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Division property is proposed as a generalized integral property at Eurocrypt 2015 by Yosuke Todo in his paper Structural evaluation by generalized integral property, And in paper Integral Cryptanalysis on Full MISTY1.

It says " linear operation xor does not affect the division property", which means if every element in the input multiset xor a constant (or a key), the Division Property of the output multiset will be the same with the Division Property of the input multiset.

Could anyone please tell me is there any provement of this conclusion?

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    $\begingroup$ It's unclear to me what "the division property" is. [Apocryphal note: this was written for the original question]. $\endgroup$
    – fgrieu
    Commented Jun 11 at 13:30
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    $\begingroup$ Bad translation of diffusion prob'ly. However I've closed it until this is clarified $\endgroup$
    – Maarten Bodewes
    Commented Jun 12 at 0:12
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    $\begingroup$ I add more information about Division Property, and explain the question, could you please reopen it? $\endgroup$
    – L0ngxing
    Commented 16 hours ago
  • $\begingroup$ While moderators can reopen a question by a single click, it's better to let community to vote for it. For this site, 3 re-open votes is enough (people can't vote negatively - i.e. there's no "objection" vote). But the most important thing for you to do now, is to clarify if you've mis-typed "Diffusion" as "Division"; or if it's indeed "Division", what it means. I'm sure people would like to have this Q re-open and learn more about the paper you're looking at. $\endgroup$
    – DannyNiu
    Commented 5 hours ago
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    $\begingroup$ I've restructured you prose, added link, and casted the 1st re-open vote. $\endgroup$
    – DannyNiu
    Commented 5 hours ago

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