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ellipticKurve256k1/README.md

Transaction

Bitcoin Transaction ECDSA over secp256k1 Signature

$$ \begin{aligned} R &= k G = (x_R, y_R) \quad &&\text{over } \mathbb{F}_p \\ r &= x_R \bmod n \\ s &= k^{-1}(z + r d) \bmod n \end{aligned} $$

Bitcoin Transaction ECDSA Verification

$$ \begin{aligned} w &= s^{-1} \bmod n \\ u_1 &= z \cdot w \bmod n \\ u_2 &= r \cdot w \bmod n \\ P &= u_1 \cdot G + u_2 \cdot Q = (x_P, y_P) \\ r' &= x_P \bmod n \end{aligned} $$


GPG Fingerprint

AFC8 10CF 10D3 8599 4346  A34F 44EB 919B FFFF 735E

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