Integer Factoring Using Small Algebraic Dependencies
Manindra Agrawal, Nitin Saxena, Shubham Sahai · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2016
Integer factoring is a curious number theory problem with wide applications in complexity and cryptography. The best known algorithm to factor a number n takes time, roughly, exp(2*log^{1/3}(n)*log^{2/3}(log(n))) (number field sieve, 1989). One basic idea used is to find two squares, possibly in a number field, that are congruent modulo n. Several variants of this idea have been utilized to get other factoring algorithms in the last century. In this work we intend to explore new ideas towards integer factoring. In particular, we adapt the AKS primality test (2004) ideas for integer factoring. In the motivating case of semiprimes n=pq, i.e. p