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Defacing paper currency is usually illegal in most countries.
Yet, I have seen "END THE FED" stamped on US money.
Not to mention telephone numbers and other small notations.
I see no harm in putting a public & private key on a US$20 or a 20. Just don't get caught!
It's actually legal in the US as long as intention is not to destroy or make them unusable.
Defacement of currency is a violation of Title 18, Section 333 of the United States Code. Under this provision, currency defacement is generally defined as follows: Whoever mutilates, cuts, disfigures, perforates, unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, Federal Reserve Bank, or Federal Reserve System, with intent to render such item(s) unfit to be reissued, shall be fined under this title or imprisoned not more than six months, or both.