Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor

Why the State Cannot “Abolish Marriage” A Partial Defense of Legal Marriage Based on the Structure of Intimate Duties

Does a liberal state have a legitimate interest in defining the terms of intimate relationships? Recently, several scholars have answered this question “no” and concluded that the state should abolish marriage, along with all other categories of intimate status. While politically infeasible, these proposals offer a powerful thought experiment. In this Article, I use this thought experiment to argue that the law cannot avoid relying on intimate status norms and has legitimate reasons to retain an intimate status like marriage. The argument has three parts. First, even if the law abolished licensed status categories, ordinary doctrines in tort, contract and equity would still tailor rights to the nature of intimate relationships. The law cannot avoid intimate status norms. Second, private law cannot avoid status because intimate relationships involve “imperfect duties.” Imperfect duties may be fulfilled in many ways, which gives intimates discretion to decide how, when and to what extent to act, constrained by subjective commitment to the relationship. Private law can enforce intimate duties only if it replaces the couples’ discretion with status norms and commitment with sanctions. Last, I argue that marital status offers a way to manage the tension created by imperfect intimate rights, permitting couples to retain discretion without abandoning protection. Spouses retain discretion during marriage because the law defers protection of marital rights until divorce, when it can uses equitable divorce rules to protect marital rights and ensure neither spouse benefits unfairly from the suspension of ordinary private law