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Explore fundamental concepts in algorithmic number theory through this 18-minute conference talk from Crypto 2025, chaired by Niv Gilboa and presented by TheIACR. Delve into computational methods and algorithms used in number theory applications within cryptography, examining theoretical foundations and practical implementations. Learn about mathematical techniques for solving number-theoretic problems efficiently, including algorithms for factorization, discrete logarithms, and primality testing. Discover how these algorithmic approaches contribute to modern cryptographic systems and security protocols. Gain insights into the intersection of pure mathematics and computational complexity as applied to cryptographic research. This presentation serves as the first part of a two-part series on algorithmic number theory, providing essential background for understanding advanced cryptographic concepts and their mathematical underpinnings.
