No Smoking Prohibited By Law

The sign says:

No Smoking
Prohibited By Law

But it should say:

No Smoking
By Law

or

Smoking Prohibited By Law

or

No Smoking
Smoking Is Prohibited By Law

Why? Because it almost sounds as if not smoking is not allowed. In other words, it sounds like everyone must smoke.

Obviously people are not really going to conclude that they must smoke when they see this sign, but all the same, the English is not quite right.