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I want to know the basic understanding of ECC algorithm for cryptography. But I am not aware of the algorithm. Can anyone provide me with a basic explanation of the algorithm?

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One can go on and on if to define and describe Elliptic Curve. I will rather suggest for you to get hold of a decent book and read for yourself. If you an issue with understanding any algorithm or basic of Elliptic Curve, I will be more than happy to help you there. For starter, you can always look at Silverman's book titled The Arithmetic of Elliptic curves. Else just go to Galbraith's webpage on Elliptic Curve Cryptography. There are bunch of nice books listed.

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