Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a name for the subset of involution functions used in most reciprocal ciphers?

I've been saying things like

A pairing is a function f that pairs up each element x with some other element y, such that

  • f(x) = y and x != y and f(y) = x, for each and every x.

Or in other words,

  • f(x) != x for each and every x, and
  • f(f(x)) == x for each and every x

(In particular, the identity function is not a pairing).

My understanding is that the Enigma machine and nearly all other reciprocal ciphers always use such a function to transform each plaintext letter to the corresponding ciphertext letter. (I suspect because of the misunderstanding that "when we encrypt a plaintext letter, obviously the encrypted ciphertext should not be the same letter").

I've been calling such a function a pairing, but I've recently discovered that term is usually used to mean something quite different.

What term should I use instead of "pairing"?

share|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.