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阿尔贝蒂《论密码》中“formula”涵义与其密码算法

The Meaning of “formula” and its Cryptographic Algorithm in Alberti’s De Cifris

  • 摘要: 阿尔贝蒂在其著作《论密码》中提出的核心概念“formula”,长期以来被解读为一种物理装置,即密码盘本身。然而,通过对《论密码》文本的细致分析及其密码算法的系统梳理,本文指出,这一传统理解未能充分揭示阿尔贝蒂的真实意图。研究表明,“formula”并非仅指代密码盘的硬件结构,而是一个具有多种映射关系和多层映射关系的密码算法。该算法通过动态调整字母与数字的对应关系,实现了加密过程的复杂性与安全性,体现了阿尔贝蒂对数学映射思想的深刻运用。本文通过探求“formula”的涵义对阿尔贝蒂的密码装置与相应算法做了澄清,为西方密码学的机械化和算法化进程提供了参考。

     

    Abstract: The core concept of “formula” proposed by Leon Battista Alberti in his treatise De Cifris has long been interpreted as referring to a physical device—namely, the cipher disk itself. However, through meticulous textual analysis of De Cifris and systematic examination of its cryptographic algorithm, this paper demonstrates that such conventional interpretation fails to fully capture Alberti's original intent. Research reveals that “formula” does not merely denote the hardware structure of the cipher disk, but rather represents a sophisticated cryptographic algorithm characterized by multiple and multi-layered mapping relationships. By dynamically adjusting correspondences between letters and numerals, this algorithm achieves both complexity and security in the encryption process, reflecting Alberti's profound application of mathematical mapping principles. Through clarifying the meaning of “formula” and its associated cryptographic mechanisms, this study not only rectifies limitations in prior scholarship but also contributes to our understanding of the mechanization and algorithmic development of Western cryptography.

     

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