Abstract

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. © 2025 Copyright held by the owner/author(s).

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. © 2025 Copyright held by the owner/author(s).

Abstract

Abstract