Subversion-resilient Authenticated key-exchange (AKE) aims to achieve the guarantees of secure AKE even in the presence of an adversary that has tampered with parts of the protocol's implementation. One way to achieve subversion-resilient AKE is the use of Reverse Firewalls (RFs), an untrusted third-party that can restore security. Recent work[17] highlights the challenges of designing RFs for practical secure channel-establishment.

Modern attestation based on Trusted Execution Environments (TEEs) can significantly reduce the risk of secret compromise, allowing users to securely perform sensitive computations such as running cryptographic protocols for authentication across security critical services. However, this has made TEEs a high-value target, driving an arms race between novel compromise attacks and continuous TEEs updates. Ideally, we want to achieve Post-Compromise Security (PCS): even after a TEE compromise, we can update it back into a secure state. However, at the same time, we would like to guarantee the privacy of users, in particular preventing providers (such as Intel, Google, or Samsung) or services from tracking users across services. This requires unlinkability, which seems incompatible with standard PCS healing mechanisms. In this work, we develop TokenWeaver, the first privacy-preserving post-compromise secure attestation method with automated formal proofs for its core properties. Our construction weaves together two types of token chains, one of which is linkable and the other is unlinkable. We provide the formal models based on the Tamarin and DeepSec provers, including protocol, security properties, and proofs for reproducibility, as well as a proof-of-concept implementation in python that shows the simplicity and applicability of our solution.

During the last decades, many advances in the field of automated security protocol analysis have seen the field mature and grow from being applicable to toy examples, to modeling intricate protocol standards and finding real-world vulnerabilities that extensive manual analysis had missed. However, modern security protocols often contain elements for which such tools were not originally designed, such as protocols that construct, by design, terms of unbounded size, such as counters, trees, and blockchains. Protocol analysis tools such as Tamarin and ProVerif have some very restricted support, but typically lack the ability to effectively reason about dynamically growing unbounded-depth terms. In this work, we introduce subterm-based proof techniques that are tailored for automated protocol analysis in the Tamarin prover. In several case studies, we show that these techniques improve automation (allow for analyzing more protocols, or remove the need for manually specified invariants), efficiency (reduce proof size for existing analyses), and expressive power (enable new kinds of properties). In particular, we provide the first automated proofs for TreeKEM, S/Key, and Tesla Scheme 2; and we show substantial benefits, most notably in WPA2 and 5G-AKA, two of the largest automated protocol proofs.

We provide the first mechanized post-quantum sound security protocol proofs. We achieve this by developing PQ-BC, a computational first-order logic that is sound with respect to quantum attackers, and corresponding mechanization support in the form of the PQ-SQUIRREL prover. Our work builds on the classical BC logic [7] and its mechanization in the SQUIRREL [5] prover. Our development of PQ-BC requires making the BC logic sound for a single interactive quantum attacker. We implement the PQ-SQuiRREL prover by modifying SQUIRREL, relying on the soundness results of PQ-BC and enforcing a set of syntactic conditions; additionally, we provide new tactics for the logic that extend the tool’s scope. Using PQ-SQUIRREL, we perform several case studies, thereby giving the first mechanical proofs of their computational post-quantum security. These include two generic constructions of KEM based key exchange, two sub-protocols from IKEv1 and IKEv2, and a proposed post-quantum variant of Signal’s X3DH protocol. Additionally, we use PQ-SQuiRREL to prove that several classical SQUIRREL case studies are already post-quantum sound.

We study decidability problems for equivalence of probabilistic programs for a core probabilistic programming language over finite fields of fixed characteristic. The programming language supports uniform sampling, addition, multiplication, and conditionals and thus is sufficiently expressive to encode Boolean and arithmetic circuits. We consider two variants of equivalence: The first one considers an interpretation over the finite field F q , while the second one, which we call universal equivalence, verifies equivalence over all extensions F q k of F q . The universal variant typically arises in provable cryptography when one wishes to prove equivalence for any length of bitstrings, i.e., elements of F 2 k for any k . While the first problem is obviously decidable, we establish its exact complexity, which lies in the counting hierarchy. To show decidability and a doubly exponential upper bound of the universal variant, we rely on results from algorithmic number theory and the possibility to compare local zeta functions associated to given polynomials. We then devise a general way to draw links between the universal probabilistic problems and widely studied problems on linear recurrence sequences. Finally, we study several variants of the equivalence problem, including a problem we call majority, motivated by differential privacy. We also define and provide some insights about program indistinguishability, proving that it is decidable for programs always returning 0 or 1.

Given the central importance of designing secure protocols, providing solid mathematical foundations and computer-assisted methods to attest for their correctness is becoming crucial. Here, we elaborate on the formal approach introduced by Bana and Comon in [10], [11], which was originally designed to analyze protocols for a fixed number of sessions, and lacks support for proof mechanization.In this paper, we present a framework and an interactive prover allowing to mechanize proofs of security protocols for an arbitrary number of sessions in the computational model. More specifically, we develop a meta-logic as well as a proof system for deriving security properties. Proofs in our system only deal with high-level, symbolic representations of protocol executions, similar to proofs in the symbolic model, but providing security guarantees at the computational level. We have implemented our approach within a new interactive prover, the Squirrel prover, taking as input protocols specified in the applied pi-calculus, and we have performed a number of case studies covering a variety of primitives (hashes, encryption, signatures, Diffie-Hellman exponentiation) and security properties (authentication, strong secrecy, unlinkability).

Passwords are still the most widespread means for authenticating users, even though they have been shown to create huge security problems. This motivated the use of additional authentication mechanisms in so-called multi-factor authentication protocols. In this article, we define a detailed threat model for this kind of protocol: While in classical protocol analysis attackers control the communication network, we take into account that many communications are performed over TLS channels, that computers may be infected by different kinds of malware, that attackers could perform phishing, and that humans may omit some actions. We formalize this model in the applied pi calculus and perform an extensive analysis and comparison of several widely used protocols—variants of Google 2-step and FIDO’s U2F (Yubico’s Security Key token). The analysis is completely automated, generating systematically all combinations of threat scenarios for each of the protocols and using the P ROVERIF tool for automated protocol analysis. To validate our model and attacks, we demonstrate their feasibility in practice, even though our experiments are run in a laboratory environment. Our analysis highlights weaknesses and strengths of the different protocols. It allows us to suggest several small modifications of the existing protocols that are easy to implement, as well as an extension of Google 2-step that improves security in several threat scenarios.

We provide a composition framework together with a variety of composition theorems allowing to split the security proof of an unbounded number of sessions of a compound protocol into simpler goals. While many proof techniques could be used to prove the subgoals, our model is particularly well suited to the Computationally Complete Symbolic Attacker (ccsA) model.

We study decidability problems for equivalence of probabilistic programs, for a core probabilistic programming language over finite fields of fixed characteristic. The programming language supports uniform sampling, addition, multiplication and conditionals and thus is sufficiently expressive to encode boolean and arithmetic circuits. We consider two variants of equivalence: the first one considers an interpretation over the finite field Fq, while the second one, which we call universal equivalence, verifies equivalence over all extensions Fqk of Fq. The universal variant typically arises in provable cryptography when one wishes to prove equivalence for any length of bitstrings, i.e., elements of F2k for any k. While the first problem is obviously decidable, we establish its exact complexity which lies in the counting hierarchy. To show decidability, and a doubly exponential upper bound, of the universal variant we rely on results from algorithmic number theory and the possibility to compare local zeta functions associated to given polynomials. Finally we study several variants of the equivalence problem, including a problem we call majority, motivated by differential privacy.

Code-based game-playing is a popular methodology for proving security of cryptographic constructions and side-channel countermeasures. This methodology relies on treating cryptographic proofs as an instance of relational program verification (between probabilistic programs), and decomposing the latter into a series of elementary relational program verification steps. In this paper, we develop principled methods for proving such elementary steps for probabilistic programs that operate over finite fields and related algebraic structures. We focus on three essential properties: program equivalence, information flow, and uniformity. We give characterizations of these properties based on deducibility and other notions from symbolic cryptography. We use (sometimes improve) tools from symbolic cryptography to obtain decision procedures or sound proof methods for program equivalence, information flow, and uniformity. Finally, we evaluate our approach using examples drawn from provable security and from side-channel analysis - for the latter, we focus on the masking countermeasure against differential power analysis. A partial implementation of our approach is integrated in EasyCrypt, a proof assistant for provable security, and in MaskVerif, a fully automated prover for masked implementations.

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, Grégoire 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 Gröbner 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.

Passwords are still the most widespread means for authenticating users, even though they have been shown to create huge security problems. This motivated the use of additional authentication mechanisms used in so-called multi-factor authentication protocols. In this paper we define a detailed threat model for this kind of protocols: while in classical protocol analysis attackers control the communication network, we take into account that many communications are performed over TLS channels, that computers may be infected by different kinds of malwares, that attackers could perform phishing, and that humans may omit some actions. We formalize this model in the applied pi calculus and perform an extensive analysis and comparison of several widely used protocols - variants of Google 2-step and FIDO's U2F. The analysis is completely automated, generating systematically all combinations of threat scenarios for each of the protocols and using the P ROVERIF tool for automated protocol analysis. Our analysis highlights weaknesses and strengths of the different protocols, and allows us to suggest several small modifications of the existing protocols which are easy to implement, yet improve their security in several threat scenarios.

Isolated Execution Environments (IEEs), such as ARM TrustZone and Intel SGX, offer the possibility to execute sensitive code in isolation from other malicious programs, running on the same machine, or a potentially corrupted OS. A key feature of IEEs is the ability to produce reports binding cryptographically a message to the program that produced it, typically ensuring that this message is the result of the given program running on an IEE. We present a symbolic model for specifying and verifying applications that make use of such features. For this we introduce the SℓAPiC process calculus, that allows to reason about reports issued at given locations. We also provide tool support, extending the SAPiC/Tamarin toolchain and demonstrate the applicability of our framework on several examples implementing secure outsourced computation (SOC), a secure licensing protocol and a one-time password protocol that all rely on such IEEs.