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In this paper we present the first formally verified implementations of Kyber and, to the best of our knowledge, the first such implementations of any post-quantum cryptosystem. We give a (readable) formal specification of Kyber in the EasyCrypt proof assistant, which is syntactically very close to the pseudocode description of the scheme as given in the most recent version of the NIST submission. We present high-assurance open-source implementations of Kyber written in the Jasmin language, along with machine-checked proofs that they are functionally correct with respect to the EasyCrypt specification. We describe a number of improvements to the EasyCrypt and Jasmin frameworks that were needed for this implementation and verification effort, and we present detailed benchmarks of our implementations, showing that our code achieves performance close to existing hand-optimized implementations in C and assembly.

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This document presents the case study for the ABZ 2023 conference. The case study introduces a safety critical interactive system called AMAN (Arrival MANager), which is a partly-autonomous scheduler of landing sequences of aircraft in airports. This interactive systems interleaves Air Traffic Controllers activities with automation in AMAN. While some AMAN systems are currently deployed in airports, we consider here only a subset of functions which represent a challenge in modelling and verification. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.