CAREER: A Physical Understanding of Secrecy

从情报简报到电子商务，社会的几乎所有层面都依赖于私人信息的安全传输。当两方或多方共享机密数据时，他们通常可以执行某些操作来加强其信息安全性。例如，有时向不受欢迎的窃听者透露部分信息实际上可以提高整体安全性。该项目旨在开发一种定量的图像，说明当受信任的各方操纵他们的数据并公开分享他们的部分信息时，保密是如何演变的。我们将采用最新发展的量子纠缠研究技术和纠缠转换理论来解决这个问题。保密的概念将被置于与量子纠缠相同的基础水平，因为两者都将被视为宝贵的物理资源，可以被操纵并用于各种信息处理任务。研究经典保密和量子纠缠之间的联系不仅将提供量子力学和经典信息论之间统一的新水平，而且还将为量子和经典物理学的不同提供新的视角。最终，在该项目中开发的对经典保密的更深入理解将导致改进的安全分析和安全传输信息的新方法。本研究计划探讨量子信息理论和经典密码学的基本问题。典型的量子密钥分发（QKD）协议（与商业QKD机器使用的协议一样）由两个独立的阶段组成——称为Alice和Bob——他们使用量子通道在他们之间交换量子信息。然而，在这个过程中，一个名为Eve的窃听者可能会与它们的状态相互作用，这样所有三个系统都可以用联合量子态ABE来描述。最终，各方测量各自的系统并获得测量结果，即经典数据。但由于量子力学的不确定性，这种测量数据只能用某种三部分概率分布PABE来描述。QKD协议的第二阶段是纯经典的，现在由Alice和Bob使用本地操作和公共通信将分发PABE转换为秘密密钥状态，这些状态是Alice和Bob之间共享的完美相关比特，但对Eve完全隐藏。这个过程被称为公钥协议或密钥蒸馏。使用秘钥状态，爱丽丝和鲍勃将能够秘密地从夏娃那里传输数据，而不管她的计算能力如何。由于使用公钥协议，分发PABE可以转换为密钥状态，因此被称为具有“秘密相关性”。共享秘密关联的经典系统的行为与共享纠缠的量子系统非常相似。特别是，量子纠缠和秘密关联都能够通过局部物理处理和全局经典通信进行转换、退化和增强。在这个项目中，将构建一个数学框架，适用于研究秘密关联的最一般的物理操作，这是目前研究文献中缺乏的。在此框架内，将开发新的分析工具来研究密钥蒸馏的关键问题以及何时可以将一种类型的秘密关联转换为另一种类型的更广泛的问题。一个特别的重点将是产生新的保密单调和措施，不完全依赖于信息论的量，如熵和互信息。此外，将引入受量子信息论中类似原语启发的新型密码范式，如随机纠缠蒸馏和纠缠梳理。这个项目的一个潜在目标是将经典保密和量子纠缠作为物理类比统一起来。在这种对应关系下，纠缠理论中的已知技术和结果可以应用于保密研究，反之亦然。

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.