Two-party quantum cryptography

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In 1984, Bennett and Brassard proposed a scheme allowing two parties to agree on a secret key provided they have access to a channel capable of transmitting quantum bits. This scheme, called quantum key distribution, is remarkable since it achieves something impossible through classical means alone. Until the mid 90's quantum information appeared to be cryptographers' best friend. Expectations were that all modern cryptographic applications could be resolved unconditionally using quantum communication whereas classical cryptography could only hope for security relying upon unproven computational assumptions out of which the majority do not hold against quantum adversaries. One essential class of cryptographic applications are the ones involving two parties willing to collaborate but otherwise not trusting each other. Many daily electronic transactions are of that kind, making two-party cryptography a critical tool for the information age. An example is our frequent interactions with ATMs asking us to identify ourselves before being granted access to our bank account. In 1995, Mayers and Lo & Chau shattered this dream when they prove that the most important cryptographic primitives for two-party cryptography cannot be implemented securely using quantum communication. On the other hand, quantum protocols have been found for weak two-party primitives otherwise impossible using classical communication alone. Unlike for key distribution, the capabilities of quantum cryptography in the two-party setting are not well understood. The project's main goal is to provide a deeper understanding for the true power of quantum cryptography in two-party applications. Improving our insight on what it can achieve in this setting could have important consequences for the design of systems providing security in electronic transactions. New systems inspired by this research could offer privacy more efficiently and under weaker assumptions. Even entirely classical protocols could benefit from this work by extending the realm of their security to adversaries in possession of quantum computers. Any satisfactory advance toward our main objective would improve our comprehension of the differences between classical and quantum information.