Correctness of Extended RSA Public Key Cryptosystem

TL;DR

This paper introduces a novel formal approach to verify the correctness of RSA-like cryptosystems, focusing on the conditions for selecting the modulus N beyond standard criteria.

Contribution

It presents explicit conditions for the validity of N in RSA-like schemes, extending the theoretical understanding of their correctness.

Findings

Derived explicit conditions for N validity in RSA

Identified cases where certain N values fail correctness

Focused on mathematical correctness, not security aspects

Abstract

This paper proposes an alternative approach to formally establishing the correctness of the RSA public key cryptosystem. The methodology presented herein deviates slightly from conventional proofs found in existing literature. Specifically, this study explores the conditions under which the choice of the positive integer N, a fundamental component of RSA, can be extended beyond the standard selection criteria. We derive explicit conditions that determine when certain values of N are valid for the encryption scheme and explain why others may fail to satisfy the correctness requirements. The scope of this paper is limited to the mathematical proof of correctness for RSA-like schemes, deliberately omitting issues related to the cryptographic security of RSA.