This paper examines the effect of the hash function irregularity on digital signature security. Digital signature is implemented as a hash function that maps large space of all possible messages to a smaller space of hash values. For the security of such a system it is important that it is difficult to find hash collision. Standard results in this area assume the best case, where hash function is regular. The irregularity of the hash function makes the security worse. We propose some irregularities and compute corresponding probabilities for finding hash collision.