Certified Quantum Security

ended

"Digital communication permeates all areas of today's daily life. Cryptographic protocols are used to secure that communication. Quantum communication and the advent of quantum computers both threaten existing cryptographic solutions, and create new opportunities for secure protocols. The security of cryptographic systems is normally ensured by mathematical proofs. Due to human error, however, these proofs often contain errors, limiting the usefulness of said proofs. This is especially true in the case of quantum protocols since human intuition is well-adapted to the classical world, but not to quantum mechanics. To resolve this problem, methods for verifying cryptographic security proofs using computers (i.e., for ""certifying"" the security) have been developed. Yet, all existing verification approaches handle classical cryptography only - for quantum protocols, no approaches exist. This project will lay the foundations for the verification of quantum cryptography. We will design logics and software tools for developing and verifying security proofs on the computer, both for classical protocols secure against quantum computer (post-quantum security) and for protocols that use quantum communication. Our main approach is the design of a logic (quantum relational Hoare logic, qRHL) for reasoning about the relationship between pairs of quantum programs, together with an ecosystem of manual and automated reasoning tools, culminating in fully certified security proofs for real-world quantum protocols. As a final result, the project will improve the security of protocols in the quantum age, by removing one possible source of human error. In addition, the project directly impacts the research community, by providing new foundations in program verification, and by providing cryptographers with new tools for the verification of their protocols. "