Efficient factoring based on partial information
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
On the power of two-point based sampling
Journal of Complexity
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Correcting errors in RSA private keys
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Factoring unbalanced moduli with known bits
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
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The problem of factoring integers in polynomial time with the help of an (infinitely powerful) oracle who answers arbitrary questions with yes or no is considered. The goal is to minimize the number of oracle questions. Let N be a given composite n-bit integer to be factored. The trivial method of asking for the bits of the smallest prime factor of N requires n/2 questions in the worst case. A non-trivial algorithm of Rivest and Shamir requires only n/3 questions for the special case where N is the product of two n/2-bit primes. In this paper, a polynomial-time oracle factoring algorithm for general integers is presented which, for any Ɛ 0, asks at most Ɛn oracle questions for sufficiently large N. Based on a conjecture related to Lenstra's conjecture on the running time of the elliptic curve factoring algorithm it is shown that the algorithm fails with probability at most N-Ɛ/2 for all sufficiently large N.