J. M. Pollard

TL;DR: Some novel methods to compute the index of any integer relative to a given primitive root of a prime p, and how a very simple factorization method results, in which a prime factor p of a number can be found in only 0(pW2) operations.

TL;DR: A novel factorization method involving probabilistic ideas is described briefly, and it is suggested that this method should be considered as a viable alternative to traditional factorization methods.

TL;DR: This paper is concerned with the problem of obtaining theoretical estimates for the number of arithmetical operations required to factorize a large integer n or test it for primality, and uses a multi-tape Turing machine for this purpose.

TL;DR: A heuristic run time analysis indicates that the number field sieve is asymptotically substantially faster than any other known factoring method, for the integers that it applies to, and can be modified to handle arbitrary integers.

TL;DR: In this paper, a Monte Carlo factorization algorithm was used to factorize the Fermat number F8 = 2256+1, which was known to be composite, but its factors were unknown.