Property of a cryptographic function

Question

What property of a cryptographic function is described below?

B = F(A) A = F(B)

Answer 1

$F$ is an involution. You don't want this property for a block cipher since the function doesn't look "random". On the other hand, a stream cipher works exactly that way, but then it's a bit misleading to think of it as a function $F$: the function is missing an important parameter, namely time.

Answer 2

Most mechanical cipher machines use a reciprocal cipher, so the machine doesn't need a separate "encode mode" and "decode mode". A reciprocal cipher is an involution.

• Cryptodox: reciprocal cipher
• Wikipedia: reciprocal cipher