Lattices and Post-Quantum Cryptography

Graduate / Professional

This course explores the role of lattices in modern cryptography. In the last decades, novel computational problems, whose hardness is related to lattices, have been instrumental in cryptography by offering: (a) a basis for "post-quantum" cryptography, (b) cryptographic constructions based on worst-case hard problems, and (c) numerous celebrated cryptographic protocols unattainable from other cryptographic assumptions. This course covers the foundations of lattice-based cryptography from fundamental definitions to advanced cryptographic constructions. More precisely, we introduce the Learning with Error (LWE) and the Short Integer Solutions (SIS) problems and study their unique properties, such as the fact that their average-case hardness is based on the worst-case hardness of lattice problems. Next, we cover lattice constructions of advanced cryptographic primitives, such as fully homomorphic encryption and signature schemes. Finally, we introduce some notions of quantum cryptography and explore the role of lattices in this area. Overall, this course offers insights on the foundations and recent advancements in lattice-based cryptography. Prerequisites: CPSC 467/567 or equivalent and linear algebra. HTBA