On the Foundations and Methods of Quantum Cryptography

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This project aims at improving our understanding of the foundations of quantum cryptography, to develop quantum tools allowing for new cryptographic primitives and a better understanding of its limits. The fact that two parties can agree upon a secret key using quantum communication (i.e. quantum key distribution) has first given hopes that the main goals of cryptography: data privacy, data authenticity, and data integrity could be provided information theoretically by quantum mechanics while, as we know, being impossible by classical means alone. Even before the security of quantum key distribution was fully established, researchers have shown that other cryptographic primitives would remain impossible even by all powerful quantum experimentalists. The picture of cryptography in a quantum world is therefore not as unconstrained as one could have first thought. In addition to the realization of classical cryptographic tasks by quantum information processing, quantum cryptography is also interested in providing means by which cryptographic techniques can be applied to quantum systems. Very often, classical primitives have a natural quantum interpretation. For instance, signing documents in order to publicly guarantee their integrity and authenticity has a natural quantum counterpart: signing quantum states. Quantum cryptography is interested in determining under what conditions, if any, these quantum primitives are possible. As an example, although signing documents can be performed securely based upon reasonable computational assumptions, signing quantum states remains impossible in this setting. On the other hand, while electronic money cannot be easily protected against double-spending, quantum money does not have this vulnerability, thanks to the uncertainty principle.