论文信息 - On Factoring Arbitrary Integers with Known Bits

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 r harmonic number.

Alexander May | Mathias Herrmann

[1] Don Coppersmith,et al. Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known , 1996, EUROCRYPT.

[2] Don Coppersmith,et al. Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities , 1997, Journal of Cryptology.

[3] Jean-Sébastien Coron,et al. Finding Small Roots of Bivariate Integer Polynomial Equations Revisited , 2004, EUROCRYPT.

[4] Dan Boneh,et al. Fast Variants of RSA , 2007 .

[5] Bagus Santoso,et al. Factorization of Square-Free Integers with High Bits Known , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[6] Adi Shamir,et al. Efficient Factoring Based on Partial Information , 1985, EUROCRYPT.