Very low cost hash function

Question

I need a hash function for a Look Up table, so that if my values are from 0 to N, I need a hash function that give me a value from 0 to n, being n << N. Another piece

Answer 1

If you're truly talking hardware (vs. software, or hardware implementation of software), and your number of hash buckets n can be written as n = 2^m - 1, the easiest is probably a maximum-length linear feedback shift register (LFSR) of which CRC is an instance.

Here's one way you could use an m-bit shift register to create a hash of a data packet (make sure all data is represented consistently as a K-bit string, if you have shorter strings then pad one end with zeros):

1. Initialize the state of the LFSR (CRC-32 uses all 1's; all zeros is probably bad)
2. Shift in the bits of your data
3. (Optional) Shift in an additional j zeros (j between m and 2m is probably a good choice); this adds some additional hashing to reduce direct correlation between input/output bits
4. Use the contents of the m-bit shift register as your hashed value.