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2 results

  • 3 - History of Integer Factorisation

  • from Part I - Cryptanalysis
  • Edited by Joppe Bos, Martijn Stam
  • Book:
    Computational Cryptography
    Published online:
    11 November 2021
    Print publication:
    02 December 2021, pp 41-77

  • 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.

  • A ONE LINE FACTORING ALGORITHM

  • Part of
  • WILLIAM B. HART
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 1 / February 2012
    Published online by Cambridge University Press:
    15 June 2012, pp. 61-69
    Print publication:
    February 2012
    • Article
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  • We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package.