Foundations of Blockchain

Operations on elliptic curves

Elliptic curves used in cryptography are curves that are constructed in a finite field. They have the following form:

y² = x³ + ax + b mod (p)

The modulus operation on p indicates that the curve is over a finite field of prime numbers of the order p. We need to understand some terminology and operations of elliptic curves before moving on to the cryptographic applications.

A finite field is a field with a finite number of elements defined by parameter p, which is a prime number. Thus, the finite field is F_p = {0, . . ., p-1}. It is represented by modulo p in the equation.

All the elements used in ECC must be agreed upon by the cryptography actors. These elements are called elliptical curve domain parameters. ...