Recorded 25 July 2022. Jonathan Katz of the University of Maryland presents "Introduction to Cryptography I" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This lecture will serve as a "crash course" in modern cryptography for those with no prior exposure to the topic. I will start by discussing the importance of provable security, emphasizing the role of definitions and complexity-theoretic assumptions. After a brief discussion of perfect secrecy and the one-time pad, I will then introduce the notions of computational security, pseudorandom generators, and pseudorandom functions, and show an example of a proof-by-reduction. Part I: Suggested reading: Katz & Lindell, "Introduction to Modern Cryptography (3rd edition)," Chapters 1, 2, and 3. Learn more online at: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-on-post-quantum-and-quantum-cryptography/?tab=overview