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.    During the last fifteen years or so, research in quantum information theory has improved a great deal our understanding of the cryptographic power and limits of quantum mechanics. One thing is clear, the quantum cryptographic landscape is very different from its classical counterpart and its outlines are still not very well understood. The anticipated outcomes of this program include a better understanding of what is possible and at what cost, new primitives that can be implemented in practice and that provide satisfactory security guarantees, and information theoretical tools allowing to shed new lights on the foundations of quantum cryptography. The program will contribute in a better understanding of how classical and quantum methods can be used together to improve cryptographic constructs for the digital age, at the outset of the quantum age.