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Modern Factoring Algorithms

Gauss and lesser mathematicians may be justified in rejoicing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. Unfortunately for Hardy, nowadays, number theoretic results form the basis of several applications in the field of cryptography. In this survey, we will present the most recent approaches on solving the factoring problem. In particular, we will study Pollard's ρ algorithm, the Quadratic and Number Field Sieve and finally, we will give a brief overview on factoring in quantum computers .