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

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.