Information flow policies are confidentiality policies that control information leakage through program execution. A common means to enforce secure information flow is through information flow type systems. Although type systems are compositional and usually enjoy decidable type checking or inference, their extensibility is very poor: type systems need to be redefined and proven sound for each new single variation of security policy and programming language for which secure information flow verification is desired. In contrast, program logics offer a general mechanism to enforce a variety of safety policies, and for this reason are favored in Proof Carrying Code, a promising security architecture for mobile code. However, the encoding of information flow policies in program logics is not straightforward, because they refer to a relation between two program executions. The purpose of this paper is to investigate logical formulations of secure information flow based on the idea of self-composition, that reduces the problem of secure information flow of a program P to a safety property for a programP derived from P , by composing P with a renaming of itself. Self-composition enables the use of standard techniques for information flow policies verification, such as program logics and model checking, suitable in Proof Carrying Code infrastructures. We illustrate the applicability of self-composition in several settings, including different security policies such as non-interference and controlled forms of declassification, and programming languages such as an imperative language with parallel composition, a non-deterministic language, and finally a language with shared mutable data structures.

Differential privacy is a notion of confidentiality that protects the privacy of individuals while allowing useful computations on their private data. Deriving differential privacy guarantees for real programs is a difficult and error-prone task that calls for principled approaches and tool support. Approaches based on linear types and static analysis have recently emerged; however, an increasing number of programs achieve privacy using techniques that cannot be analyzed by these approaches. Examples include programs that aim for weaker, approximate differential privacy guarantees, programs that use the Exponential mechanism, and randomized programs that achieve differential privacy without using any standard mechanism. Providing support for reasoning about the privacy of such programs has been an open problem.We report on CertiPriv, a machine-checked framework for reasoning about differential privacy built on top of the Coq proof assistant. The central component of CertiPriv is a quantitative extension of a probabilistic relational Hoare logic that enables one to derive differential privacy guarantees for programs from first principles. We demonstrate the expressiveness of CertiPriv using a number of examples whose formal analysis is out of the reach of previous techniques. In particular, we provide the first machine-checked proofs of correctness of the Laplacian and Exponential mechanisms and of the privacy of randomized and streaming algorithms from the recent literature.

As cryptographic proofs have become essentially unverifiable, cryptographers have argued in favor of developing techniques that help tame the complexity of their proofs. Game-based techniques provide a popular approach in which proofs are structured as sequences of games, and in which proof steps establish the validity of transitions between successive games. Code-based techniques form an instance of this approach that takes a code-centric view of games, and that relies on programming language theory to justify proof steps. While code-based techniques contribute to formalize the security statements precisely and to carry out proofs systematically , typical proofs are so long and involved that formal verification is necessary to achieve a high degree of confidence. We present CertiCrypt, a framework that enables the machine-checked construction and verification of code-based proofs. CertiCrypt is built upon the general-purpose proof assistant Coq, and draws on many areas, including probability, complexity, algebra, and semantics of programming languages. CertiCrypt provides certified tools to reason about the equivalence of probabilistic programs, including a relational Hoare logic, a theory of observational equivalence, verified program transformations, and game-based techniques such as reasoning about failure events. The usefulness of CertiCrypt is demonstrated through classical examples, including a proof of semantic security of OAEP (with a bound that improves upon [9]), and a proof of existential unforgeability of FDH signatures. Our work provides a first yet significant step towards Halevi's ambitious programme [21] of providing tool support for cryptographic proofs.

Differential power analysis (DPA) is a side-channel attack in which an adversary retrieves cryptographic material by measuring and analyzing the power consumption of the device on which the cryptographic algorithm under attack executes. An effective countermeasure against DPA is to mask secrets by probabilistically encoding them over a set of shares, and to run masked algorithms that compute on these encodings. Masked algorithms are often expected to provide, at least, a certain level of probing security. Leveraging the deep connections between probabilistic information flow and probing security, we develop a precise, scalable, and fully automated methodology to verify the probing security of masked algorithms, and generate them from unprotected descriptions of the algorithm. Our methodology relies on several contributions of independent interest, including a stronger notion of probing security that supports compositional reasoning, and a type system for enforcing an expressive class of probing policies. Finally, we validate our methodology on examples that go significantly beyond the state-of-the-art

In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem. Our methods are based on the observation that differential privacy has deep connections with a generalization of probabilistic couplings, an established mathematical tool for reasoning about stochastic processes. Even when the composition theorem is not helpful, we can often prove privacy by a coupling argument. We demonstrate our methods on two algorithms: the Exponential mechanism and the Above Threshold algorithm, the critical component of the famous Sparse Vector algorithm. We verify these examples in a relational program logic apRHL+, which can construct approximate couplings. This logic extends the existing apRHL logic with more general rules for the Laplace mechanism and the one-sided Laplace mechanism, and new structural rules enabling pointwise reasoning about privacy; all the rules are inspired by the connection with coupling. While our paper is presented from a formal verification perspective, we believe that its main insight is of independent interest for the differential privacy community