Abstract We report our experience in the formal verification of the reference implementation of the Beacon Chain. The Beacon Chain is the backbone component of the new Proof-of-Stake Ethereum 2.0 network: it is in charge of tracking information about the validators, their stakes, their attestations (votes) and if some validators are found to be dishonest, to slash them (they lose some of their stakes). The Beacon Chain is mission-critical and any bug in it could compromise the whole network. The Beacon Chain reference implementation developed by the Ethereum Foundation is written in Python, and provides a detailed operational description of the state machine each Beacon Chain’s network participant (node) must implement. We have formally specified and verified the absence of runtime errors in (a large and critical part of) the Beacon Chain reference implementation using the verification-friendly language Dafny. During the course of this work, we have uncovered several issues, proposed verified fixes. We have also synthesised functional correctness specifications that enable us to provide guarantees beyond runtime errors. Our software artefact with the code and proofs in Dafny is available at https://github.com/ConsenSys/eth2.0-dafny .

In symmetric cryptology the resistance to attacks depends critically on the nonlinearity properties of the Boolean functions describing cipher components like Substitution boxes (S‐boxes). Some of the most effective methods known to generate functions that satisfy multiple criteria are based on evolutionary heuristics. In this paper, we improve on these algorithms by employing an adaptive strategy. Additionally, using recent improvements in the understanding of these combinatorial structures, we discover essential properties of the graph formed by affine equivalence classes of Boolean functions, which offers several advantages as a conceptual model for multiobjective seeking evolutionary heuristics. Finally, we propose the first major global cooperative effort to discover new bounds for cryptographic properties of Boolean functions.

We present a new heuristic algorithm that efficiently generates Boolean Bent functions, which have desirable cryptographic properties including maximum nonlinearity. By using an evolutionary approach to design, we discover an easy way to find the algebraic normal forms of new bent functions. These algorithms run efficiently, making them suitable for engineering the components of modern symmetric encryption algorithms. In addition, we enable the algorithm to determine when new classes of bent functions have been discovered, by developing more a more effective approach to the equivalence class distinguishing problem. These results allow the efficient automated generation of many optimal Boolean functions that can be guaranteed to be affine non-equivalent, thus offering far more accurate classification of bent functions than previously available.

In symmetric cryptology (which is an essential part of modern computer security), the resistance to attacks depends critically on the nonlinearity properties of the Boolean functions describing cipher components like S-boxes. Some of the most effective methods known to generate functions that satisfy multiple criteria are based on evolutionary heuristics. In this paper, we improve on these algorithms by employing an adaptive strategy. Additionally, using recent improvements in the understanding of these combinatorial structures, we discover essential properties of the graph formed by affine equivalence classes of Boolean functions, which offers several advantages as a conceptual model for multiobjective seeking evolutionary heuristics. Finally, we propose the first major global cooperative effort to discover new bounds for cryptographic properties of Boolean functions.