Abstract
For hundreds of years, cipher designers have operated on the principle that plain-text tokens must map to a single ciphertext character, and vice versa. It is widely understood that this bijective mapping ensures that an encrypted token can be decrypted to recover the original plaintext token. However, other mappings that violate this 1:1 principle of mapping have been shown to be possible and practical. Among those mappings are polyphonic and polyalphabetic ciphers (mappings). The 1:1 principle remains relevant but must be expanded to encompass all possible mappings from plaintext to ciphertext. With the constraint of a single (plaintext) token mapping to a single (ciphertext) token, cipher designers can explore other types of ciphers that have desirable security characteristics. This paper redefines the 1:1 principle in terms of sets and explores its implications. This paper does not intend to present implementations and, by extension, does not present experimental evidence, both of which certainly deserve attention in forthcoming future work.