Implementations of the Transport Layer Security (TLS) protocol must handle a variety of protocol versions and extensions, authentication modes, and key exchange methods. Confusingly, each combination may prescribe a different message sequence between the client and the server. We address the problem of designing a robust composite state machine that correctly multiplexes between these different protocol modes. We systematically test popular open-source TLS implementations for state machine bugs and discover several critical security vulnerabilities that have lain hidden in these libraries for years, and have now finally been patched due to our disclosures. Several of these vulnerabilities, including the recently publicized FREAK flaw, enable a network attacker to break into TLS connections between authenticated clients and servers. We argue that state machine bugs stem from incorrect compositions of individually correct state machines. We present the first verified implementation of a composite TLS state machine in C that can be embedded into OpenSSL and accounts for all its supported cipher suites. Our attacks expose the need for the formal verification of core components in cryptographic protocol libraries, our implementation demonstrates that such mechanized proofs are within reach, even for mainstream TLS implementations.

The record layer is the main bridge between TLS applications and internal sub-protocols. Its core functionality is an elaborate form of authenticated encryption: streams of messages for each sub-protocol (handshake, alert, and application data) are fragmented, multiplexed, and encrypted with optional padding to hide their lengths. Conversely, the sub-protocols may provide fresh keys or signal stream termination to the record layer. Compared to prior versions, TLS 1.3 discards obsolete schemes in favor of a common construction for Authenticated Encryption with Associated Data (AEAD), instantiated with algorithms such as AES-GCM and ChaCha20-Poly1305. It differs from TLS 1.2 in its use of padding, associated data and nonces. It also encrypts the content-type used to multiplex between sub-protocols. New protocol features such as early application data (0-RTT and 0.5-RTT) and late handshake messages require additional keys and a more general model of stateful encryption. We build and verify a reference implementation of the TLS record layer and its cryptographic algorithms in F*, a dependently typed language where security and functional guarantees can be specified as pre-and post-conditions. We reduce the high-level security of the record layer to cryptographic assumptions on its ciphers. Each step in the reduction is verified by typing an F* module, for each step that involves a cryptographic assumption, this module precisely captures the corresponding game. We first verify the functional correctness and injectivity properties of our implementations of one-time MAC algorithms (Poly1305 and GHASH) and provide a generic proof of their security given these two properties. We show the security of a generic AEAD construction built from any secure one-time MAC and PRF. We extend AEAD, first to stream encryption, then to length-hiding, multiplexed encryption. Finally, we build a security model of the record layer against an adversary that controls the TLS sub-protocols. We compute concrete security bounds for the AES_128_GCM, AES_256_GCM, and CHACHA20_POLY1305 ciphersuites, and derive recommended limits on sent data before re-keying. We plug our implementation of the record layer into the miTLS library, confirm that they interoperate with Chrome and Firefox, and report initial performance results. Combining our functional correctness, security, and experimental results, we conclude that the new TLS record layer (as described in RFCs and cryptographic standards) is provably secure, and we provide its first verified implementation.

The HTTPS ecosystem is the foundation on which Internet security is built. At the heart of this ecosystem is the Transport Layer Security (TLS) protocol, which in turn uses the X.509 public-key infrastructure and numerous cryptographic constructions and algorithms. Unfortunately, this ecosystem is extremely brittle, with headline-grabbing attacks and emergency patches many times a year. We describe our ongoing efforts in Everest (The Everest VERified End-to-end Secure Transport) a project that aims to build and deploy a verified version of TLS and other components of HTTPS, replacing the current infrastructure with proven, secure software. Aiming both at full verification and usability, we conduct high-level code-based, game-playing proofs of security on cryptographic implementations that yield efficient, deployable code, at the level of C and assembly. Concretely, we use F*, a dependently typed language for programming, meta-programming, and proving at a high level, while relying on low-level DSLs embedded within F* for programming low-level components when necessary for performance and, sometimes, side-channel resistance. To compose the pieces, we compile all our code to source-like C and assembly, suitable for deployment and integration with existing code bases, as well as audit by independent security experts. Our main results so far include (1) the design of Low*, a subset of F* designed for C-like imperative programming but with high-level verification support, and KreMLin, a compiler that extracts Low* programs to C; (2) an implementation of the TLS-1.3 record layer in Low*, together with a proof of its concrete cryptographic security; (3) Vale, a new DSL for verified assembly language, and several optimized cryptographic primitives proven functionally correct and side-channel resistant. In an early deployment, all our verified software is integrated and deployed within libcurl, a widely used library of networking protocols.

The Transport Layer Security (TLS) protocol supports various authentication modes, key exchange methods, and protocol extensions. Confusingly, each combination may prescribe a different message seq...

The Transport Layer Security (TLS) protocol supports various authentication modes, key exchange methods, and protocol extensions. Confusingly, each combination may prescribe a different message sequence between the client and the server, and thus a key challenge for TLS implementations is to define a composite state machine that correctly handles these combinations. If the state machine is too restrictive, the implementation may fail to interoperate with others; if it is too liberal, it may allow unexpected message sequences that break the security of the protocol. We systematically test popular TLS implementations and find unexpected transitions in many of their state machines that have stayed hidden for years. We show how some of these flaws lead to critical security vulnerabilities, such as FREAK. While testing can help find such bugs, formal verification can prevent them entirely. To this end, we implement and formally verify a new composite state machine for OpenSSL, a popular TLS library.

HACL* is a verified portable C cryptographic library that implements modern cryptographic primitives such as the ChaCha20 and Salsa20 encryption algorithms, Poly1305 and HMAC message authentication, SHA-256 and SHA-512 hash functions, the Curve25519 elliptic curve, and Ed25519 signatures. HACL* is written in the F* programming language and then compiled to readable C code. The F* source code for each cryptographic primitive is verified for memory safety, mitigations against timing side-channels, and functional correctness with respect to a succinct high-level specification of the primitive derived from its published standard. The translation from F* to C preserves these properties and the generated C code can itself be compiled via the CompCert verified C compiler or mainstream compilers like GCC or CLANG. When compiled with GCC on 64-bit platforms, our primitives are as fast as the fastest pure C implementations in OpenSSL and libsodium, significantly faster than the reference C code in TweetNaCl, and between 1.1x-5.7x slower than the fastest hand-optimized vectorized assembly code in SUPERCOP. HACL* implements the NaCl cryptographic API and can be used as a drop-in replacement for NaCl libraries like libsodium and TweetNaCl. HACL* provides the cryptographic components for a new mandatory ciphersuite in TLS 1.3 and is being developed as the main cryptographic provider for the miTLS verified implementation. Primitives from HACL* are also being integrated within Mozilla's NSS cryptographic library. Our results show that writing fast, verified, and usable C cryptographic libraries is now practical.

We present Low*, a language for low-level programming and verification, and its application to high-assurance optimized cryptographic libraries. Low* is a shallow embedding of a small, sequential, well-behaved subset of C in F*, a dependently- typed variant of ML aimed at program verification. Departing from ML, Low* does not involve any garbage collection or implicit heap allocation; instead, it has a structured memory model à la CompCert, and it provides the control required for writing efficient low-level security-critical code. By virtue of typing, any Low* program is memory safe. In addition, the programmer can make full use of the verification power of F* to write high-level specifications and verify the functional correctness of Low* code using a combination of SMT automation and sophisticated manual proofs. At extraction time, specifications and proofs are erased, and the remaining code enjoys a predictable translation to C. We prove that this translation preserves semantics and side-channel resistance. We provide a new compiler back-end from Low* to C and, to evaluate our approach, we implement and verify various cryptographic algorithms, constructions, and tools for a total of about 28,000 lines of code. We show that our Low* code delivers performance competitive with existing (unverified) C cryptographic libraries, suggesting our approach may be applicable to larger-scale low-level software.

We present a new, completely redesigned, version of F*, a language that works both as a proof assistant as well as a general-purpose, verification-oriented, effectful programming language. In support of these complementary roles, F* is a dependently typed, higher-order, call-by-value language with _primitive_ effects including state, exceptions, divergence and IO. Although primitive, programmers choose the granularity at which to specify effects by equipping each effect with a monadic, predicate transformer semantics. F* uses this to efficiently compute weakest preconditions and discharges the resulting proof obligations using a combination of SMT solving and manual proofs. Isolated from the effects, the core of F* is a language of pure functions used to write specifications and proof terms---its consistency is maintained by a semantic termination check based on a well-founded order. We evaluate our design on more than 55,000 lines of F* we have authored in the last year, focusing on three main case studies. Showcasing its use as a general-purpose programming language, F* is programmed (but not verified) in F*, and bootstraps in both OCaml and F#. Our experience confirms F*'s pay-as-you-go cost model: writing idiomatic ML-like code with no finer specifications imposes no user burden. As a verification-oriented language, our most significant evaluation of F* is in verifying several key modules in an implementation of the TLS-1.2 protocol standard. For the modules we considered, we are able to prove more properties, with fewer annotations using F* than in a prior verified implementation of TLS-1.2. Finally, as a proof assistant, we discuss our use of F* in mechanizing the metatheory of a range of lambda calculi, starting from the simply typed lambda calculus to System F-omega and even micro-F*, a sizeable fragment of F* itself---these proofs make essential use of F*'s flexible combination of SMT automation and constructive proofs, enabling a tactic-free style of programming and proving at a relatively large scale.

In response to increasing demand for elliptic curve cryptography, and specifically for curves that are free from the suspicion of influence by the NSA, new elliptic curves such as Curve25519 and Curve448 are currently being standardized, implemented, and deployed in major protocols such as Transport Layer Security. As with all new cryptographic code, the correctness of these curve implementations is of concern, because any bug or backdoor in this code can potentially compromise the security of important Internet protocols. We present a principled approach towards the verification of elliptic curve implementations by writing them in the dependently-typed programming language F* and proving them functionally correct against a readable mathematical specification derived from a previous Coq development. A key technical innovation in our work is the use of templates to write and verify arbitrary precision arithmetic once and for all for a variety of Bignum representations used in different curves. We also show how to use abstract types to enforce a coding discipline that mitigates side-channels at the source level. We present a verified F* library that implements the popular curves Curve25519, Curve448, and NIST-P256, and we show how developers can add new curves to this library with minimal programming and verification effort.

VerifyThis 2015 was a one-day program verification competition which took place on April 12th, 2015 in London, UK, as part of the European Joint Conferences on Theory and Practice of Software (ETAPS 2015). It was the fourth instalment in the VerifyThis competition series. This article provides an overview of the VerifyThis 2015 event, the challenges that were posed during the competition, and a high-level overview of the solutions to these challenges. It concludes with the results of the competition and some ideas and thoughts for future instalments of VerifyThis.