secp256k1 The elliptic curve Bitcoin uses for all signatures (ECDSA + Schnorr). Defined by SECG ( ). Parameters The curve equation: . Point operations - Point addition : P + Q with chord-and-tangent rule mod p. - Scalar multiplication : is the public key for private scalar k. - Point doubling : 2P via tangent line. - Point at infinity : identity for the group. Key encoding Public key (full) - Uncompressed (65 bytes) : (32-byte each). - Compressed (33 bytes) : if y even, if y odd. x-only (BIP340, Taproot) - 32 bytes : just . Implicit even-y convention. - Used in Schnorr signatures and Taproot…