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Recently reading about CPA, CCA safety security proof. After reading a few papers, the author is in the process of proof. The challenger maintains some lists. I really don’t understand why the challenger wants to maintain some lists, and some of the following steps need to check the list, and some do not need to check?

For example, the security proof of this paper (Thm. phase1) https://ieeexplore.ieee.org/document/8662560

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  • $\begingroup$ Interesting question, but it could be enhanced by providing more details about where the lists are introduced and your own thoughts about it. $\endgroup$
    – Maarten Bodewes ♦
    Commented Apr 15, 2021 at 21:34
  • $\begingroup$ Would this be your answer at crypto.stackexchange.com/a/72662/82720? $\endgroup$
    – Cloud Cho
    Commented Apr 17, 2021 at 6:36
  • $\begingroup$ @CloudCho Thank you for your answer, but it seems not. I want to know why the challenger maintains some lists or table on the paper. What is the intention? $\endgroup$
    – Hung LI
    Commented Apr 22, 2021 at 5:42
  • $\begingroup$ @MaartenBodewes It is currently speculated to maintain the consistency of the query $\endgroup$
    – Hung LI
    Commented Apr 22, 2021 at 5:46

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