New hash function designs

1 Known designs Let n be a natural number and M denotes the message represented by n-bit In case the message length is not a multiple of n, it should be padded somehow. We do not specify how at this point. Most of the known hash functions are based on the Merkle-Damg ˙ ard construction. First, a compression function f (h, m) is determined, where m is an n-bit input and another input h is of the hash value size r. The initial value h 0 of r-bit length is fixed. Then one computes h i = f (h i−1 , m i) for i = 1, 2,. .. , s and puts H(M) = h s , which is the hash value of M. Two properties of the modern hash functions based on the Merkle-Damg ˙ ard construction are observed: 1. The compression function is commonly a many round construction of some very simple round functions. Some of them heavily use bit logical operations which are not very compatible with modern 32 and 64-bit computers. 2. The computation of the final hash value H(m) can't be distributed over several processors. That is, in order to compute h i all h 1 , h 2 ,. .. , h i−1 should be computed before. Our new design solves the above two problems. That is, in order to process one n-bit message block, one n-bit modular multiplication and few of n-bit modular additions and n-bit XOR's are calculated. So the hash value computation is especially efficient on 64-bit machines. The whole hash computation of long messages is easily distributed over any number of processors with tree hash 1