Implementing Lattice-Based Cryptography

Abstract

The thesis is about implementation of LWE/MLWE encryption schemes in C++ and the use of the Number Theoretic Transform (NTT) in order to get faster mul- tiplication operations over certain rings. We explore how much speed up we get by using NTT in our different schemes, comparing performance of our NTT im- plementation with the MulMod function of the NTL Library and the schoolbook multiplication. We use Cooley-Turkey algorithm in the NTT forward step and Gentleman-Sande algorithm in the NTT inverse step with ordinary modular re- duction. After some experiments we came to the conclusion that, when we are working on R_q = Z_q[X ]/(X^N + 1), for relative small N with our NTT implemen- taion we get a performance similar compared to the MulMod function and for all N we get much better results compared to the schoolbook multiplication.