New tools for designing and analysing MPC/FHE/ZK-friendly primitives

Recently, new symmetric primitives have been proposed for advanced protocols such as multi-party computation, in combination with fully homomorphic encryption, or in various zero-knowledge proof systems. These protocols have put forward the need to minimize the number of multiplications performed by the primitive in large finite fields. Classical symmetric algorithms are then inappropriate in this context, and these protocols have to be combined with symmetric primitives with particular properties. While the number of such primitives has increased significantly, only a few cryptanalysis works have been proposed.

In this talk, we will present new tools for both design and cryptanalysis. First, we will propose a security analysis of the MiMC block cipher, one of the first primitives proposed in this new context, giving a detailed understanding of the evolution of the algebraic degree of this cipher. We will also discuss the algebraic degree of Chaghri, a FHE-friendly cipher. Finally, we will move on to the designer’s side to introduce a new vision for the design of such primitives, exploiting a previously unknown link with the CCZ-equivalence.