Length of the hash value

Question

How do the length of the hash value affects security?

Answer 1

The essential cryptographic properties of the hash function are that it is both one-mode and collision-free. The most fundamental attack we may mount on the hash function is to select inputs to hash function at random till either we find some input which will give us the target output value we are looking for (thus contradicting the one-way property), or we discover two inputs which produce the same output (thus contradicting the collision-free property).

Assume the hash function generates an n-bit long output. When we are trying to discover some input which will generate some target output value y, then because each output is equally likely we anticipate have to try 2n possible input values.