In this talk, we will introduce the fundamentals of quantum computing and explore the significant risks it poses to current cybersecurity systems, particularly public-key cryptography. We will then present post-quantum cryptography (PQC) as a promising solution to these challenges, and provide an overview of the global efforts—led by institutions like NIST—to standardize quantum-resistant algorithms.

A brief survey of the main mathematical areas behind PQC will follow, including lattices, multivariate polynomials, hash-based signatures, and error-correcting codes. Finally, we will discuss the current limitations and challenges in transitioning to post-quantum systems, such as performance trade-offs, key and signature sizes, and compatibility with existing internet protocols.