Quantifying Lattice Cryptosystem Security in the Presence of Side Information

Abstract

Lattice-based cryptosystems are promising candidates for secure, quantum- resistant encryption. We studied how their security is affected by additional ”side information” about system secrets. Building on prior geometric models, we implemented algorithms to compute a maximally inscribed ellipsoid, provid- ing a more conservative estimate of side information’s impact. We also inves- tigated and quantified a novel technique for embedding lattice cryptosystems into this geometric state space. Additionally, our team applied this improved mathematical framework towards two concrete lattice cryptosystems, CKKS and Kyber. For CKKS, the team investigated the tradeoff in concrete secu- rity versus message precision for various levels of noise flooding. For Kyber, we analyzed power consumption data to infer information about the secret key. Overall, our research provides more information about the overall security of the algorithms that protect people’s privacy in an increasingly interconnected world.