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I want to study to understand such algorithms as the AKS specifically but as I am new to this I do not know where to start?

Hetzav Artax
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  • Do you know modular arithmetic? If not, learn it. It's very easy and will help you a lot when learning about more advanced subjects. – Mastrem Nov 11 '16 at 08:37
  • @Mastrem yes I do. But I understand it has to do with group theory and such right? – Hetzav Artax Nov 11 '16 at 08:46
  • The aks test... – Hetzav Artax Nov 11 '16 at 08:47
  • Well, the test itself is an equivalence relation mod $n$, so modular arithmetic would at least be a start. There are some playlists on youtube about group theory, most of it is pretty basic but also not hard to understand. – Mastrem Nov 11 '16 at 08:49
  • @Mastrem and I asume then that that is all you need or are there many more subjects needed to understand aks? – Hetzav Artax Nov 11 '16 at 08:58
  • @Mastrem I am very sorry for being a bit uneducated I meant the whole algorithm and the optimizations that make it fast. Not only the test. I am sorry. – Hetzav Artax Nov 11 '16 at 09:02
  • No problem, I've never really looked into it myself. I'm just looking at the wikipedia page here and looking at what you'll need at least to understand the test. If you don't understand the test, you can't really understand the optimizations of the test. I suggest you take a look at http://www-alg.ist.hokudai.ac.jp/~thomas/SEMINAR/notes.pdf and if you don't understand it, simply google it or look at wikipedia. It seems like you'll need a bit of group theory, modular arithmetic, Fermat's little theorem and the binomial theorem. – Mastrem Nov 11 '16 at 09:15
  • by the way, those notes aren't mine or anything, I just googled 'primes in p' and this was the first thing that came up. – Mastrem Nov 11 '16 at 09:16
  • In the appendix of those notes, they say exactly what you need to know with examples and all. – Mastrem Nov 11 '16 at 09:20
  • Possible duplicate of http://math.stackexchange.com/questions/52221/understanding-aks. – lhf Nov 11 '16 at 09:20

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The book Primality Testing in Polynomial Time by Dietzfelbinger is very nice and tries to give all basic concepts.

lhf
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