Abstract
Jasmin is a programming language for high-speed and high-assurance cryptography. Correctness proofs of Jasmin programs are typically carried out deductively in EasyCrypt. This allows generality, modularity and composable reasoning, but does not scale well for low-level architecture-specific routines. CryptoLine offers a semi-automatic approach to formally verify algebraically-rich low-level cryptographic routines. CryptoLine proofs are self-contained: they are not integrated into higher-level formal verification developments. This paper shows how to soundly use CryptoLine to discharge subgoals in functional correctness proofs for complex Jasmin programs. We extend Jasmin with annotations and provide an automatic translation into a CryptoLine model, where most complex transformations are certified. We also formalize and implement the automatic extraction of the semantics of a CryptoLine proof to EasyCrypt. Our motivating use-case is the X-Wing hybrid KEM, for which we present the first formally verified implementation.

Abstract
Decryption errors play a crucial role in the security of KEMs based on Fujisaki-Okamoto because the concrete security guarantees provided by this transformation directly depend on the probability of such an event being bounded by a small real number. In this paper we present an approach to formally verify the claims of statistical probabilistic bounds for incorrect decryption in lattice-based KEM constructions. Our main motivating example is the PKE encryption scheme underlying ML-KEM. We formalize the statistical event that is used in the literature to heuristically approximate ML-KEM decryption errors and confirm that the upper bounds given in the literature for this event are correct. We consider FrodoKEM as an additional example, to demonstrate the wider applicability of the approach and the verification of a correctness bound without heuristic approximations. We also discuss other (non-approximate) approaches to bounding the probability of ML-KEM decryption.

Abstract
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.

Abstract
KEM-to-PAKE compilers have been recently proposed to leverage postquantum KEM standardization efforts. These typically follow the Encrypted Key Exchange (EKE) paradigm, where the KEM public key is encrypted under a password. While KEM implementations generally aim to execute all secret-dependent computations in constant time, such guarantees do not always extend to computations that depend only on the public key, as public keys are generally assumed to be public. A notable example is ML-KEM, where public keys include a short seed ? from which a large matrix is expanded prior to algebraic computations. This expansion procedure relies on rejection sampling which is, typically, implemented as a variable-time algorithm. However, compilers that follow the EKE paradigm must treat the public key as secret, since knowledge of the public key hidden in a ciphertext enables an offline dictionary attack on the password; therefore, instantiating these compilers with off-the-shelf implementations of ML-KEM or encrypting the public key under a password using variable-time methods (e.g., cycle walking or rejection sampling, as proposed in related PAKE literature) can be problematic. In this paper we show two approaches which yield ML-KEM-based PAKEs resilient to timing attacks. First, we explore constant-time alternatives to ML-KEM rejection sampling, but as one might expect, such methods impose a performance penalty on ML-KEM. Our second approach introduces a new ML-KEM-to-PAKE compiler that mitigates this issue by design: Our proposal transmits the seed ? in the clear, decoupling password-dependent computations from the seed expansion step. This means that off-the-shelf implementations of ML-KEM can be used. Our new protocol Tempo builds on an idea from CHIC (Asiacrypt’24), which considered splitting the KEM public key, and extends the NoIC protocol and proof (ePrint:2025/231) to show protocol simulation in the UC framework, assuming ML-KEM security under adversarially chosen seeds. We justify this assumption via a new hardness assumption, which we call Oracle-MLWE, and show that it is asymptotically equivalent to the MLWE problem in the Random Oracle Model. © 2026, Ruhr-University of Bochum. All rights reserved.

Abstract
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.

Abstract