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We model and analyze the Signal end-to-end messaging protocol within the UC framework. In particular: - We formulate an ideal functionality that captures end-to-end secure messaging, in a setting with PKI and an untrusted server, against an adversary that has full control over the network and can adaptively and momentarily compromise parties at any time and obtain their entire internal states. In particular our analysis captures the forward secrecy and recovery-of-security properties of Signal and the conditions under which they break. - We model the main components of the Signal architecture (PKI and long-term keys, the backbone continuous-key-exchange or "asymmetric ratchet," epoch-level symmetric ratchets, authenticated encryption) as individual ideal functionalities that are realized and analyzed separately and then composed using the UC and Global-State UC theorems. - We show how the ideal functionalities representing these components can be realized using standard cryptographic primitives under minimal hardness assumptions. Our modeling introduces additional innovations that enable arguing about the security of Signal irrespective of the underlying communication medium, as well as secure composition of dynamically generated modules that share state. These features, together with the basic modularity of the UC framework, will hopefully facilitate the use of both Signal-as-a-whole and its individual components within cryptographic applications. Two other features of our modeling are the treatment of fully adaptive corruptions, and making minimal use of random oracle abstractions. In particular, we show how to realize continuous key exchange in the plain model, while preserving security against adaptive corruptions. 

Abstract Hypothesis testing is one of the most common types of data analysis and forms the backbone of scientific research in many disciplines. Analysis of variance (ANOVA) in particular is used to detect dependence between a categorical and a numerical variable. Here we show how one can carry out this hypothesis test under the restrictions of differential privacy. We show that the F -statistic, the optimal test statistic in the public setting, is no longer optimal in the private setting, and we develop a new test statistic F 1 with much higher statistical power. We show how to rigorously compute a reference distribution for the F 1 statistic and give an algorithm that outputs accurate p -values. We implement our test and experimentally optimize several parameters. We then compare our test to the only previous work on private ANOVA testing, using the same effect size as that work. We see an order of magnitude improvement, with our test requiring only 7% as much data to detect the effect.