All hash functions operate using the following general principles. The input (message, file, etc.) is viewed as a sequence of n-bit blocks.

**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 2^{n}.
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 2^{128},
the hash function on this type of data has an effectiveness of 2^{112}.

**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.

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Cryptography and Network Security : Simple Hash Functions |

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