Polynomial Multiplication for Post-Quantum Cryptography

With the advance of quantum computers, there is an urgent need to find replacements for public-key cryptography threatened by Shor’s quantum algorithm. This thesis presents work towards understanding post-quantum replacements for key-encapsulation mechanisms and digital signatures from an implementation perspective. The focus of this thesis lies on polynomial multiplication which is at the core of most post-quantum cryptography based on hard lattice problems. The first part covers cryptographic schemes specifically designed to benefit from a particular polynomial multiplication technique: Number-theoretic transforms. The second part covers the other lattice-based schemes that were designed without tailoring parameter choices to a specific multiplication algorithm