Cloning Games: A General Framework for Unclonable Primitives

The powerful no-cloning principle of quantum mechanics can be leveraged to achieve interesting primitives, referred to as unclonable primitives, that are impossible to achieve classically. In the past few years, we have witnessed a surge of new unclonable primitives. While prior works have mainly focused on establishing feasibility results, another equally important direction, that of understanding the relationship between different unclonable primitives is still in its nascent stages. Moving forward, we need a more systematic study of unclonable primitives.

To this end, we introduce a new framework called cloning games. This framework captures many fundamental unclonable primitives such as quantum money, copy-protection, unclonable encryption, single-decryptor encryption, and many more. By reasoning about different types of cloning games, we obtain many interesting implications to unclonable cryptography, including the following:

1. We obtain the first construction of information-theoretically secure single-decryptor encryption in the one-time setting.

2. We construct unclonable encryption in the quantum random oracle model based on BB84 states, improving upon the previous work, which used coset states. Our work also provides a simpler security proof for the previous work.

3. We construct copy-protection for single-bit point functions in the quantum random oracle model based on BB84 states, improving upon the previous work, which used coset states, and additionally, providing a simpler proof.

4. We establish a relationship between different challenge distributions of copy-protection schemes and single-decryptor encryption schemes.

5. Finally, we present a new construction of one-time encryption with certified deletion.