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Is it possible to have 2 points on the secp256k1 curve with same x coordinates but different y coordinates?

Moussa by Moussa
February 3, 2025
in Bitcoin
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peer discovery – how to obtain the IP addresses of nodes for mining pools?
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Absolutely.

If (X, Y) satisfies the curve equation y2 = x3 + 7 (mod p), then so does (X, -Y), which modulo p equals (X, p-Y).

This means that for every valid X coordinate on the curve, there are exactly two different Y coordinates for it. Moreover, these points correspond to private keys that are each other’s negation.



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