# Random Oracle Model for an ideal block cipher vs Ideal Cipher Model

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?

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