Abstract. Relational program logics are formalisms for specifying and verifying properties about two programs or two runs of the same program. These properties range from correctness of compiler optimizations or equivalence between two implementations of an abstract data type, to properties like non-interference or determinism. Yet the current technology for relational verification remains underdeveloped. We provide a general notion of product program that supports a direct reduction of relational verification to standard verification. We illustrate the benefits of our method with selected examples, including non-interference, standard loop optimizations, and a state-of-the-art optimization for incremental computation. All examples have been verified using the Why tool.

Abstract. Relational Hoare Logic is a generalization of Hoare logic that allows reasoning about executions of two programs, or two executions of the same program. It can be used to verify that a program is robust or (information flow) secure, and that two programs are observationally equivalent. Product programs provide a means to reduce verification of relational judgments to the verification of a (standard) Hoare judgment, and open the possibility of applying standard verification tools to relational properties. However, previous notions of product programs are defined for deterministic and structured programs. Moreover, these notions are symmetric, and cannot be applied to properties such as refinement, which are asymmetric and involve universal quantification on the traces of the first program and existential quantification on the traces of the second program. Asymmetric products generalize previous notions of products in three directions: they are based on a control-flow graph representation of programs, they are applicable to non-deterministic languages, and they are by construction asymmetric. Thanks to these characteristics, asymmetric products allow to validate abstraction/refinement relations between two programs, and to prove the correctness of advanced loop optimizations that could not be handled by our previous work. We validate their effectiveness by applying a prototype implementation to verify representative examples from translation validation and predicate abstraction.

A common theme in program verification is to relate two programs, for instance to show that they are equivalent, or that one refines the other. Such relationships can be formally established using relational program logics, which are tailored to reason about relations between two programs, or product constructions which allow to build from two programs a product program that emulates the behavior of both input programs. Similarly, product programs and relational program logics can be used to reason about 2-safety properties, an important class of properties that reason about two executions of the same program, and includes as instances non-interference, continuity, and determinism. In this paper, we consider several notions of product programs and explore their relationship with different relational program logics. Moreover, we present applications of product programs to program robustness, non-interference, translation validation, and differential privacy.

International audienceComputer-aided verification provides effective means of analyzing the security of cryptographic primitives. However, it has remained a challenge to achieve fully automated analyses yielding guarantees that hold against computational (rather than symbolic) attacks. This paper meets this challenge for public-key encryption schemes built from trapdoor permutations and hash functions. Using a novel combination of techniques from computational and symbolic cryptography, we present proof systems for analyzing the chosen-plaintext and chosen-ciphertext security of such schemes in the random oracle model. Building on these proof systems, we develop a toolset that bundles together fully automated proof and attack finding algorithms. We use this toolset to build a comprehensive database of encryption schemes that records attacks against insecure schemes, and proofs with concrete bounds for secure ones

Existing pattern-based compiler technology is unable to effectively exploit the full potential of SIMD architectures. We present a new program synthesis based technique for auto-vectorizing performance critical innermost loops. Our synthesis technique is applicable to a wide range of loops, consistently produces performant SIMD code, and generates correctness proofs for the output code. The synthesis technique, which leverages existing work on relational verification methods, is a novel combination of deductive loop restructuring, synthesis condition generation and a new inductive synthesis algorithm for producing loop-free code fragments. The inductive synthesis algorithm wraps an optimized depth-first exploration of code sequences inside a CEGIS loop. Our technique is able to quickly produce SIMD implementations (up to 9 instructions in 0.12 seconds) for a wide range of fundamental looping structures. The resulting SIMD implementations outperform the original loops by 2.0×-3.7×.Motivating Example. Consider the program fragment in Figure 1, which consists of a loop that traverses an array of widget structs (of length len). The loop body checks if the values in the tag and score fields satisfy certain properties and if so returns 1 immediately. If no such widget is found then 0 is returned.

Secure multi-execution (SME) is a dynamic technique to ensure secure information flow. In a nutshell, SME enforces security by running one execution of the program per security level, and by reinterpreting input/output operations w.r.t. their associated security level. SME is sound, in the sense that the execution of a program under SME is non-interfering, and precise, in the sense that for programs that are non-interfering in the usual sense, the semantics of a program under SME coincides with its standard semantics. A further virtue of SME is that its core idea is language-independent; it can be applied to a broad range of languages. A downside of SME is the fact that existing implementation techniques require modifications to the runtime environment, e.g. the browser for Web applications. In this article, we develop an alternative approach where the effect of SME is achieved through program transformation, without modifications to the runtime, thus supporting server-side deployment on the web. We show on an exemplary language with input/output and dynamic code evaluation (modeled after JavaScript's eval) that our transformation is sound and precise. The crux of the proof is a simulation between the execution of the transformed program and the SME execution of the original program. This proof has been machine-checked using the Agda proof assistant. We also report on prototype implementations for a small fragment of Python and a substantial subset of JavaScript.

Existing pattern-based compiler technology is unable to effectively exploit the full potential of SIMD architectures. We present a new program synthesis based technique for auto-vectorizing performance critical innermost loops. Our synthesis technique is applicable to a wide range of loops, consistently produces performant SIMD code, and generates correctness proofs for the output code. The synthesis technique, which leverages existing work on relational verification methods, is a novel combination of deductive loop restructuring, synthesis condition generation and a new inductive synthesis algorithm for producing loop-free code fragments. The inductive synthesis algorithm wraps an optimized depth-first exploration of code sequences inside a CEGIS loop. Our technique is able to quickly produce SIMD implementations (up to 9 instructions in 0.12 seconds) for a wide range of fundamental looping structures. The resulting SIMD implementations outperform the original loops by 2.0×-3.7×.

Using EasyCrypt, we formalize a new modular security proof for one-round authenticated key exchange protocols in the random oracle model. Our proof improves earlier work by Kudla and Paterson (ASIACRYPT 2005) in three significant ways: we consider a stronger adversary model, we provide support tailored to protocols that utilize the Naxos trick, and we support proofs under the Computational DH assumption not relying on Gap oracles. Furthermore, our modular proof can be used to obtain concrete security proofs for protocols with or without adversarial key registration. We use this support to investigate, still using EasyCrypt, the connection between proofs without Gap assumptions and adversarial key registration. For the case of honestly generated keys, we obtain the first proofs of the Naxos and Nets protocols under the Computational DH assumption. For the case of adversarial key registration, we obtain machine-checked and modular variants of the well-known proofs for Naxos, Nets, and Naxos + .