Abstract
In this paper we propose an algorithm of factoring any integer N which has k different prime factors with the same bit-length, when \((\frac{1}{k+2}+\frac{\epsilon}{k(k-1)})\log N\) high-order bits of each prime factor are given. For a fixed ε, the running time of our algorithm is heuristic polynomial in (logN). Our factoring algorithm is based on a new lattice-based algorithm of solving any k-variate polynomial equation over ℤ, which might be an independent interest.
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Santoso, B., Kunihiro, N., Kanayama, N., Ohta, K. (2006). Factorization of Square-Free Integers with High Bits Known. In: Nguyen, P.Q. (eds) Progress in Cryptology - VIETCRYPT 2006. VIETCRYPT 2006. Lecture Notes in Computer Science, vol 4341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11958239_8
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DOI: https://doi.org/10.1007/11958239_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68799-3
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