How can I verify or test the mutual authentication algorithms? Do you have any simulation tool or other software tool that can be used for this purpose? Please guide.
there are many tools for protocol verification. such as AVISPA and SPIN. I used AVISPA to verify a mutual authentication protocol. It has a library of verified authentication protocols which is very helpful
If you want to try something less common but equally powerful, I suggest you to use Casper/FDR. There are a few papers online which apply it to mutual authentication protocols.