Explore the intricacies of cryptography and number theory in this 25-minute conference talk from MathCrypt 2022. Delve into the topic of "Mildly Short Vectors in Ideals of Cyclotomic Fields Without Quantum Computers" as presented by TheIACR. Learn about the close principal multiple problem, norm relations, S-Units derived from norm relations, and ideal decomposition. Discover the applications of these concepts and their complexity. Gain insights into cutting-edge research in mathematical cryptography and its implications for non-quantum computing environments.