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I am a Computer Science student and interested to learn Cryptography to be a researcher in this field. I heard that Number Theory is useful for Cryptography since there are some Crypto systems based on it. I really like Number Theory and have started reading Elementary Number Theory by Burton. So far I have been reading the theorems and trying to prove them myself. Will my approach be useful for Cryptography?

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closed as primarily opinion-based by e-sushi Jul 11 '17 at 10:09

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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It's better to study cryptography and refer to number theory (and other fields) when it's needed.

Nevertheless, Math is very important, if you want to be something better than 'press any key' cryptographer. Mostly, you will need Group Theory, Linear Algebra, Graph Theory, Automata Theory, Complexity, Number Theory, some bits of Functional/Mathematical analysis, a bit of Complex analysis, some knowledge about polynomials, and of course, Probability Theory.

Before obtaining a degree in Security I got Masters in Math and, looking back, it helped me a lot, compared to other students. And yes, your approach will be useful.

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  • $\begingroup$ Is your undergrad in Math or Computer Science? From which university did you get your Math masters? $\endgroup$ – alu Jul 12 '17 at 8:29
  • $\begingroup$ Bc. + Masters Math in Ukraine (V. N. Karazin Kharkiv National University), then another Masters (Security) in CZ (Masaryk University) $\endgroup$ – Valentyn Kuznietsov Jul 12 '17 at 9:41
  • $\begingroup$ After I read your answer, this idea came to my mind, that I could also get an MS in Mathematics. What are your thoughts on this? Considering my undergrad is in Computer Science. My ultimate goal is to get a PhD in Cryptography. $\endgroup$ – alu Jul 12 '17 at 9:57
  • $\begingroup$ Unfortunately, I don't know the level of your Math, and almost always Bc. in Computer Science sucks hard in terms of Math (but of course depends on the Uni): all Computer Science Math courses are equal like max 2-4 months on the Faculty of Mathematics. Also, I don't know if it is possible to get Masters in Math without Bc. - Bc. just has a lot of basic courses. I think it's better to ask your potential supervisor. If you'd like to have a 'PhD in Cryptography', probably you can complete some Math courses during your PhD - no need to have all kinds of Math by obtaining the corresponding degree. $\endgroup$ – Valentyn Kuznietsov Jul 12 '17 at 10:07
  • $\begingroup$ You won't need two years of differential equations, topology, the theory of materials, some weird types of geometry, mechanics, mathematical physics and all that stuff in crypto. $\endgroup$ – Valentyn Kuznietsov Jul 12 '17 at 10:08

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