Software Implementations of Polynomial Multiplications for Lattice-Based Cryptosystems

<jats:p>This thesis studies the implementation aspects of polynomial multiplication in lattice-based cryptosystems Dilithium, Kyber, Saber, NTRU, and NTRU Prime. As hardware gradually evolves and enormous platforms are in use nowadays, systematic surveys and studies with numerical justification of the merits and drawbacks of implementation techniques require a lot of effort. This thesis systematically covers the relevant mathematical background, various optimization techniques and implementation aspects of polynomial multiplication, and relates them to the optimized implementations across various platforms.</jats:p>