Simple Hash Functions

SIMPLE HASH FUNCTIONS

All hash functions operate using the following general principles. The input (message, file, etc.) is viewed as a sequence of n-bit blocks. The input is processed one block at a time in an iterative fashion to produce an n-bit hash function.

One of the simplest hash functions is the bit-by-bit exclusive-OR (XOR) of every block. This can be expressed as follows:

Thus, the probability that a data error will result in an unchanged hash value is 2ⁿ. With more predictably formatted data, the function is less effective. For example, in most normal text files, the high-order bit of each octet is always zero. So if a 128-bit hash value is used, instead of an effectiveness of 2¹²⁸, the hash function on this type of data has an effectiveness of 2¹¹².

A simple way to improve matters is to perform a one-bit circular shift, or rotation, on the hash value after each block is processed. The procedure can be summarized as follows:

Initially set the n-bit hash value to zero.

Process each successive n-bit block of data as follows:

                                                             i.      Rotate the current hash value to the left by one bit.

                                                           ii.      XOR the block into the hash value.