The subject of this thesis is the study of cryptographic hash functions, which utilize block ciphers as underlying chain functions. It is mainly concerned with the analysis of the three hash algorithms, the Whirlpool, Gr&oslash / stl and Grindahl. All these hash functions have underlying block ciphers that are modified versions of the Advance Encryption Standard and we investigate the behavior of these block ciphers under the integral attack. Statistical tests, such as the avalanche test and the collision test, are the regular tools for examining the hash function security. In this work, we inspect the statistical behavior the three hash functions and search for collisions. Although it is very difficult to obtain collisions for the actual algorithms, we find some collisions under slight modifications of the original constructions. The ease or difficulty of finding a collision for a modified version also shows the respective importance of the specific hash function branch, missing in the modified version.