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

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

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

• Key distribution
• "shared-key" Archive.org copy of a defunct site explains why most mechanical cipher machines use a reciprocal cipher.^[1]

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1. ↑ As of Oct 2016, the originally referenced domain redirects to a domain containing phishing and adult content.