This article discusses the provable security of pseudo-random-function (PRF) modes of an iterated hash function using a block cipher. The iterated hash function uses the Matyas-Meyer-Oseas (MMO) mode for the compression function and the Merkle-Damgård with a permutation (MDP) for the domain extension transform. It is shown that the keyed-via-IV mode and the key-prefix mode of the iterated hash function are pseudorandom functions if the underlying block cipher is a pseudorandom permutation under a related-key attack with respect to the permutation used in MDP. More precisely, the key-prefix mode also requires that E_IV(K) ⊕ K is pseudoramdom, where E is the underlying block cipher, IV is the fixed initial value of the hash function, and K is a secret key. It is also confirmed that the MMO compression function is the best choice with MDP among the block-cipher-based compression functions in the Preneel-Govaerts-Vandewalle model in terms of the provable security.