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I know that most of the math related to cryptography is number theory/abstract algebra/probability, but I was wondering if there are some algorithms that make use of other fields of math like real/complex analysis, differential equations or linear algebra? Also, what is highest level of mathematics required for cryptography?

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  • $\begingroup$ Also, what is highest level There is no limit, eg. because crypto is continously evolving. $\endgroup$ – deviantfan Oct 6 '17 at 3:14
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    $\begingroup$ Related: What is the lowest level of mathematics required in order to understand how encryption algorithms work? $\endgroup$ – deviantfan Oct 6 '17 at 3:14
  • $\begingroup$ "I know that most of the math related to cryptography is number theory/abstract algebra" Nope, it's mostly probability. $\endgroup$ – fkraiem Oct 6 '17 at 3:21
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    $\begingroup$ There are plenty of linear algebra concepts, and it can be quite useful. Vector spaces show up everywhere when dealing with finite fields, and finite fields are all over crypto. $\endgroup$ – SAI Peregrinus Oct 6 '17 at 3:31
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    $\begingroup$ @SAIPeregrinus Or when dealing with lattices... I wonder if this question might not be primarily opinion based. It really depends on the crypto you want to do. Whatever you do in crypto, you'll always benefit from a good basis in math, and analysis is a very rigorous branch of math, thus a good thing to learn. But I'd say the most "complex" pieces of crypto I've seen so far are all dealing with strange algebraic constructs. $\endgroup$ – Lery Oct 6 '17 at 9:13
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It would be hard to find a category of mathematics not related in some way to cryptography, here is a list of applied mathematics by subject area. Even very abstract mathematics could be future cryptographic tools waiting to happen:

"A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. "

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