The Design Principle of Hash Function with Merkle-Damgård Construction

The paper discusses the security of compression function and hash function with Merkle-Damg̊ard construction and provides the complexity bound of finding a collision and primage of hash function based on the condition probability of compression function y = F (x, k). we make a conclusion that in Merkle-Dammåard construction, the requirement of free start collision resistant and free start collision resistant on compression function is not necessary and it is enough if the compression function with properties of fix start collision resistant and fix start preimage resistant. However, the condition probability PY |X=x(y) and PY |K=k(y) of compression function y = F (x, k) have much influence on the security of the hash function. The best design of compression function should have properties of that y is uniformly distributed for all x and k. KeyWord: Hash Function, Block Cipher, Merkle-Damg̊ard Construction