General attacks on compression functions based on key alternating ciphers

In this paper we consider the security of compression functions based on key alternating ciphers. Specifically, we focus on the PGV compression functions. It is known that there are 12 PGV compression functions which can be proved to be both optimum collision resistance and preimage resistance when the underlying block cipher is ideal. However, we present new general collision and preimages attacks on these 12 PGV compression functions when a key alternating cipher is instantiated. Compare with the best generic collision and preimage attack on compression functions, our attacks reduce the attacking complexity by 2 rounds of the round function in the underlined block cipher. Take the 10-round AES block cipher as example, our attacks only need 8 rounds querying complexity, while the default birthday and exhaustive attacks need complete 10 rounds of querying complexity.