Paper 2010/631

Black-box property of Cryptographic Hash Functions

Michal Rjaško

Abstract

We define a new black-box property for cryptographic hash function families $H:\{0,1{\}}^K\times \{0,1{\}}^{\ast }\to \{0,1{\}}^y$ which guarantees that for a randomly chosen hash function $H_K$ 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 $H_K$. If a hash function family is pseudo-random and has the black-box property then a randomly chosen hash function $H_K$ 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 ${\text{HMAC}}^f$ is Prf-BB. On the other hand we show that the Merkle-Damg\aa rd 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.