Black-Box Property of Cryptographic Hash Functions

We define a new black-box property for cryptographic hash function families H : {0, 1}×{0, 1}∗ → {0, 1} which guarantees that for a randomly chosen hash function HK from the family, everything “non-trivial” we are able to compute having access to the key K, we can compute only with oracle access to HK . If a hash function family is pseudo-random and has the black-box property then a randomly chosen hash function HK from the family is resistant to all non-trivial types of attack. We also show that the HMAC domain extension transform is Prf-BB preserving, i.e. if a compression function f is pseudo-random and has black-box property (Prf-BB for short) then HMAC is Prf-BB. On the other hand we show that the Merkle-Damg̊ard construction is not Prf-BB preserving. Finally we show that every pseudo-random oracle preserving domain extension transform is Prf-BB preserving and vice-versa. Hence, Prf-BB seems to be an all-in-one property for cryptographic hash function families, which guarantees their “total” security.