# Integer Factoring

@article{Lenstra2000IntegerF, title={Integer Factoring}, author={A. K. Lenstra}, journal={Designs, Codes and Cryptography}, year={2000}, volume={19}, pages={101-128} }

Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization.

#### 60 Citations

A geometric approach to integer factorization

- Computer Science, Mathematics
- ArXiv
- 2018

This work gives a geometric approach to integer factorization based on special approximations of segments of the curve represented by y=n/x, where $n$ is the integer whose factorization the authors need. Expand

A log-log speedup for exponent one-fifth deterministic integer factorisation

- Mathematics
- 2021

Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer N may be rigorously and deterministically factored into… Expand

A Survey of Techniques Used in Algebraic and Number Theoretic Algorithms

- 2005

We survey some of the important tools and techniques used in designing algorithms for problems in algebra and number theory. We focus on the computational efficiency of these tools and show how they… Expand

Computational methods in public key cryptology

- Computer Science
- 2002

These notes informally review the most common methods from computational number theory that have applications in public key cryptology.

Quantum Algorithms for Integer Factorization

- Computer Science
- 2015

If IFP can be solved in polynomial-time, then RSA and many other cryptographic systems can be broken completely and efficiently. Expand

A time-space tradeoff for Lehman's deterministic integer factorization method

- Computer Science, Mathematics
- Math. Comput.
- 2021

This paper constructs a time-space tradeoff for Lawrence's generalization and applies it together with Lehman's result to obtain a deterministic integer factorization algorithm with runtime complexity $O(N^{2/9+o(1)})$. Expand

Factoring Based Cryptography

- Computer Science
- 2019

This chapter discusses various factoring based cryptographic systems and protocols in the context of public-key cryptography. Expand

A babystep-giantstep method for faster deterministic integer factorization

- Mathematics, Computer Science
- Math. Comput.
- 2018

This paper combines Strassen's approach with a babystep-giantstep method to improve the currently best known bound by a superpolynomial factor. Expand

Analysis of Pollard's Rho Factoring Method

- Mathematics
- 2019

A comprehensive heuristic analysis of the Pollard’s Rho Method (PRM) is given. The analysis is based on ultimate periods and tails distribution of sequences. If n is the composite number to be… Expand

A special purpose integer factorization algorithm

- Computer Science
- CCSEIT
- 2012

A special purpose factorization algorithm is proposed to find the factors of a composite number which is the product of two primes and the efficiency of the scheme is proved theoretically. Expand

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