Generating random factorisations of polynomial values
Dmitry Badziahin

TL;DR
This paper presents algorithms for efficiently generating random factorizations of polynomial values, enabling applications like RSA key construction and demonstrating the density of factor ratios.
Contribution
The paper introduces novel algorithms for random factorization of polynomial values and shows the density of factor ratios, with applications to cryptography.
Findings
Algorithms for random factorization of quadratic and cubic polynomial values
Construction of RSA keys with specific size and information content
Proof that ratios of factors are dense in positive real numbers
Abstract
We construct algorithms that efficiently generate random factorisations of values as products of two integers, where is a given quadratic or cubic monic polynomial. In other words, the algorithms produce random triples that solve the Diophantine equation . In the case where is cubic, such an algorithm allows the construction of an RSA key of bits that can be described using about bits of information. We also show how to construct a solution with the ratio arbitrarily close to any given positive real number. This proves that among all solutions of the ratios are dense in .
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Taxonomy
TopicsPolynomial and algebraic computation · Analytic Number Theory Research · Algebraic Geometry and Number Theory
