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Explore advanced mathematical foundations in cryptography through this 19-minute conference talk presented at TCC 2024, the third installment in a five-part Math & Foundations session chaired by Siyao Guo. Delve into cutting-edge research and theoretical developments that underpin modern cryptographic systems, gaining insights from leading experts in the field. Access supplementary materials including research papers and presentation slides through the official TCC 2024 program to deepen your understanding of the mathematical principles driving contemporary cryptographic innovations.