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Many proofs of interactive cryptographic protocols (e.g., as in Universal Composability) operate by proving the protocol at hand to be observationally equivalent to an idealized specification. While pervasive, formal tool support for observational equivalence of cryptographic protocols is still a nascent area of research. Current mechanization efforts tend to either focus on diff-equivalence, which establishes observational equivalence between protocols with identical control structures, or require an explicit witness for the observational equivalence in the form of a bisimulation relation. Our goal is to simplify proofs for cryptographic protocols by introducing a core calculus, IPDL, for cryptographic observational equivalences. Via IPDL, we aim to address a number of theoretical issues for cryptographic proofs in a simple manner, including probabilistic behaviors, distributed message-passing, and resource-bounded adversaries and simulators. We demonstrate IPDL on a number of case studies, including a distributed coin toss protocol, Oblivious Transfer, and the GMW multi-party computation protocol. All proofs of case studies are mechanized via an embedding of IPDL into the Coq proof assistant. 

Modern distributed systems involve interactions between principals with limited trust, so cryptographic mechanisms are needed to protect confidentiality and integrity. At the same time, most developers lack the training to securely employ cryptography. We present Viaduct, a compiler that transforms high-level programs into secure, efficient distributed realizations. Viaduct's source language allows developers to declaratively specify security policies by annotating their programs with information flow labels. The compiler uses these labels to synthesize distributed programs that use cryptography efficiently while still defending the source-level security policy. The approach is general, and can be easily extended with new security mechanisms. Our implementation of the compiler comes with an extensible runtime system that includes plug-in support for multiparty computation, commitments, and zero-knowledge proofs. We have evaluated the system on a set of benchmarks, and the results indicate that our approach is feasible and can use cryptography in efficient, nontrivial ways. 

Symbolic methods have been used extensively for proving security of cryptographic protocols in the Dolev-Yao model, and more recently for proving security of cryptographic primitives and constructions in the computational model. However, existing methods for proving security of cryptographic constructions in the computational model often require significant expertise and interaction, or are fairly limited in scope and expressivity. This paper introduces a symbolic approach for proving security of cryptographic constructions based on the Learning With Errors assumption (Regev, STOC 2005). Such constructions are instances of lattice-based cryptography and are extremely important due to their potential role in post-quantum cryptography. Following (Barthe, Gre ́goire and Schmidt, CCS 2015), our approach combines a computational logic and deducibility problems—a standard tool for representing the adversary’s knowledge, the Dolev-Yao model. The computational logic is used to capture (indistinguishability-based) security notions and drive the security proofs whereas deducibility problems are used as side-conditions to control that rules of the logic are applied correctly. We then use AutoLWE, an implementation of the logic, to deliver very short or even automatic proofs of several emblematic constructions, including CPA- PKE (Gentry et al., STOC 2008), (Hierarchical) Identity-Based Encryption (Agrawal et al. Eurocrypt 2010), Inner Product Encryption (Agrawal et al. Asiacrypt 2011), CCA-PKE (Micciancio et al., Eurocrypt 2012). The main technical novelty beyond AutoLWE is a set of (semi-)decision procedures for deducibility problems, using extensions of Grobner basis computations for subalgebras in the (non-)commutative setting (instead of ideals in the commutative setting). Our procedures cover the theory of matrices, which is required for lattice-based assumption, as well as the theory of non-commutative rings, fields, and Diffie-Hellman exponentiation, in its standard, bilinear and multilinear forms. Additionally, AutoLWE supports oracle-relative assumptions, which are used specifically to apply (advanced forms of) the Leftover Hash Lemma, an information-theoretical tool widely used in lattice-based proofs.