I have to implement a simple hashing algorithm.
Input data:
- Value (16-bit integer).
- Key (any length).
Output data:
- 6-bit hash (number 0-63).
Requirements:
- It should be practically impossible to predict hash value if you only have the input value but not the key. More specific: if I known hash(x) for x < M, it should be hard to predict hash(M) without knowing the key.
Possible solutions:
- Keep full mapping as a key. So the key has length 2^16*6 bits. It’s too long for my case.
- Linear code. Key is a generator matrix. It’s length is 16*6. But it’s easy to find generator matrix using several known hash values.
Are there any other possibilities?
A HMAC seems to be what you want. So a possibility for you could be to use a SHA-based HMAC and just use a substring of the resulting hash. This should be relatively safe, since the bits of a cryptographic hash should be as independent and unpredictable as possible.
Depending on your environment, this could however take too much processing time, so you might have to chose a simpler hashing scheme to construct your HMAC.
Original Answer the discussion in the comments is based on:
Since you can forget cryptographic properties anyway (it is trivial to find collisions via bruteforce attacks on a 5-bit hash) you might as well use something like CRC or Hamming Codes and get error-detection for free