I am trying to understand some concepts such as DH problem and its variants. I have the following question from the book I read. (note that I translated the question from my language to english)

Assume that two parties are using DH to make key exchange, so they need to use a group with an element x in it. Let's also assume that our group have large order, but our selected element x is not. For example, say that the order of x is 30, then compare DH and decisional DH for this case.

In my opinion, because of our element x has small order, it is clearly open to brute-force attacks for DH (maybe I am wrong), but what about DDH problem here, will having a small order cause a problem?

  • 1
    $\begingroup$ When quoting something, always provide a link or reference, even if it is not English. $\endgroup$
    – schroeder
    Dec 2, 2023 at 20:28
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    $\begingroup$ The wiki quote If it were possible to efficiently compute discrete logs in G G, then the DDH assumption would not hold in G G $\endgroup$
    – kelalaka
    Dec 2, 2023 at 20:37


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