I've had a look at several signature schemes (DSA, ECDSA for the most common ones), and am wondering about whether there exist a scheme that would have the following properties :
- Be asymmetric (one need a private key to sign, one can verify with a public key)
- Have a very short signature size (less than 50 bits)
- Be secure by today's standards (hard to find the private key knowing a signature and the signed text)
I wouldn't even care if several signatures were valid for one text, as long as they are verifiable with the public key.
My intuition is that that "being" secure is inherently linked to the size of the encryption key, which itself has an impact on the size of the signature. As far as I could see, ECDSA gives shorter signatures than DSA with the same level of security, but the signatures are still too big for my use...
Any thoughts / links to signature schemes welcome.
edit: I read about BLS at some point too, but couldn't really find out whether it is doable to get a scheme secure enough with a signature less than 50 bits long.
edit2 : I should add that the goal is to use that for a OTP scheme, so the size of messages to sign would be small (< 512 bytes), and collisions wouldn't be a big problem : assuming the two parties know the message, I'd want for one of them to verify that the other has a private key, using a very short signature.