Four Integer Factorization Algorithms

TL;DR

This paper discusses four integer factorization algorithms, analyzing their theoretical performance on hard-to-factor integers, with complexities ranging from exponential to logarithmic time, highlighting their efficiency and limitations.

Contribution

It provides a detailed theoretical analysis of four factorization algorithms, emphasizing their performance on specific hard-to-factor integers.

Findings

Algorithms range from exponential to logarithmic complexity.

Performance varies significantly based on integer properties.

Insights into algorithm efficiency on balanced integers.

Abstract

The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running time complexity of these algorithms ranges from deterministic exponential time complexity O(N^(1/2)) to heuristic and unconditional logarithmic time complexity O((log N)^c), c > 0 constant.