PGV-Style Block-Cipher-Based Hash Families and Black-Box Analysis

In [1] it was proved that 20 of 64 PGV hash functions [2] based on block cipher are collision-resistant and one-way in the black-box model of the underlying block cipher. Here, we generalize the definition of PGV-hash function into a hash family and we will prove that, aside from the previously reported 20 hash functions, we have 22 more collision-resistant and one-way hash families. As all these 42 families are keyed hash family, these are also target-collision-resistant. All these 42 hash families have tight upper and lower bounds on (target) collision-resistant and one-wayness. key words: hash function, block cipher, black-box model, provable security