CAREER: A Physical Understanding of Secrecy

Southern Illinois University At Carbondale, Carbondale IL

Investigators

Abstract

From intelligence briefings to ecommerce, nearly all levels of society rely on the secure transmission of private information. When two or more parties share secret data, often there are certain actions they can perform to strengthen their information security. For example, sometimes revealing partial information to an unwanted eavesdropper can actually improve the overall security. This project seeks to develop a quantitative picture of how secrecy evolves as the trusted parties manipulate their data and publicly share part of their information with one another. A novel approach to this problem will be adopted through the use of recently developed techniques in the study of quantum entanglement and the theory of entanglement transformations. The notion of secrecy will be placed on the same fundamental level as quantum entanglement in that both will be viewed as precious physical resources that can be manipulated and used for various information processing tasks. Investigating the connection between classical secrecy and quantum entanglement will not only offer a new level of unification between quantum mechanics and classical information theory, but it will also yield a fresh perspective on how quantum and classical physics differ. Ultimately, the deeper understanding of classical secrecy developed in this project will lead to improved security analysis and new methodologies for securely transmitting information. This research program investigates fundamental questions in quantum information theory and classical cryptography. A typical quantum key distribution (QKD) protocol (like those employed by commercial QKD machines) consists of two separate phases - called Alice and Bob - who use a quantum channel to exchange quantum information between them. However, in this process an eavesdropper - named Eve - may interact with their state so that all three systems are described by the joint quantum state ρABE. Eventually the parties measure their respective systems and obtain measurement outcomes, i.e. classical data. But due to the indeterminism of quantum mechanics, this measurement data can only be described by some tripartite probability distribution PABE. The second phase of the QKD protocol is purely classical and now consists of Alice and Bob using local operations and public communication to convert the distribution PABE into secret key states, which are perfectly correlated bits shared between Alice and Bob, yet completely hidden from Eve. This process is known as public key agreement, or secret key distillation. Using secret key states, Alice and Bob will be able to transmit data secretly from Eve, regardless of her computational power. The distribution PABE is said to possess "secret correlations" since using public key agreement, it can be converted into secret key states. Classical systems that share secret correlations behave remarkably similar to quantum systems that share entanglement. In particular, both quantum entanglement and secret correlations are capable of being transformed, degraded, and enhanced through local physical processing and global classical communication. In this project, a mathematical framework will be constructed that is suitable for studying the most general physical manipulations of secret correlations, something currently lacking in the research literature. Within this framework, new analytic tools will be developed to study the crucial problem of secret key distillation and the broader question of when one type of secret correlations can be transformed into another. A particular focus will be on generating new secrecy monotones and measures that do not rely exclusively on information-theoretic quantities such as entropy and mutual information. Additionally, novel cryptographic paradigms will be introduced that are inspired by similar primitives in quantum information theory, such as random entanglement distillation and entanglement combing. An underlying goal of this project will be to unify classical secrecy and quantum entanglement as physical analogs. Under such a correspondence, known techniques and results in entanglement theory can be applied in the study of secrecy, and vice versa.