On The Oracle Complexity Of Factoring Integers

On The Oracle Complexity Of Factoring Integers (1996)

by Ueli M. Maurer

Venue:	COMPUTATIONAL COMPLEXITY
Citations:	4 - 0 self

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Datum	Value	Source
TITLE	On The Oracle Complexity Of Factoring Integers	user correction - Legacy Corrections
AUTHOR NAME	Ueli M. Maurer	user correction
ABSTRACT	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, where n = dlog 2 Ne. 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 ffl ? 0, asks at most ffln oracle questions for sufficiently large N , thus solving an open problem posed by Rivest and Shamir. Based on a plausible 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 ...	user correction
YEAR	1996	INFERENCE
VENUE	COMPUTATIONAL COMPLEXITY	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	237--247	INFERENCE
VOLUME	5	INFERENCE
CITATIONS	14 found	ParsCit 1.0