We propose a hybrid formal verification approach that combines high-level deductive reasoning and circuit-based reasoning and apply it to highly optimized cryptographic assembly code. Our approach permits scaling up formal verification in two complementary directions: 1) it reduces the proof effort required for low-level functions where the computation logics are obfuscated by the intricate use of architecture-specific instructions and 2) it permits amortizing the effort of proving one implementation by using equivalence checking to propagate the guarantees to other implementations of the same computation using different optimizations or targeting different architectures. We demonstrate our approach via an extension to the EasyCrypt proof assistant and by revisiting formally verified implementations of ML-KEM in Jasmin. As a result, we obtain the first formally verified implementation of ML-KEM that offers performance comparable to the fastest non-verified implementation in x86-64 architectures.

We revisit the privacy and security analyses of FIDO2, a widely deployed standard for passwordless authentication on the Web. We discuss previous works and conclude that each of them has at least one of the following limitations: (i) impractical trusted setup assumptions, (ii) security models that are inadequate in light of state of the art of practical attacks, (iii) not analyzing FIDO2 as a whole, especially for its privacy guarantees. Our work addresses these gaps and proposes revised security models for privacy and authentication. Equipped with our new models, we analyze FIDO2 modularly and focus on its component protocols, WebAuthn and CTAP2, clarifying their exact security guarantees. In particular, our results, for the first time, establish privacy guarantees for FIDO2 as a whole. Furthermore, we suggest minor modifications that can help FIDO2 provably meet stronger privacy and authentication definitions and withstand known and novel attacks.

FIDO2 is becoming a defacto standard for passwordless authentication. Using FIDO2 and WebAuthn, web applications can enable users to associate cryptographic credentials to their profiles, and then rely on an external authenticator (e.g., a hardware token plugged into the USB port) to perform strong signature-based authentication when accessing their accounts. The security of FIDO2 has been theoretically validated, but these analyses follow the threat model adopted in the FIDO2 design and explicitly exclude some attack vectors as being out of scope. In this paper we show that two of these attacks, which appear to be folklore in the community, are actually straightforward to launch in practice (user PIN extraction, impersonation and rogue key registration). We demonstrate a deployment over vanilla Linux distributions and commercial FIDO2 authenticators. We discuss the potential impact of our results, which we believe will contribute to the improvement of future versions of the protocol.