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Trying to understand Elliptic Curve maths with 256-bit numbers seems like hard to explain/understand. I wonder if by lowering down the possible numbers get's a little bit easier.

closed as too broad by David Grayson, Raghav Sood, Andrew Chow Oct 3 '18 at 17:41

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It's my opinion that mechanical explanations of ECC are almost completely worthless to people, and mostly just generate false understanding. Exactly how two points get added to each other isn't an important thing to understand in order to understand ECC any more than understanding van der waals forces is important to someone trying to oil paint. So my advice is to find explanations that talk about the abstract algebra of ECC rather than the mechanics of group operations. :)

But some people just love the mechanics. So if you must, find a tutorial that uses secp256k1 (the 'bitcoin' curve) and replace the field size P with 79 (so you would be doing arithmetic mod 79 instead of 115...663), and N with 67 (instead of 115...337). 'a' stays 0, 'b' stays 7. For G you might choose {60, 10}.

The resulting curve should have all the same algebraic properties as secp256k1 (except for being discrete log insecure due to being so small). To check your math, G * 29 = {37, 10}. Meaning that the pubkey for private key 29 is the point at {37, 10} with the above parameters.

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