Elliptic curve secp256k1: the Bitcoin digital signature

ECDSA is the digital signature scheme used in Bitcoin architecture that adopts an elliptic curve called secp256k1, standardized by the Standards for Efficient Cryptography Group (SECG).

ECDSA suggests (a = 0) and (b = 7) as parameters in the following equation:

For a more formal presentation, you can read the document reported by the SECG at https://www.secg.org/sec2-v2.pdf, where you can find the recommended parameters for the 256 bits associated with a Koblitz curve and the other bit-length sister curves.

This is the representation of secp256k1 in the real plane:

Figure 7.6: secp256k1 elliptic curve

As we know, the elliptic curve has a part visible in the real plane and another representation in the imaginary plane. The form of an elliptic curve can be represented in 3D by a torus when the points are defined in a finite field, just as you can see in the following figure:

Figure 7.7: 3D...