# Factorizing RSA Keys, An Improved Analogue Solution

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## Abstract

Factorization is notoriously difficult. Though the problem is not known to be **NP**-hard, neither efficient, *algorithmic* solution nor technologically practicable, *quantum-computer* solution has been found. This apparent complexity, which renders infeasible the factorization of sufficiently large values, makes secure the RSA cryptographic system.

Given the lack of a practicable factorization system from algorithmic or quantum-computing models, we ask whether efficient solution exists elsewhere; this motivates the *analogue* system presented here. The system’s complexity is prohibitive of its factorizing arbitrary, natural numbers, though the problem is mitigated when factorizing *n* = *pq* for primes *p* and *q* of similar size, and, hence, when factorizing *RSA keys*.

Ultimately, though, we argue that the system’s polynomial time and space complexities are testament not to its power, but to the inadequacy of traditional, Turing-machine-based complexity theory; we propose *precision complexity* (defined in our previous paper^{4)}) as a more relevant measure, and advocate, more generally, non-standard complexity analyses for non-standard computers.

## Keywords:

Factorization Analogue Computer Computational Complexity Precision Complexity RSA Cryptography## Preview

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