A monte carlo method for factorization

  title={A monte carlo method for factorization},
  author={John M. Pollard},
  journal={BIT Numerical Mathematics},
  • J. Pollard
  • Published 1 September 1975
  • Computer Science
  • BIT Numerical Mathematics
We describe briefly a novel factorization method involving probabilistic ideas. 
Integer Factoring
Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization.
On cullen numbers
A table of Karst which gives the factorizations ofCn=n2n+1 is completed ton=101.
The Primality of # 1031
A description is given of a technique for proving Ä1031 (= (101031 l)/9) a prime.
An improved Monte Carlo factorization algorithm
A cycle-finding algorithm is described which is about 36 percent faster than Floyd's (on the average), and applied to give a Monte Carlo factorization algorithm which is similar to Pollard's but about 24 percent faster.
New integer factorizations
New factorizations of Fibonacci numbers, Lucas numbers, and numbers of the form 2" + I are presented together with the strategy (a combination of known factorization methods) used to obtain them.
Multi-Base Chains for Faster Elliptic Curve Cryptography
MULTI-BASE CHAINS for FASTER ELLIPTIC CURVE CRYPTOGRAPHY are proposed for use in the next generation of search and recovery operations.
Analysis of cryptographic hash functions.
  • Jian Guo
  • Computer Science, Mathematics
  • 2011
Quantum Computational Number Theory
  • S. Yan
  • Computer Science, Physics
    Springer International Publishing
  • 2015
This paper presents a meta-modelling scheme that automates the very labor-intensive and therefore time-heavy and expensive process of integrating discrete logarithms into a discrete-time model.
On not storing the path of a random walk
We describe a novel form of Monte Carlo method with which to study self-avoiding random walks; we do not (in any sense) store the path of the walk being considered. As we show, the problem is related
Time-Space Tradeoffs and Query Complexity in Statistics, Coding Theory, and Quantum Computing
Time-Space Tradeoffs and Query Complexity in Statistics, Coding Theory, and Quantum Computing


A design for a number theory package with an optimized trial division routine
A number theory package is described which uses doubly linked list structures for storing multiprecise integers and an optimally coded trial division routine can be used to determine the unique factorization of large integers.
Theorems on factorization and primality testing
This paper is concerned with the problem of obtaining theoretical estimates for the number of arithmetical operations required to factorize a large integer n or test it for primality, and uses a multi-tape Turing machine for this purpose.
A method of factoring and the factorization of
The continued fraction method for factoring integers, which was introduced by D. H. Lehmer and R. E. Powers, is discussed along with its computer implementation. The power of the method is