3 - History of Integer Factorisation

Summary

In Chapter 3, History of Integer Factorisation, Samuel S. Wagstaff, Jr gives a thorough overview of the hardness of one of the cornerstones of modern public-key cryptography. The history starts with the early effort by Eratosthenes and his sieve, eventually leading to the modern number field sieve, currently the asymptotically fastest general-purpose integer factorisation method known. Also included are 'special' integer factorisation methods like the elliptic-curve method, where the run-time depends mainly on the size of the unknown prime divisor. Modern factorisation efforts often include a gradual escalation of different methods, so it is essential to be familiar with a wide range of methods and the essence of all relevant algorithms is explained clearly.