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Verifiable encryption: Comparison between FS01 and CS03

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Consider the following two verifiable encryption schemes for Discrete Logarithm.

FS01: “One Round Threshold Discrete-Log Key Generation without Private Channels” by Pierre-Alain Fouque and Jacques Stern, Section 3.2, "A Proof of Fairness".

CS03: “Practical Verifiable Encryption and Decryption of Discrete Logarithms” by Jan Camenisch and Victor Shoup.

They both rely on Paillier Encryption and originate from around the same time.

Question: Does somebody have a deeper understanding of similarity and differences? Is one to be preferred over the other?

I sit in a Tesla and translated this thread with Ai:

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