ITR/SI(SPIII): An Information Theoretic Approach to Secret Key Generation for Encrypted Communication in a Network

信息安全是通信网络中一个至关重要的问题。我们提出了一种在网络节点之间实现完整性、身份验证和隐私的新方法。我们解决的主要挑战是在这样的网络中生成和建立密钥，以便在节点之间进行后续的安全加密通信。我们的方法基于信息论，提供了对密钥生成问题的新见解，并为密码系统设计中的新技术和算法的发展提供了希望。我们的方法基于最近的理论发展，它的一个重要优势在于它能够确保提高信息安全水平。它使用严格的信息论保密或安全概念，而不是所有当前使用的密码系统所基于的计算安全和复杂性理论安全概念。信息论保密的统计概念实际上保证了合法消息和秘钥对被认为具有窃听和窃听能力的对手是隐藏的，而且在计算资源方面不受限制。这与现有的安全概念形成鲜明对比，后者依赖于当前解决某些潜在计算问题所面临的困难；质数分解和量子计算的最新进展指出了基于这种安全概念的密码系统的潜在漏洞。我们的方法的第二个重要优点是，它可以在开始和在层中系统地研究密钥生成，将不同层的密钥分配给网络中不同的节点子集。此特性对于保证拓扑变化的网络中的信息安全特别重要，特别是当某些节点被禁用或不再被授权和可靠时。在这种情况下，幸存或剩余的授权节点可以从一层密钥切换到另一层密钥，以维护它们之间的信息安全。提出的研究计划解决了与上述网络密钥生成相关的几个重要问题。主要目标是通过在不安全的公共通道上交换“相关”信息，并通过从嘈杂但安全的通道中提取“共同随机性”来建立密钥；这些密钥必须被隐藏起来，以防对手窃听公共频道，并可能拥有额外的窃听能力。将对节点之间的交换施加显式的“lq\lq速率限制”，描述与使用共享公共信道相关的带宽限制，例如在无线环境中。一项创新功能和有用的技术装置涉及引入“lq助手”节点（例如，密钥建立协议中的集中式或可信服务器），该节点在适当时可以通过向节点提供额外的相关信息或计算资源来促进密钥生成。在另一个与当前实践显著不同的地方，密钥将使用随机化方法生成，并借鉴源编码和信道编码的多用户信息理论技术。我们提出的研究预计将导致几个重要的和创新的贡献。首先，我们的信息理论框架将为节点网络中的密钥生成问题提供新的有价值的理论见解，同时补充当前基于计算复杂性的方法。其次，我们在密钥设计中使用的数据压缩和信道编码技术将导致对层中生成密钥的新颖实用技术和算法的探索。第三，我们提出的框架将为现有密钥密码系统提供的信息理论安全程度的定量和比较评估提供一种手段，从而支持或削弱当前的安全性主张。所提出的工作的一个重要组成部分是开发用于在网络中分层生成密钥的新算法和配套软件。最后，通过引入新的模型和技术，所提出的工作将导致信息论的潜在进展。

Information security is an issue of critical importance in communication networks. We propose a novel approach for achieving integrity,authentication and privacy among the nodes of a network. The principal challenge that we address concerns the generation and establishment of secret keys in such a network for subsequent secure encrypted communication among the nodes. Our approach, which is based on information theory, provides new insights into the problem of secret key generation, and holds promise for the development of novel techniques and algorithms in the design of cryptosystems. An important strength of our approach, which is based on recent theoretical developments, lies in its ability to assure an enhanced level of information security. It uses a stringent notion of information theoretic secrecy or security rather than the notions of computational security and complexity-theoretic security on which all currently used cryptosystems are based. The statistical notion of information theoretic secrecy guarantees that legitimate messages and secret keys are, in effect, concealed from an adversary who is assumed to possess wiretapping and eavesdropping capabilities, and is, furthermore, not limited in terms of computational resources. This is in contrast with the existing notion of security which relies on the difficulty currently faced in solving certain underlying computational problems; recent advances in factorization into primes and quantum computing point to the potential vulnerability of cryptosystems based on this notion of security. A second important strength of our approach is that it enables a systematic study of secret key generation, at the outset and in layers, with different layers of secret keys being assigned to different subsets of nodes in the network. This feature is particularly relevant for guaranteeing information security in networks with changing topologies, particularly when some nodes are either disabled or cease to be authorized and reliable. In such situations, the surviving or remaining authorized nodes can switch from one layer of secret keys to another so as to maintain information security among themselves. The proposed program of research addresses several important issues associated with with the aforementioned generation of secret keys in a network. A prime objective is the establishment of secret keys by means of exchanges of "correlated" information over insecure public channels, and through the extraction of "common randomness" from noisy but secure channels; such keys must be concealed from an adversary who can eavesdrop on the public channels, and may possess additional wiretapping capabilities. Explicit \lq\lq rate constraints" will be imposed on exchanges between the nodes, depicting bandwidth limitations associated with the use of shared public channels, e.g., in a wireless environment. An innovative feature, and a useful technical device, involves the introduction of a \lq\lq helper" node (e.g., a centralized or trusted server in a key establishment protocol)which, when appropriate, can serve to facilitate secret key generation by the nodes by furnishing them additional correlated information or computational resources. In another significant departure from current practice, secret keys will be generated using randomization methods and drawing on techniques from the multi-user information theory of source coding and channel coding. Our proposed research is expected to lead to several significant and innovative contributions. Firstly, our information theoretic framework will provide new and valuable theoretical insights into the problem of secret key generation in a network of nodes,while complementing the current approach based on computational complexity. Second, our use of techniques for data compression and channel coding in thedesign of secret keys will lead to an exploration of novel practical techniques and algorithms for secretkey generation in layers. Third, our proposed framework will afford a means for a quantitative and comparative assessment of the extent of information theoretic security provided by existing secret key cryptosystems, thereby buttressing or weakening current claims of security. An important component of the proposed work is the development of new algorithms and accompanying software for the layered generation of secret keys in a network. Finally, the proposed work will lead to potential advances in information theory through the introduction of new models and techniques.