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Some security proof involving an ideal function use the Random Oracle Model (ROM). They posit a thing that given integer $b$ and bistring $M$, returns what it previously returned for that input $(b,M)$ if it ever received it, and otherwise returns a random $b$-bit bitstring.

Some security proof involving an ideal permutation use the Bijective Random Oracle Model (BROM). They posit a thing that given a bistring $B$, returns what it previously returned for that input $B$ if it ever received it, and otherwise returns a random bitstring the same size as $B$ among those it never returned.

Some security proof involving an ideal block cipher could similarly posit a thing that given bitstrings $B$ and $K$, returns what it previously returned for that input $(B,K)$ if it ever received it, and otherwise returns a random bitstring the same size as $B$ among those it never returned for an input with the given $K$.

Is there a name+acronym for that model? Otherwise, make that the Keyed Bijective Random Oracle Model (KBROM).

Could we say that the ROM is to random member of a Pseudo-Random Function family (PRF), what the BROM is to random member of a Pseudo-Random Permutation family (PRP), and what that KBROM is to a random member of a Pseudo-Random Block-Cipher family (PRBC)?

How do KBROM and PRBC relate to the Ideal Cipher Model used in e.g. J.-S. Coron, T. Holenstein, R. Künzler, J. Patarin, Y. Seurin, and S. Tessaro's How to Build an Ideal Cipher: The Indifferentiability of the Feistel Construction, in JoC, 2016?

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  • $\begingroup$ Do you just mean the Ideal cipher model? Here you get an independent uniform random permutation for each key. $\endgroup$ – Aleph May 6 at 13:45

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