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.

翻译：本文提出了一种形式化证明RSA公钥密码系统正确性的替代方法。所提出的方法论与现有文献中的传统证明略有不同。具体而言，本研究探讨了RSA基本组成部分——正整数N的选择条件在何种情况下可以扩展至标准选择准则之外。我们推导出明确的条件以判定哪些N值适用于该加密方案，并解释了其他数值为何无法满足正确性要求。本文研究范围仅限于类RSA方案正确性的数学证明，刻意省略了与RSA密码安全性相关的问题。