abbr. **SJ GMU
ISSN 2657-5841 (printed)
ISSN 2657-6988 (online)**

**DOI: 10.26408**

abbr. **SJ GMU
ISSN 2657-5841 (printed)
ISSN 2657-6988 (online)**

You are welcome to visit the new website at sjgmu.umg.edu.pl.

1

CSIRO, Sydney, Australia,

Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, e-mail: josef.pieprzyk@csiro.au

Abstract:

Integer factorization is one of the oldest mathematical problems. Initially, the interest in factorization was motivated by curiosity about behaviour of prime numbers, which are the basic building blocks of all other integers. Early factorization algorithms were not very efficient. However, this dramatically has changed after the invention of the well-known RSA public-key cryptosystem. The reason for this was simple. Finding an efficient factoring algorithm is equivalent to breaking RSA.

The work overviews development of integer factoring algorithms. It starts from the classical sieve of Eratosthenes, covers the Fermat algorithm and explains the quadratic sieve, which is a good representative of modern factoring algorithms. The progress in factoring is illustrated by examples of RSA challenge moduli, which have been factorized by groups of mathematicians and cryptographers. Shor's quantum factorization algorithm with polynomial complexity is described and the impact on public-key encryption is discussed.

Keywords:

Cryptography, Number Theory, Public-key Cryptography, Factorization, RSA Cryptosystems, Quantum Computing, Shor Algorithm

Issue:

Pages:

7

20

Doi:

Submitted:

21.08.2018

Accepted:

15.10.2018

Published:

30.03.2019

Download full text in pdf:

This article is an open access article distributed under a Creative Commoms Attribution (CCBY 4.0) licence

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