A Generalization of PGV-Hash Functions and Security Analysis in Black-Box Model

In [1] it was proved that 20 out of 64 PGV-hash functions [2] based on block cipher are collision resistant and one-way-secure in black-box model of the underlying block cipher. Here, we generalize the definition of PGV-hash function into a hash family and prove that besides the previous 20 hash functions we have 22 more collision resistant and one-way secure hash families. As all these 42 families are keyed hash families, these become target collision resistant also. All these 42 hash families have tight upper and lower bounds on (target) collision resistant and one-way-ness.

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