Abstract. We present EasyCrypt, an automated tool for elaborating security proofs of cryptographic systems from proof sketches-compact, formal representations of the essence of a proof as a sequence of games and hints. Proof sketches are checked automatically using off-the-shelf SMT solvers and automated theorem provers, and then compiled into verifiable proofs in the CertiCrypt framework. The tool supports most common reasoning patterns and is significantly easier to use than its predecessors. We argue that EasyCrypt is a plausible candidate for adoption by working cryptographers and illustrate its application to security proofs of the Cramer-Shoup and Hashed ElGamal cryptosystems.

Abstract. In this paper, we study the problem of automatically verifying higherorder masking countermeasures. This problem is important in practice (weaknesses have been discovered in schemes that were thought secure), but is inherently exponential: for t-order masking, it involves proving that every subset of t intermediate variables is distributed independently of the secrets. Some type systems have been proposed to help cryptographers check their proofs, but many of these approaches are insufficient for higher-order implementations. We propose a new method, based on program verification techniques, to check the independence of sets of intermediate variables from some secrets. Our new language-based characterization of the problem also allows us to design and implement several algorithms that greatly reduce the number of sets of variables that need to be considered to prove this independence property on all valid adversary observations. The result of these algorithms is either a proof of security or a set of observations on which the independence property cannot be proved. We focus on AES implementations to check the validity of our algorithms. We also confirm the tool's ability to give useful information when proofs fail, by rediscovering existing attacks and discovering new ones.

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

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.

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

We present a way to enjoy the power of SAT and SMT provers in Coq without compromising soundness. This requires these provers to return not only a yes/no answer, but also a proof witness that can be independently rechecked. We present such a checker, written and fully certified in Coq. It is conceived in a modular way, in order to tame the proofs' complexity and to be extendable. It can currently check witnesses from the SAT solver ZChaff and from the SMT solver veriT. Experiments highlight the efficiency of this checker. On top of it, new reflexive Coq tactics have been built that can decide a subset of Coq's logic by calling external provers and carefully checking their answers.

Software-based countermeasures provide effective mitigation against side-channel attacks, often with minimal efficiency and deployment overheads. Their effectiveness is often amenable to rigorous analysis: specifically, several popular countermeasures can be formalized as information flow policies, and correct implementation of the countermeasures can be verified with state-of-the-art analysis and verification techniques. However, in absence of further justification, the guarantees only hold for the language (source, target, or intermediate representation) on which the analysis is performed. We consider the problem of preserving side-channel countermeasures by compilation for cryptographic "constant-time", a popular countermeasure against cache-based timing attacks. We present a general method, based on the notion of constant-timesimulation, for proving that a compilation pass preserves the constant-time countermeasure. Using the Coq proof assistant, we verify the correctness of our method and of several representative instantiations.