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I recently started learning about encryption. I read about how elliptic curves can be used to create pseudo random numbers (and how the nsa might have abused this fact to create a backdoor in encryptions software).

So as I understand in an elliptic curve takes the form of $y^2=x^3-3x+b$. The algorithm provide by NIST in appendix A1 http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf describes how a set of pseudo random number can be generated using a very big prime number.

In the context of learning more about pseudo random numbers I would like to create my own pseudo random number generator based on the algorithm. Preferable I would like to do this using a small primes number so I can also practice breaking encryption based on it.

Now the problem is I am not that great in Maths or programming yet... so sketch in the NIST document is a little vague in my eyes. Essentially I have not clue where to start build my program.

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You may hope for an English subtitle version of media.ccc.de/browse/congress/2013/30C3_-5502-de-saal_2-20131229230‌​0-zwischen_supersicherer_verschlusselung_und_klartext_liegt_nur_ein_falsches_bi‌​t-_qbi.html ("Between supergood encryption and clear text is just one bit" - typical misconceptions of crypto: "long keys are better than short ones", "Coding RSA or AES is easy", "Want random? Take java.util.random" and othe rmisconceptions) –  Hagen von Eitzen Jan 11 at 22:42
    
Also check this out: arstechnica.com/security/2013/10/… –  user2612743 Jan 11 at 23:41
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One problem I see with your question: If you know what the term "the group of points of an elliptic curve over a finite field" means, the specification is not vague. If you don't (which is nothing to be ashamed of), it seems that a lot of explaining is necessary - and that means you should split your question to digestible bits. –  Hagen von Eitzen Jan 12 at 12:25
    
@HagenvonEitzen Well it might be a little vague for me. As I understand it the finite field has to do with the clock arithmetic involved..Is that true? –  Niels B Jan 13 at 11:33

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