I wouldn't worry about the government "finding out."
You're not put in a government database for something like "Asperger's."
If they do explicitly ask about a diagnosis on your application, I would tell the truth about it, though. If not, don't say anything.
The government is not as thorough when screening candidates for civilian positions that don't require a security clearance. If you already happen to have one, more power to you.
Even if a security clearance is required, I don't believe "Asperger's" back in your school days would disqualify you.