What is an approximate length for a digital signature (SHA) in this case?

Question

What is an approximate length for a digital signature (SHA) given the following?

Using RFID tags, size ranging from 100 to 2000 bytes (8000 bits), our project is setting aside a portion for a digital signature against its fixed data, which includes an unique 8-byte serial number and with 32 to 64 bytes of factory data.

The signature, obviously longer leads to more security, will be for authentication (repudiation is not important). As the fixed data and signature can consume a sizable percentage of the tags, and 2013 technology being what it is (signature can't be too short), I looking to approximate the minimal size needed to securely authenticate data.

Example tag allocation
Fixed data 64 bytes
Unique Serial Number 8 bytes
Digital Signature ?? (32 - 64+ bytes, 256 - 512+ bits) I'm thinking 64 bytes, but that takes a good chunk of space - maybe overkill.

A prompt answer is not required.

To authenticate 64+8 bytes, what minimal digital signature length is recommended?

Answer 1

BLS signatures are $\:2\hspace{-0.04 in}\cdot\hspace{-0.03 in}k\:$ bits long, where $k$ is the security parameter, and the probability of a forgery is $\hspace{.01 in}\epsilon$.


Pseudorandom MACs (such as HMAC) can be truncated to $L\hspace{.01 in}$ bits, and the probability
of forgery (by someone who is outside of the system) will be $\: \frac{\text{# of tries}}{2^{\hspace{.01 in}L}}+\epsilon \;\;$.

(As alluded to in my comment, the verifier(s) can trivially forge valid authenticators for the MAC approach.)