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This lecture by the instructor covers the concept of nonce-based cryptography, focusing on retaining security in cryptographic schemes when randomness fails. The presentation outlines the motivations behind the paper 'Retaining Security when Randomness Fails', discusses security goals and definitions, introduces non-space public key encryption, and explores the applications of nonce-based cryptography. The lecture delves into the challenges posed by randomness failures, the need for new security definitions, the role of hedge extractors, and the construction of nonce-based public key encryption. It also explains the security goals of non-space privacy one and non-space privacy two, the use of hedge extractors in creating deterministic schemes, and the advantages of nonce-based signatures in overcoming randomness failures in existing signature schemes.