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When discussing asymmetric cryptography with less technical folk, a lock analogy breaks down quickly as locks are conceptualized as being symmetric. Hence, "key" is a poor word that came from symmetric cryptography; one really needs to discuss the signature or authentication code.
A better analogy may be a transparent display case, where only authorized people can put things into the case. To check a copy outside the case is true, one would want to go to the official display case and compare. This isn't a great analogy because there's no analog to the signature, but it gets the asymmetry across.
Perhaps we might do a bit better? Suppose your friend gave you a poster copy of a famous painting from the Metropolitan Museum. On the poster is the curatorial accession number. You could go to the MET and check if your poster matches the painting, which should have matching accession number on the label.
So far our analogy covers asymmetry but is still centralized. The museum also distributes a catalog of its posters/paintings. Catalog entries have a thumb print of the painting and its accession number. So, if you could find a trusted copy of that catalog, say at your local library, you might also use this to check the painting's authenticity without having to travel to the museum. Alas, this analogy fails since the whole catalog need not be shared (just the public key).
These analogies are still problematic. This is an involved and novel cryptographic process, and for the interested policy maker or their trusted advisors, it's probably much better if we teach the real process with worked examples.