Secret trials and convictions? Don't exist in the US. Also, evidence cannot be used in court but withheld from defense attorneys. You're just making this stuff up. There are no secret prisons either. If you're talking about battlefield prisons for captured combatants, that's obviously different than the criminal justice system, and is par for the course in warfare.

You can definitely have secret warrants. How could you not? Imagine if the cops had to publish the details of wiretaps. What use would they be? Nevertheless, the secrecy must be justified and approved by a judge every few months.