Less is More: On Copy Complexity in Quantum Cryptography

Quantum cryptographic definitions are often sensitive to the number of copies of the cryptographic states revealed to an adversary. Making definitional changes to the number of copies accessible to an adversary can drastically affect various aspects including the computational hardness, feasibility, and applicability of the resulting cryptographic scheme. This phenomenon appears in many places in quantum cryptography, including quantum pseudorandomness and unclonable cryptography.

To address this, we present a generic approach to boost single-copy security to multi-copy security and apply this approach to many settings. As a consequence, we obtain the following new results:

• One-copy stretch pseudorandom state generators (under mild assumptions) imply the existence of t-copy stretch pseudorandom state generators, for any fixed polynomial t.

• One-query pseudorandom unitaries with short keys (under mild assumptions) imply the existence of t-query pseudorandom unitaries with short keys, for any fixed polynomial t.

• Assuming post-quantum pseudorandom functions exist, i.i.d.-copy secure uncloneable primitives imply identical-copy secure uncloneable primitives. In other words, many-time secure uncloneable primitives with mixed state output imply the same primitives with pure state output. This gives the first constructions of identical-copy secure public-key quantum money and quantum copy-protection.