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If the point (X,Y) is on the elliptic curve y2 = x3 + ax + b, then the point (X,-Y) is also on that curve. Substitution yields (-y)2 = x3 + ax + b, which is the same equation. In fact, it is the case that if kG = (X,Y), then (-k)G = (N-k)G = (X,P-Y), where the multiplications with G are point multiplications, N is the curve order, and P is the field size (P =...


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As mentioned in other replies, the y^2 = x^3 + 7 equation has two roots (two valid y values for every x). EC point multiplication with scalar is defined here so in your example to get the result for -10 * G pick one of the algorithms in the link and substitute P = G and d = -10 mod (curve order)


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How subtraction works P - Q = P + (-Q) where -Q is the negated Q. (- changes the sign, or in another words, subtracts from the modulus) An example: On this website. For this example, set p = 523; Let the generator (P) be (10, 22). I have 4P and I need 3P. I do the following to calculate 4P - P: Set n = 4 to find 4P = (-236, 235) For n = 1 to find P = (10, 22)...


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There is no such thing as negative numbers on the elliptic curve used by Bitcoin because it is an elliptic curve over a finite field. It is a cyclic group of points composed of positive-integers. You might want to learn about modulo arithmetic and cyclic groups


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However, the sites that I found, wants some ID, registration, their own wallets etc. How can I find simplest site for this purpose? You can find few in this list: https://github.com/cointastical/P2P-Trading-Exchanges I created a paper Bitcoin wallet by using https://www.bitaddress.org. I won't consider it safe and the best way to use bitcoin. If you ...


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The output script (typically referred to as the scriptPubKey, but for some reason blockchain.com is calling it pkscript) tells you where to find the public key(s). It depends on the output script used. The public key(s) could be found in any of the three places. In your example, the output script is a Pay to Script Hash (P2SH) script. This tells us that the ...


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I have to deserialize xpub key then use its derivation path to get a child path or normal key. From a normal key, it is easy to convert the public key to address. You can refer to this source code. https://github.com/tatumio/tatum-java/blob/master/src/main/java/io/tatum/wallet/Address.java#L24 Thanks


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