On oracle factoring of integers
Andrzej D\k{a}browski, Jacek Pomyka{\l}a, Igor E. Shparlinski
TL;DR
This paper introduces an oracle-based factorization algorithm that leverages elliptic curve point counts in residue rings to efficiently find nontrivial factors of most positive integers.
Contribution
It presents a novel oracle factorization method utilizing elliptic curve point counts in residue rings, advancing integer factorization techniques.
Findings
Effective for almost all positive integers
Utilizes elliptic curve point counts in residue rings
Provides a new approach to integer factorization
Abstract
We present an oracle factorisation algorithm which finds a nontrivial factor of almost all positive integers based on the knowledge of the number of points on certain elliptic curves in residue rings modulo .
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Taxonomy
TopicsCryptography and Residue Arithmetic · Coding theory and cryptography · Polynomial and algebraic computation