A New Concept of Hash Functions SNMAC Using a Special Block Cipher and NMAC/HMAC Constructions

In this paper, we present new security proofs of well-known hash constructions NMAC/HMAC proposed by Bellare et al. in 1996. We show that block ciphers should be used in hash functions in another way than it has been so far. We introduce a new cryptographic primitive called special block cipher (SBC) which is resistant to attacks specific for block ciphers used in hash functions. We propose to use SBC in the NMAC/HMAC constructions, what gives rise to the new concept of hash functions called Special NMAC (SNMAC). From our new NMAC/HMAC security proofs it follows that SNMAC hash functions are computationally resistant to preimage and collision attacks. Moreover, at CRYPTO 2005 Coron et al. proved that SNMAC is indifferentiable from a random oracle in the limit. SNMAC construction is general and it enables various proposals using different instances of the special block ciphers. We propose a special block cipher DN (Double Net) and define hash function HDN (Hash Double Net) as the SNMAC construction based on DN.