Clémence Bouvier. Butterfly Constructions: From Boolean Foundations to Remaining Challenges over Prime Fields.

In this talk, we revisit the Butterfly construction and explore it beyond its native Boolean setting. While the behaviour of butterflies over binary fields is now well understood, extending the analysis to prime fields introduces new challenges. In particular, exponential sums are more difficult to control, thereby complicating linear cryptanalysis. However, by applying techniques from modern algebraic geometry, such as Deligne's theorem, we can derive bounds on the linear behaviour of butterflies over prime fields. This highlights the link between symmetric cryptography and cohomology, offering new perspectives in the analysis of the Butterfly construction and other similar designs.