Abstract. Modern cryptography relies on digital signature schemes built from a variety of computational assumptions, ranging from lattices and error-correcting codes to multivariate polynomial systems. While these constructions often appear highly specialized, the MPC-in-the-Head paradigm provides a remarkably generic framework that can transform virtually any hard computational problem into a practical signature scheme.

This talk focuses on the latest MPC-in-the-Head frameworks that have made this paradigm practical for real-world post-quantum signatures. We will explain the key ideas behind these modern constructions, how they efficiently instantiate the MPC-in-the-Head approach, and how successive generations of protocols have significantly improved performance while preserving the generic nature of the framework.

Through representative examples, we will show how these frameworks enable the construction of competitive signature schemes from fundamentally different hardness assumptions, including code-based, multivariate, and symmetric cryptography. The goal of this presentation is to provide an accessible overview of the modern MPC-in-the-Head landscape and to illustrate why it has become one of the most versatile approaches to designing post-quantum digital signatures.