Proving Cryptographic C Programs Secure with General-Purpose Verification Tools

Security protocols, such as TLS or Kerberos, and security devices such as the Trusted Platform Module (TPM), Hardware Security Modules (HSMs) or PKCS#11 tokens, are central to many computer interactions. Yet, such security critical components are still often found vulnerable to attack after their deployment, either because the specification is insecure, or because of implementation errors. Techniques exist to construct machine-checked proofs of security properties for abstract specifications. However, this may leave the final executable code, often written in lower level languages such as C, vulnerable both to logical errors, and low-level flaws. Recent work on verifying security properties of C code is often based on soundly extracting, from C programs, protocol models on which security properties can be proved. However, in such methods, any change in the C code, however trivial, may require one to perform a new and complex security proof. Our goal is therefore to develop or identify a framework in which security properties of cryptographic systems can be formally proved, and that can also be used to soundly verify, using existing general-purpose tools, that a C program shares the same security properties. We argue that the current state of general-purpose verification tools for the C language, as well as for functional languages, is sufficient to achieve this goal, and illustrate our argument by developing two verification frameworks around the VCC verifier. In the symbolic model, we illustrate our method by proving authentication and weak secrecy for implementations of several network security protocols. In the computational model, we illustrate our method by proving authentication and strong secrecy properties for an exemplary key management API, inspired by the TPM

A Note on \u27Further Improving Efficiency of Higher-Order Masking Scheme by Decreasing Randomness Complexity\u27

Zhang, Qiu and Zhou propose two optimised masked algorithms for computing functions of the form $x \mapsto x \cdot \ell(x)$ for any linear function $\ell$. They claim security properties. We disprove their first claim by exhibiting a first order flaw that is present in their first proposed algorithm scheme at all orders. We put their second claim into question by showing that their proposed algorithm, as published, is not well-defined at all orders, making use of variables before defining them. We then also exhibit a counterexample at order 2, that we believe generalises to all even orders

Certified computer-aided cryptography: efficient provably secure machine code from high-level implementations

We present a computer-aided framework for proving concrete security bounds for cryptographic machine code implementations. The front-end of the framework is an interactive verification tool that extends the EasyCrypt framework to reason about relational properties of C-like programs extended with idealised probabilistic operations in the style of code-based security proofs. The framework also incorporates an extension of the CompCert certified compiler to support trusted libraries providing complex arithmetic calculations or instantiating idealized components such as sampling operations. This certified compiler allows us to carry to executable code the security guarantees established at the high-level, and is also instrumented to detect when compilation may interfere with side-channel countermeasures deployed in source code. We demonstrate the applicability of the framework by applying it to the RSA-OAEP encryption scheme, as standard- ized in PKCS#1 v2.1. The outcome is a rigorous analysis of the advantage of an adversary to break the security of as- sembly implementations of the algorithms specified by the standard. The example also provides two contributions of independent interest: it bridges the gap between computer-assisted security proofs and real-world cryptographic implementations as described by standards such as PKCS,and demonstrates the use of the CompCert certified compiler in the context of cryptographic software development.ONR -Office of Naval Research(N000141210914

Bringing State-Separating Proofs to EasyCrypt - A Security Proof for Cryptobox

Machine-checked cryptography aims to reinforce confidence in the primitives and protocols that underpin all digital security. However, machine-checked proof techniques remain in practice difficult to apply to real-world constructions. A particular challenge is structured reasoning about complex constructions at different levels of abstraction. The State-Separating Proofs (SSP) methodology for guiding cryptographic proofs by Brzuska, Delignat-Lavaud, Fournet, Kohbrok and Kohlweiss (ASIACRYPT\u2718) is a promising contestant to support such reasoning. In this work, we explore how SSPs can guide EasyCrypt formalisations of proofs for modular constructions. Concretely, we propose a mapping from SSP to EasyCrypt concepts which enables us to enhance cryptographic proofs with SSP insights while maintaining compatibility with existing EasyCrypt proof support. To showcase our insights, we develop a formal security proof for the Cryptobox family of public-key authenticated encryption schemes based on non-interactive key exchange and symmetric authenticated encryption. As a side effect, we obtain the first formal security proof for NaCl\u27s instantiation of Cryptobox. Finally we discuss changes to the practice of SSP on paper and potential implications for future tool designers

Verifying constant-time implementations

The constant-time programming discipline is an effective countermeasure against timing attacks, which can lead to complete breaks of otherwise secure systems. However, adhering to constant-time programming is hard on its own, and extremely hard under additional efficiency and legacy constraints. This makes automated verification of constant-time code an essential component for building secure software. We propose a novel approach for verifying constant- time security of real-world code. Our approach is able to validate implementations that locally and intentionally violate the constant-time policy, when such violations are benign and leak no more information than the pub- lic outputs of the computation. Such implementations, which are used in cryptographic libraries to obtain impor- tant speedups or to comply with legacy APIs, would be declared insecure by all prior solutions. We implement our approach in a publicly available, cross-platform, and fully automated prototype, ct-verif, that leverages the SMACK and Boogie tools and verifies optimized LLVM implementations. We present verifica- tion results obtained over a wide range of constant-time components from the NaCl, OpenSSL, FourQ and other off-the-shelf libraries. The diversity and scale of our ex- amples, as well as the fact that we deal with top-level APIs rather than being limited to low-level leaf functions, distinguishes ct-verif from prior tools. Our approach is based on a simple reduction of constant-time security of a program P to safety of a prod- uct program Q that simulates two executions of P. We formalize and verify the reduction for a core high-level language using the Coq proof assistant.The first two authors were funded by Project “TEC4Growth - Pervasive Intelligence, Enhancers and Proofs of Concept with Industrial Impact/NORTE-01-0145-FEDER-000020”, which is fi- nanced by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF). The third and fourth authors were supported by projects S2013/ICE2731 N-GREENS Software-CM and ONR Grants N000141210914 (AutoCrypt) and N000141512750 (SynCrypt). The fourth author was also supported by FP7 Marie Cure Actions-COFUND 291803 (Amarout II). We thank Peter Schwabe for providing us with a collection of negative examples. We thank Hovav Shacham, Craig Costello and Patrick Longa for helpful observations on our verification results. TEC4Growth - Pervasive Intelligence, Enhancers and Proofs of Concept with Industrial Impact/NORTE-01-0145-FEDER-000020info:eu-repo/semantics/publishedVersio

Certified computer-aided cryptography: efficient provably secure machine code from high-level implementations

We present a computer-aided framework for proving concrete security bounds for cryptographic machine code implementations. The front-end of the framework is an interactive verification tool that extends the EasyCrypt framework to reason about relational properties of C-like programs extended with idealised probabilistic operations in the style of code-based security proofs. The framework also incorporates an extension of the CompCert certified compiler to support trusted libraries providing complex arithmetic calculations or instantiating idealised components such as sampling operations. This certified compiler allows us to carry to executable code the security guarantees established at the high-level, and is also instrumented to detect when compilation may interfere with side-channel countermeasures deployed in source code. We demonstrate the applicability of the framework with the RSA-OAEP encryption scheme, as standardized in PKCS#1 v2.1. The outcome is a rigorous analysis of the advantage of an adversary to break the security of assembly implementations of the algorithms specified by the standard. The example also provides two contributions of independent interest: it is the first application of computer-aided cryptographic tools to real-world security, and the first application of CompCert to cryptographic software

Guiding a general-purpose C verifier to prove cryptographic protocols

We describe how to verify security properties of C code for cryptographic protocols by using a general-purpose verifier. We prove security theorems in the symbolic model of cryptography. Our techniques include: use of ghost state to attach formal algebraic terms to concrete byte arrays and to detect collisions when two distinct terms map to the same byte array; decoration of a crypto API with contracts based on symbolic terms; and expression of the attacker model in terms of C programs. We rely on the general-purpose verifier VCC; we guide VCC to prove security simply by writing suitable header files and annotations in implementation files, rather than by changing VCC itself. We formalize the symbolic model in Coq in order to justify the addition of axioms to VCC.Comment: To appear in Journal of Computer Securit

Machine-checked proofs for electronic voting: privacy and verifiability for Belenios

International audienceWe present a machine-checked security analysis of Belenios-a deployed voting protocol used already in more than 200 elections. Belenios extends Helios with an explicit registration authority to obtain eligibility guarantees. We offer two main results. First, we build upon a recent framework for proving ballot privacy in EasyCrypt. Inspired by our application to Belenios, we adapt and extend the privacy security notions to account for protocols that include a registration phase. Our analysis identifies a trust assumption which is missing in the existing (pen and paper) analysis of Belenios: ballot privacy does not hold if the registrar misbehaves, even if the role of the registrar is seemingly to provide eligibility guarantees. Second, we develop a novel framework for proving strong verifiability in EasyCrypt and apply it to Belenios. In the process, we clarify several aspects of the pen-and-paper proof, such as how to deal with revote policies. Together, our results yield the first machine-checked analysis of both ballot privacy and verifiability properties for a deployed electronic voting protocol. Perhaps more importantly, we identify several issues regarding the applicability of existing definitions of privacy and verifiability to systems other than Helios. While we show how to adapt the definitions to the particular case of Belenios, our findings indicate the need for more general security notions for electronic voting protocols with registration authorities

Mechanised Models and Proofs for Distance-Bounding

In relay attacks, a man-in-the-middle adversary impersonates a legitimate party and makes it this party appear to be of an authenticator, when in fact they are not. In order to counteract relay attacks, distance-bounding protocols provide a means for a verifier (e.g., an payment terminal) to estimate his relative distance to a prover (e.g., a bankcard). We propose FlexiDB, a new cryptographic model for distance bounding, parameterised by different types of fine-grained corruptions. FlexiDB allows to consider classical cases but also new, generalised corruption settings. In these settings, we exhibit new attack strategies on existing protocols. Finally, we propose a proof-of-concept mechanisation of FlexiDB in the interactive cryptographic prover EasyCrypt. We use this to exhibit a flavour of man-in-the-middle security on a variant of MasterCard\u27s contactless-payment protocol

Verified Proofs of Higher-Order Masking

In this paper, we study the problem of automatically verifying higher-order 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 \emph{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\u27s ability to give useful information when proofs fail, by rediscovering existing attacks and discovering new ones