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How do product ciphers combine transposition and substitution operations?

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A Vigenere cipher table displays the alphabet in both the top row and left column, with rows shifted to create a grid for encryption and decryption. Highlighted letters illustrate how to use the table. An explanation and example using the words cipher, key, and plaintext appears to the right. — cryptology In encrypting plaintext, the cipher letter is found at the intersection of the column headed by the plaintext letter and the row indexed by the key letter. To decrypt ciphertext, the plaintext letter is found at the head of the column determined by the intersection of the diagonal containing the cipher letter and the row containing the key letter.

A product cipher enhances security by subjecting plaintext to multiple layers of encryption, specifically by combining transposition ciphers and substitution ciphers.1

These operations function as follows:
* Substitution: Replaces plaintext elements—such as individual symbols or pairs of symbols—with different symbols or groups of symbols, maintaining the original sequence.2
* Transposition: Rearranges the order of the symbols within the message without altering the symbols themselves.2

In practice, these are often combined through a process known as superencryption. For example, in fractionation systems like the ADFGVX cipher, plaintext is first converted into multiple symbols (such as pairs) via substitution. This intermediate ciphertext is then arranged in a matrix and subjected to a final transposition, where columns are read out in a specific order determined by a keyword. By layering these distinct mathematical operations, the resulting ciphertext becomes significantly more resistant to cryptanalysis than a single-method cipher.1