Montgomery's method of polynomial selection for the number field sieve
Nicholas Coxon (INRIA Nancy - Grand Est / LORIA)
TL;DR
This paper analyzes Montgomery's polynomial selection method for the number field sieve, focusing on the construction of small modular geometric progressions crucial for efficient integer factorization.
Contribution
It provides a detailed analysis of Montgomery's method and investigates the existence of suitable geometric progressions for polynomial generation.
Findings
Analysis of Montgomery's polynomial selection method
Existence conditions for small modular geometric progressions
Insights into optimizing polynomial generation for the number field sieve
Abstract
The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on the construction of small modular geometric progressions. Montgomery's method is analysed in this paper and the existence of suitable geometric progressions is considered.
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