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.

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SPHINCS+ is a post-quantum signature scheme that, at the time of writing, is being standardized as SLH-DSA. It is the most conservative option for post-quantum signatures, but the original tight proofs of security were flawed- as reported by Kudinov, Kiktenko and Fedorov in 2020. In this work, we formally prove a tight security bound for SPHINCS+ using the EasyCrypt proof assistant, establishing greater confidence in the general security of the scheme and that of the parameter sets considered for standardization. To this end, we reconstruct the tight security proof presented by Hulsing and Kudinov (in 2022) in a modular way. A small but important part of this effort involves a complex argument relating four different games at once, of a form not yet formalized in EasyCrypt (to the best of our knowledge). We describe our approach to overcoming this major challenge, and develop a general formal verification technique aimed at this type of reasoning. Enhancing the set of reusable EasyCrypt artifacts previously produced in the formal verification of stateful hash-based cryptographic constructions, we (1) improve and extend the existing libraries for hash functions and (2) develop new libraries for fundamental concepts related to hash-based cryptographic constructions, including Merkle trees. These enhancements, along with the formal verification technique we develop, further ease future formal verification endeavors in EasyCrypt, especially those concerning hash-based cryptographic constructions.