Is there any standard present to measure strength of a generated key using true random number generator? I was wondering how to measure the security strength of a generated secret key for the below protocol:
&quot;A 128 bit random number is generated by TRNG and the random number will be used as a private key for Diffie-Hellman key exchange protocol. Two entities generate the shared secret key and that will be used as a session key for symmetric encryption.&quot;
My questions are:

Is there any standard way to measure how secure the generated key is?
What are the properties that the generated key should have to be resistant to attacks? Is there any paper/Standard document available that has the list of such properties?

Thanks.
The NIST special publication 800-90B is probably your go to here. It is the approach used to meet the FIPS 140-3 requirements which are accepted by as good assurance by a large population.
Different approaches are taken for TRNGs that are believed to produce independent, identically distributed outputs and others. One of the key measurements is the minimum entropy ($H_\infty$ in the Shannon-Renyi sense) that tracks the most probable output of some fixed size output. If the only information available to the attacker is the minimum entropy of the key, their guessing work should be at least on the order of $2^{H_\infty}$.
ETA: as pointed out in the comments, because your question is specifically about Diffie-Hellman, there are subexhaustive attacks. In particular 128-bit keys can be recovered with 64-bits of group operations using Pollard rho/baby step-giant step/Pollard kangaroo.