I am new here and fairly new to cryptography, so if I say something wrong, let me know.
I am trying to set up a system where a user can receive a temporary license key over the phone, put it into the system, and get the privileges and expiration date which was encoded into the license key.
The limitation for this key is about 100 bits. About 27 will hold the properties of the key, and the rest will be a signature verifying someone didn't make their own license key.
I think we can get away with having a smaller signature size than usual because we are using a cryptography IC which can hold private keys and hash data using SHA-256, and it takes some time to do this (maybe 100ms). If we used this in the verification of a signature, it would keep a hacker from using their supercomputer to crack keys quickly.
For the crypto calculations done in software and not on the crypto IC, we want to use public key crpytography, and ECC seems like the best option right now due to the already relatively short signatures.
Assuming the random component can be calculated based on the 27 data bits (and will always be different for a different license key), can I make the other half of the ECC signature only take up 73 bits? How would this be done?