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Learn about computing generators in cyclotomic integer rings in this 21-minute conference talk presented at Eurocrypt 2017. Explore the Principal Ideal Problem, key generation process, and algorithm complexity reduction. Dive into topics such as smoothness chance trick and implementation wizardry. Gain insights from researchers Jean-François Biasse, Thomas Espitau, Pierre-Alain Fouque, Alexandre Gélin, and Paul Kirchner as they discuss their paper on this cryptographic subject.