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What property of a cryptographic function is described below?

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

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Self-invertibility. – Arturo Magidin Mar 8 '11 at 2:26

$F$ 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.

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your answer looks broken – user7939 Mar 8 '11 at 4:05
That's quite probable; in what way? – Yuval Filmus Mar 8 '11 at 4:46

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.

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