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This lecture covers the Random Oracle Model, Hybrid ElGamal, and the Fujisaki Okamoto Transform. It delves into topics such as Fiat-Shamir and Schnorr signature paradigms, proving security in cryptographic schemes, and the security notions in cryptographic systems. The instructor explains the Fiat-Shamir Signature Paradigm, the concept of existential unforgeability under chosen message attacks, and the implications of the Fiat-Shamir Signature Paradigm in the Random Oracle Model.