Spectre attacks void the guarantees of constant-time cryptographic code by leaking secrets during speculative execution. Recent research shows that such code can be protected from Spectre-v1 attacks with minimal overhead, but leaves open the question of protecting against other Spectre variants. In this work, we design, validate, implement, and verify a new approach to protect cryptographic code against all known classes of Spectre attacks, in particular Spectre-RSB. Our approach combines a new value-dependent information-flow type system that ensures that no secrets leak even under speculative execution and a compiler transformation that enables it on the generated low-level code. We first prove the soundness of the type system and the correctness of the compiler transformation using the Coq proof assistant. We then implement our approach in the Jasmin framework for high-assurance cryptography and demonstrate that the overhead incurred by all Spectre protections is below 2% for most cryptographic primitives and reaches only about 5--7% for the more complex post-quantum key-encapsulationkmechanism Kyber.

Compilers often weaken or even discard software-based countermeasures commonly used to protect programs against side-channel attacks; worse, they may also introduce vulnerabilities that attackers can exploit. The solution to this problemis to develop compilers that preserve such countermeasures. Prior work establishes that (a mildly modified version of) the CompCert and Jasmin formally verified compilers preserve constant-time, an information flow policy that ensures that programs are protected against timing side-channel attacks. However, nothing is known about preservation of speculative constant-time, a strengthening of the constant-time policythat ensures that programs are protected against Spectre-v1 attacks. We first show that preservation of speculative constant-time fails in practice by providing examples of secure programs whose compilation is not speculative constant-time using GCC (GCC -O0 and GCC -O1) and Jasmin. Then, we define a proof-of-concept compiler that distills some of the critical passes of the Jasmin compiler and use the C oq proof assistant to prove that it preserves speculative constant-time. Finally, we patch the Jasmin speculative constant-time type checker and demonstrate that all cryptographic implementations written in Jasmin can be fixed with minimal impact.

The current gold standard of cryptographic software is to write efficient libraries with systematic protections against timing attacks. In order to meet this goal, cryptographic engineers increasingly use high-assurance cryptography tools. These tools guide programmers and provide rigorous guarantees that can be verified independently by library users. However, high-assurance tools reason about overly simple execution models that elide transient execution leakage. Thus, implementations validated by high-assurance cryptography tools remain potentially vulnerable to transient execution attacks such as Spectre or Meltdown. Moreover, proposed countermeasures are not used in practice due to performance overhead.We propose, analyze, implement and evaluate an approach for writing efficient cryptographic implementations that are protected against Spectre v1 attacks. Our approach ensures speculative constant-time, an information flow property which guarantees that programs are protected against Spectre v1. Speculative constant-time is enforced by means of a (value-dependent) information flow type system. The type system tracks security levels depending on whether execution is misspeculating. We implement our approach in the Jasmin framework for high-assurance cryptography, and use it for protecting all implementations of an experimental cryptographic library that includes highly optimized implementations of symmetric primitives, of elliptic-curve cryptography, and of Kyber, a lattice-based KEM recently selected by NIST for standardization. The performance impact of our protections is very low; for example, less than 1% for Kyber and essentially zero for X25519.

Cryptographic constant-time (CT) is a popular programming discipline used by cryptographic libraries to protect themselves against timing attacks. The CT discipline aims to enforce that program execution does not leak secrets, where leakage is defined by a formal leakage model. In practice, different leakage models coexist, sometimes even within a single library, both to reflect different architectures and to accommodate different security-efficiency trade-offs.

Many security properties of interest are captured by instrumented semantics that model the functional behavior and the leakage of programs. For several important properties, including cryptographic constant-time (CCT), leakage models are sufficiently abstract that one can define instrumented semantics for high-level and low-level programs. One important goal is then to relate leakage of source programs and leakage of their compilation---this can be used, e.g., to prove preservation of CCT. To simplify this task, we put forward the idea of structured leakage. In contrast to the usual modeling of leakage as a sequence of observations, structured leakage is tightly coupled with the operational semantics of programs. This coupling greatly simplifies the definition of leakage transformers that map the leakage of source programs to leakage of their compilation and yields more precise statements about the preservation of security properties. We illustrate our methods on the Jasmin compiler and prove preservation results for two policies of interest: CCT and cost.

We develop a new approach for building cryptographic implementations. Our approach goes the last mile and delivers assembly code that is provably functionally correct, protected against side-channels, and as efficient as hand-written assembly. We illustrate our approach using ChaCha20-Poly1305, one of the two ciphersuites recommended in TLS 1.3, and deliver formally verified vectorized implementations which outperform the fastest non-verified code.We realize our approach by combining the Jasmin framework, which offers in a single language features of high-level and low-level programming, and the EasyCrypt proof assistant, which offers a versatile verification infrastructure that supports proofs of functional correctness and equivalence checking. Neither of these tools had been used for functional correctness before. Taken together, these infrastructures empower programmers to develop efficient and verified implementations by "game hopping", starting from reference implementations that are proved functionally correct against a specification, and gradually introducing program optimizations that are proved correct by equivalence checking.We also make several contributions of independent interest, including a new and extensible verified compiler for Jasmin, with a richer memory model and support for vectorized instructions, and a new embedding of Jasmin in EasyCrypt. © 2020 IEEE.

Timing side-channels are arguably one of the main sources of vulnerabilities in cryptographic implementations. One effective mitigation against timing side-channels is to write programs that do not perform secret-dependent branches and memory accesses. This mitigation, known as "cryptographic constant-time", is adopted by several popular cryptographic libraries. This paper focuses on compilation of cryptographic constant-time programs, and more specifically on the following question: is the code generated by a realistic compiler for a constant-time source program itself provably constant-time? Surprisingly, we answer the question positively for a mildly modified version of the CompCert compiler, a formally verified and moderately optimizing compiler for C. Concretely, we modify the CompCert compiler to eliminate sources of potential leakage. Then, we instrument the operational semantics of CompCert intermediate languages so as to be able to capture cryptographic constant-time. Finally, we prove that the modified CompCert compiler preserves constant-time. Our mechanization maximizes reuse of the CompCert correctness proof, through the use of new proof techniques for proving preservation of constant-time. These techniques achieve complementary trade-offs between generality and tractability of proof effort, and are of independent interest.

We present a high-assurance and high-speed implementation of the SHA-3 hash function. Our implementation is written in the Jasmin programming language, and is formally verified for functional correctness, provable security and timing attack resistance in the EasyCrypt proof assistant. Our implementation is the first to achieve simultaneously the four desirable properties (efficiency, correctness, provable security, and side-channel protection) for a non-trivial cryptographic primitive. Concretely, our mechanized proofs show that: 1) the SHA-3 hash function is indifferentiable from a random oracle, and thus is resistant against collision, first and second preimage attacks; 2) the SHA-3 hash function is correctly implemented by a vectorized x86 implementation. Furthermore, the implementation is provably protected against timing attacks in an idealized model of timing leaks. The proofs include new EasyCrypt libraries of independent interest for programmable random oracles and modular indifferentiability proofs.

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 counter-measures 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-time-simulation, 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.

Jasmin is a framework for developing high-speed and high-assurance cryptographic software. The framework is structured around the Jasmin programming language and its compiler. The language is designed for enhancing portability of programs and for simplifying verification tasks. The compiler is designed to achieve predictability and efficiency of the output code (currently limited to x64 platforms), and is formally verified in the Coq proof assistant. Using the supercop framework, we evaluate the Jasmin compiler on representative cryptographic routines and conclude that the code generated by the compiler is as efficient as fast, hand-crafted, implementations. Moreover, the framework includes highly automated tools for proving memory safety and constant-time security (for protecting against cache-based timing attacks). We also demonstrate the effectiveness of the verification tools on a large set of cryptographic routines.

We present a high-assurance software stack for secure function evaluation (SFE). Our stack consists of three components: i. a verified compiler (CircGen) that translates C programs into Boolean circuits; ii. a verified implementation of Yao's SFE protocol based on garbled circuits and oblivious transfer; and iii. transparent application integration and communications via FRESCO, an open-source framework for secure multiparty computation (MPC). CircGen is a general purpose tool that builds on CompCert, a verified optimizing compiler for C. It can be used in arbitrary Boolean circuit-based cryptography deployments. The security of our SFE protocol implementation is formally verified using EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, and it leverages a new formalization of garbled circuits based on the framework of Bellare, Hoang, and Rogaway (CCS 2012). We conduct a practical evaluation of our approach, and conclude that it is competitive with state-of-the-art (unverified) approaches. Our work provides concrete evidence of the feasibility of building efficient, verified, implementations of higher-level cryptographic systems. All our development is publicly available.

Motivated by applications to security and high efficiency, we propose an automated methodology for validating on low-level intermediate representations the results of a source-level static analysis. Our methodology relies on two main ingredients: a relative-safety checker, an instance of a relational verifier which proves that a program is "safer" than another, and a transformation of programs into defensive form which verifies the analysis results at runtime. We prove the soundness of the methodology, and provide a formally verified instantiation based on the Verasco verified C static analyzer and the CompCert verified C compiler. We experiment with the effectiveness of our approach with client optimizations at RTL level, and static analyses for cache-based timing side-channels and memory usage at pre-assembly levels.

In cryptology, verifiable computing aims at verifying the remote execution of a program on an untrusted machine, based on its I/O and constant-sized evidence collected during its execution. Recent cryptographic schemes and compilers enable practical verifiable computations for some programs written in C, but their soundness with regards to C semantics remains informal and poorly understood. We present the first certified, semantics-preserving compiler for verifiable computing. Based on CompCert and developed in Coq, our compiler targets an architecture whose instructions consist solely of quadratic equations over a large finite field, amenable to succinct verification using the Pinocchio cryptographic scheme. We explain how to encode the integer operations of a C program first to quadratic equations, then to a single cryptographically-checkable polynomial test. We formally prove that, when compilation succeeds, there is a correct execution of the source program for any I/O that pass this test. We link our compiler to the Pinocchio cryptographic runtime, and report experimental results as we compile, run, and verify the execution of sample C programs.

Abstract interpretation provides advanced techniques to infer numerical invariants on programs. There is an abundant literature about numerical abstract domains that operate on scalar variables. This work deals with lifting these techniques to a realistic C memory model. We present an abstract memory functor that takes as argument any standard numerical abstract domain, and builds a memory abstract domain that finely tracks properties about memory contents, taking into account union types, pointer arithmetic and type casts. This functor is implemented and verified inside the Coq proof assistant with respect to the CompCert compiler memory model. Using the Coq extraction mechanism, it is fully executable and used by the Verasco C static analyzer.

This paper reports on the design and soundness proof, using the Coq proof assistant, of Verasco, a static analyzer based on abstract interpretation for most of the ISO C 1999 language (excluding recursion and dynamic allocation). Verasco establishes the absence of run-time errors in the analyzed programs. It enjoys a modular architecture that supports the extensible combination of multiple abstract domains, both relational and non-relational. Verasco integrates with the CompCert formally-verified C compiler so that not only the soundness of the analysis results is guaranteed with mathematical certitude, but also the fact that these guarantees carry over to the compiled code.

We consider the verified compilation of high-level managed languages like Java or C# whose intermediate representations provide support for shared-memory synchronization and automatic memory management. In this environment, the interactions between application threads and the language runtime (e.g., the garbage collector) are regulated by compiler-injected code snippets. Example of snippets include allocation fast paths among others. In our TOPLAS paper we propose a refinement-based proof methodology that precisely relates concurrent code expressed at different abstraction levels, cognizant throughout of the relaxed memory semantics of the underlying processor. Our technique allows the compiler writer to reason compositionally about the atomicity of low-level concurrent code used to implement managed services. We illustrate our approach with examples taken from the verification of a concurrent garbage collector.

We consider the verified compilation of high-level managed languages like Java or C# whose intermediate representations provide support for shared-memory synchronization and automatic memory management. Our development is framed in the context of the Total Store Order relaxed memory model. Ensuring complier correctness is challenging because high-level actions are translated into sequences of nonatomic actions with compiler-injected snippets of racy code; the behavior of this code depends not only on the actions of other threads but also on out-of-order executions performed by the processor. A naïve proof of correctness would require reasoning over all possible thread interleavings. In this article, we propose a refinement-based proof methodology that precisely relates concurrent code expressed at different abstraction levels, cognizant throughout of the relaxed memory semantics of the underlying processor. Our technique allows the compiler writer to reason compositionally about the atomicity of low-level concurrent code used to implement managed services. We illustrate our approach with examples taken from the verification of a concurrent garbage collector.

Recent advances in verification have made it possible to envision trusted implementations of real-world languages. Java with its type-safety and fully specified semantics would appear to be an ideal candidate; yet, the complexity of the translation steps used in production virtual machines have made it a challenging target for verifying compiler technology. One of Java's key innovations, its memory model, poses significant obstacles to such an endeavor. The Java Memory Model is an ambitious attempt at specifying the behavior of multithreaded programs in a portable, hardware agnostic, way. While experts have an intuitive grasp of the properties that the model should enjoy, the specification is complex and not well-suited for integration within a verifying compiler infrastructure. Moreover, the specification is given in an axiomatic style that is distant from the intuitive reordering-based reasonings traditionally used to justify or rule out behaviors, and ill suited to the kind of operational reasoning one would expect to employ in a compiler. This paper takes a step back, and introduces a Buffered Memory Model (BMM) for Java. We choose a pragmatic point in the design space sacrificing generality in favor of a model that is fully characterized in terms of the reorderings it allows, amenable to formal reasoning, and which can be efficiently applied to a specific hardware family, namely x86 multiprocessors. Although the BMM restricts the reorderings compilers are allowed to perform, it serves as the key enabling device to achieving a verification pathway from bytecode to machine instructions. Despite its restrictions, we show that it is backwards compatible with the Java Memory Model and that it does not cripple performance on TSO architectures.