Does sha-1 ever produce collisions for input messages less than 160bits?

Question

I have a 128bit ID that I want to perform a one way hash on, but I don't want to ever get the same digest for an input message. Does anyone know if sha-1, or an alternative, is guaranteed not to produce collisions for the set of messages less than its output digest size? This is at least theoretically possible...

I also considered using RSA, and discarding the private key to give me a one-way encrypt, but I need to store the result in a 32 char DB field, and the encryption schemes available to me don't produce anything small enough.

Any suggestions of another way of producing a deterministic, non-reversable and collision free transform of the original value are welcome.

Answer 1

Cryptographic hashes give a very good approximation of a random number for a given input. So how many random hashes do you need in a room until you get the same 160 bits? It about the square root (disclaimer: I am not a statistician). So you should expect to see clashes at around 80-bits.

I guess practicalities mean you should know when cosmic rays will be a bigger problem than collisions.