The implications between C-SPR and CRn (n′, n) visited

The compression function is wildly used via many kinds of iterations in the construction of the modern hash function intended for use with standard digital signatures following the hash-and-sign mode. Some variants of second-preimage resistance(SPR)[1] assumptions of the keyless compression function, called c-SPR, r-SPR and e-SPR, have been put forth by Halevi and Krawczyk[2], in order to obtain higher security properties for the dedicated-key hash function by iteration. In this paper, we compare one variant, called c-SPR, with CRn (n′, n) which has been raised by Mironov[3]. We give several different schemes of the dedicated-key compression functions firstly, the relations between c-SPR and CRn (n′, n) differ in different schemes. In the second part of this paper, we provide a full picture of the relations between c-SPR and CRn (n′, n), and give the additional restrictions that ensure c-SPR of the keyless compression function to be the necessary or sufficient conditions of CRn (n′, n) of the dedicated-key compression function separately.