PhD Proposal: A Framework for Constructive Quantum Cryptography

Nishant Rodrigues
01.31.2022 12:00 to 14:00


The classical Constructive Cryptography framework simplifies cryptographic proofs by reasoning about systems at higher levels of abstraction and then moving to lower levels only as necessary. We begin by discussing constructive cryptography in the classical setting. This includes defining basic properties of systems within the framework, and algebraic rules for how systems compose together. For the final thesis, we want to address the question of whether the classical framework can be extended to quantum cryptographic protocols.An example of a system widely used in cryptographic protocols is a random bit generator. We introduce the notion of random bit generators in the constructive framework. This includes describing ideal and real random bit generators. In the quantum case, we consider ideal quantum random bit generators, then introduce some state preparation and bit-flip errors to define real quantum random bit generators. We show that the ideal and real generators are close to each other using a distance metric.Since we are interested in quantum protocols, we focus our attention to Quantum Key Distribution (QKD), which is a major branch within quantum cryptography. The goal of QKD is to establish a shared classical secret key between two parties, without leaking the key to an adversary. The devices used in the QKD protocol could be faulty, subject to noise, or even be programmed by the adversary. Device-independent QKD attempts to address this issue using maximally entangled quantum states and Bell inequalities that help identify if the statistics we see during the protocol are correct, and whether there is interference from an adversary. We develop a fully device-independent quantum key distribution protocol based on synchronous correlations, that is symmetric between the two parties involved in the protocol. By symmetric we mean that the actions performed by the two parties is completely interchangeable, which is typically not the case in existing DI-QKD protocols.Our QKD scheme uses random bits to select the measurements each player performs on their respective qubit. As a result, random bit generators are crucial components in the QKD scheme. The QKD scheme assumes that we use ideal random number generators, however, in a real world implementation, there are errors due to the environment and other factors, and so the ideal random bit generator is switched with a real random bit generator. The next natural step, and the proposed work for the dissertation is to show a composable proof of the QKD protocol using real random bit generators in the constructive framework.Examining Committee:

Chair:Co-Char:Department Representative:

Dr. Xiaodi Wu Dr. Brad LackeyDr. David Mount