An overview of elliptic curves

Around 1985, Victor Miller and Neal Koblitz pioneered elliptic curves for cryptographic uses. Later on, Hendrik Lenstra showed us how to use them to factorize an integer number.

Elliptic curves are essentially a geometrical representation of particular mathematical equations on the Cartesian plane. We will start to analyze their geometrical models in the 2D plane, conscious that their extended and deeper representation is in 3D or 4D, involving irrational and imaginary numbers. Don't worry now about these issues; it will become clearer later on in this chapter.

Elliptic Curves Cryptography (ECC) is used to implement some algorithms we have seen in previous chapters, such as RSA, Diffie–Hellman (D–H), and ElGamal.

Moreover, after the advent of the revolution in digital currency, a particular type of elliptic curve called secp256K1 and a digital signature algorithm called Elliptic Curve Digital Signature Algorithm (ECDSA) have...