# Cryptography/Symmetric Ciphers

A **symmetric key cipher** (also called a **secret-key cipher**, or a **one-key cipher**, or a **private-key cipher**, or a **shared-key cipher**) is one that uses the same (necessarily secret) key to encrypt messages as it does to decrypt messages.

Until the invention of asymmetric key cryptography (commonly termed "public key / private key" crypto) in the 1970s, all ciphers were symmetric. Each party to the communication needed a key to encrypt a messages; and a recipient needed a copy of the same key to decrypt the message. This presented a significant problem, as it required all parties to have a secure communication system (e.g. face-to-face meeting or secure courier) in order to distribute the required keys. The number of secure transfers required rises impossibly, and wholly impractically, quickly with the number of participants.

### Formal Definition[edit]

Any cryptosystem based on a symmetric key cipher conforms to the following definition:

- M : message to be enciphered
- K : a secret key
- E : enciphering function
- D : deciphering function
- C : enciphered message. C := E(M, K)
- For all M, C, and K, M = D(C,K) = D(E(M,K),K)

### Reciprocal Ciphers[edit]

Some shared-key ciphers are also "reciprocal ciphers." A reciprocal cipher applies the same transformation to decrypt a message as the one used to encrypt it. In the language of the formal definition above, E = D for a reciprocal cipher.

An example of a reciprocal cipher is Rot 13, in which the same alphabetic shift is used in both cases.

## Further Reading[edit]

- Key distribution
- "shared-key" Archive.org copy of a defunct site explains why most mechanical cipher machines use a reciprocal cipher.
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