On Factoring Arbitrary Integers with Known Bits

: We study the factoring with known bits problem, where we are given a composite integer N = p1p2 . . . pr and oracle access to the bits of the prime factors pi, i = 1, . . . , r. Our goal is to find the full factorization of N in polynomial time with a minimal number of calls to the oracle. We present a rigorous algorithm that efficiently factors N given (1 − 1 r Hr) log N bits, where Hr denotes the rth harmonic number.

• Type: Conference
• Year: 2007
• Where: GI
• Authors: Mathias Herrmann, Alexander May
• Keywords: Composite Integer, GI 2007, Oracle Access, Prime Factors, Theoretical Computer Science