We introduce asymmetric fingerprinting, where only the buyer knows the fingerprinted copy, and the merchant, upon finding it somewhere, can find out and prove to third parties whose copy it was. We present a detailed definition of this concept and constructions. The first construction is based on a quite general symmetric fingerprinting scheme and general crypto- graphic primitives; it is provably secure if all these underlying schemes are. We also present more specific and more efficient constructions.