Speeding Fermat's factoring method

Speeding Fermat's factoring method

A factoring method is presented which, heuristically, splits composite n in O(n1/4+ ) steps. There are two ideas: an integer approximation to √ (q/p) provides an O(n1/2+ ) algorithm in which n is represented as the difference of two rational squares; observing that if a prime m divides a square, then m2 divides that square, a heuristic speed-up to O(n1/4+ ) steps is achieved. The method is well...

Speeding up Discrete Log and Factoring Based Schemes via Precomputations

We present fast and practical methods for generating randomly distributed pairs of the form (x; g x mod p) or (x; x e mod N), using precomputation. These generation schemes are of wide applicability for speeding-up public key systems that depend on exponentiation and ooer a smooth memory-speed trade-oo. The steps involving exponenti-ation in these systems can be reduced signiicantly in many cas...

Turning Euler's Factoring Method into a Factoring Algorithm

An algorithm is presented which, given a positive integer n, will either factor n or prove it to be prime. The algorithm takes O(«) steps.

Factoring Networks by a Statistical Method

We show that it is possible to factor a multi-layered classiication network with a large output layer into a number of smaller networks, where the product of the sizes of the output layers equals the size of the original output layer. No assumptions of statistical independence are required.

A Sieve Method for Factoring Numbers