of solving multivariate integer polynomial equations

Nguyen Trung Thanh (Universität Düsseldorf)

Thursday  22 July 2010, 15.00, b-it  1.25 (cosec meeting room)

I would like to propose a method of solving $k$-variate integer polynomial equations of total degree $\delta$, based on lattice reduction techniques. This is an extension of the work of J. S. Coron at Eurocrypt 2004 and Santoso, Kunihiro, Kanayama and Ohta at Vietcrypt 2006. As a consequence, we can construct the algorithm for factoring an integer $N=p_1\ldots p_k$ in which $p_1,\ldots, p_k$ are the different primes has the same length bits with high bits known of each $p_i$. The algorithm runs in polynomial time in $(\log N)$.


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