We study the problem of finding solutions to linear equations modulo an unknown divisor p of a known composite integer N. An important application of this problem is factorization of N with given bits of p. It is well-known that this problem is polynomial-time solvable if at most half of the bits of p are unknown and if the unknown bits are located in one consecutive block. We introduce an heuristic algorithm that extends factoring with known bits to an arbitrary number n of blocks. Surprisingly, we are able to show that ln (2)∈≈∈70% of the bits are sufficient for any n in order to find the factorization. The algorithm's running time is however exponential in the parameter n. Thus, our algorithm is polynomial time only for blocks. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Herrmann, M., & May, A. (2008). Solving linear equations modulo divisors: On factoring given any bits. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5350 LNCS, pp. 406–424). https://doi.org/10.1007/978-3-540-89255-7_25
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