What is a somewhat secure way of generating a 64 bit signature?

Question

I would like to sign a device, and I have 64 bits to store my signature in the device. This device has a MAC address and some other details (about 30 bytes worth) I can mangle to create my signature.

If possible, I would like the method to be one-way, so that I can verify that the signature is valid without knowing how to create a valid signature. Most public-private keys have this feature but they generate signatures that are 48 bytes long (I only have 8 bytes).

Implementation in Python is a plus.

Thanks

EDIT: Thanks for the advice everyone. It sounds like there is no secure way to do this, only a way that is moderately inconvenient to attackers. I'll probably use a cryptographic hash combined with secret bit-shuffling. This will be as secure as any other link in my (very weak) 'security'.

Answer 1

Hash functions and digital signatures are very different things.

The size of a digital signature depends on the underlying hash function and the key length. So in theory, you can create an RSA implementation that generates 64-bit signatures, but that'd be an extremely weak signature.

For smaller key lengths, you might want to look at elliptic curve cryptography.

EDIT: Yes, I'm a cryptographer.

EDIT 2: Yet if you only need a hash function, you can look at elf64 or RIPEMD-64 as Fernando Miguélez suggested.

EDIT 3: Doing the math, you'd need to use 16-bit keys in ECC to generate 64-bit signatures, which is very weak. For ECC, anything less than 128 bits can be considered weak. For RSA this is 1024 bits.

Answer 2

Basically what you need is a 64-bit cryptographic hash funcion, such as Ripemd-64 or elf-64. Then you encrypt the hash with a cryptographic method and you got a 64 bit signature. The only problem is, from the point of view of a non-cryptoanalyst, that 64 bit offers a much weaker signature than typical over-128 bit hash. Nonetheless it could still be suitable for your application.

Answer 3

You could just use a standard hashing function (MD5 SHA1) and only use the first or last 30 bytes.
The number of bytes a hashing function generates is fairly arbitrary - it's obviously a trade off between space and uniqueness. There is nothing special about the lenght of the signature they use.

Edit - sorry I was thinking that MD5 returned 32bytes- it actaulyl returns 16bytes but is ussually written as 32hex digits.