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I am going through the paper "Mental Poker Revisited" by Barnett and Smart.

I understood Section 5 in which the author explains Chaum-Pedersen (CP) protocol and how it is used in methods such as Key Generation, Verifiable Masking Protocol, Verifiable Remasking Protocol, Verifying Decryption Protocol and Joining the game.

I am somewhat unclear in understanding "Mask-Shuffling the deck" in section 4.2 which uses the zero-knowledge proof explained in Figure 1. This function is not explained the way methods in section 5 are explained. How, this method is to be concretized or implemented (similar to the way methods in section 5 are concretized or implemented). If required, how we will be using Chaum-Pedersen (CP) protocol here?

Please help me in understanding.

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