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I have been studying RSA cryptography and want to extend this to ECC. I am interested in any books on the topic, that start off with basic principles of elliptic curves as I have almost zero knowledge of them. Can you reccomend any books, or combination of books.

(I do have a good working understanding of group theory pre-postgrad level anyway)

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You should have a look at Silverman's "The Arithmetic of Elliptic Curves". The new 2nd edition includes a chapter on "algorithmic aspects" and, in particular, Ch XI.4 deals with elliptic curve cryptography. If you are looking for a more elementary treatment, look at Washington's "Elliptic Curves: Number Theory and Cryptography". –  Álvaro Lozano-Robledo Aug 17 '11 at 12:24
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I'm not sure why its off topic. –  JarvisP Aug 17 '11 at 12:31
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Thinking about it, I agree with FV, regarding closure. math.stackexchange.com should be a good place to ask this. –  quid Aug 17 '11 at 12:32
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JarvisP, I had not seen your comment before mine: The point is that the purpose of this site is only research-level questions. However, the site I link to has a broader scope, but is otherwise very similar. –  quid Aug 17 '11 at 12:35
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See also a previous MO question mathoverflow.net/questions/25924/… –  Andrey Rekalo Aug 17 '11 at 12:35
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closed as off topic by Felipe Voloch, quid, Franz Lemmermeyer, Ryan Budney, Yemon Choi Aug 18 '11 at 1:43

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