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I'm writing a high school math paper on RSA and I'm wondering if it's possible to relate calculus to RSA. Is calculus used for any part of RSA? It can be for proving equations/theorems, for generating keys, for cracking RSA, etc.

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No. ${}{}{}\;\;$ – Ricky Demer Jan 5 '14 at 6:30
Every part of math is related to any other if you try hard enough. – Thomas Jan 5 '14 at 6:38
@Ricky - Yes: Analytic Number Theory. To O.P.: Not in any meaningful way without what in America is graduate level mathematics. – figlesquidge Jan 5 '14 at 11:12
I read a bunch of Wikipedia articles about Analytic Number Theory, isn't it about the distribution of prime numbers? Can you tell me what is the graduate level mathematics? I can try understanding it. – Leo Jiang Jan 6 '14 at 22:44
A good reason why the simple answer is no (to the question): calculus is about mostly continuous functions, when cryptography deals with discrete function only. – fgrieu Mar 28 '14 at 11:37

Generally, no. There is no calculus in the design and implementation of the RSA. There are two things that could add some analysis in the whole scheme of things:

  • Maybe involving the Prime Number Theorem, which explains why we won't run out of prime numbers to choose from. Some proofs of the theorem use complex analysis (including the simplest known proof, from Donald J. Newman).

  • About primality testing: In the paper describing the AKS algorithm, "PRIMES is in P", there is a lemma (3.1) which is proven here. Analysis is used in the proof.

You can see that calculus is not directly connected to the RSA cryptosystem but there are some fundamentals that need calculus to be proven.

The quote below is generally true:

Every part of math is related to any other if you try hard enough. – Thomas

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