A=zG computed using the double and add algorithm (https://www.youtube.com/watch?v=5ITRACsmCvQ). Where z is the multiple and G is the

Formula: (x1, y1) + (x2, y2) = (((x1 * y2) + (y1 * x2)/(1 + D * x1 * x2 * y1 * y2)) , ((y1 * y2) - (A * x1 * x2)/(1 - D * x1 * x

Computes the gcd and reverses the process to express the gcd as a linear combination in the form ax + by = gcd(a, b). The Extended Eucli

We check if a point is on the curve using the condition: y**2 mod p == (x**3 + ax + b) mod p

Identity is {x=0, y=1, t = 0, z =1} The equivalence class is therefore is {x=0, y=k, t = 0, z=k} for all k where k!=0

Computes the GCD of a and b using the Euclidean Algorithm

Generates a random private-public key pair

Compute the Legendre symbol a|p using Euler's criterion. p is a prime, a is relatively prime to p (if p divides a, then a|p =

Formula: 2(x1, y1) = ((2(x1 * y1)) / ((y1 ** 2) + (A(x1 ** 2))) , ((((y1 ** 2) - A(x1 ** 2)) / (2 - (y1 ** 2) - A(x1 ** 2))))

Return None if the bytes are not in canonical form. Canonical here means that the integer representation of the bytes must be

The phi of any prime number p is p - 1. To find the phi of n where n is a product of two primes p, q can be computed as (ɸ(n) = ɸ(p)

Using Double and Add : https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Double-and-add

According to the spec(FIPS PUB 202), section B.2, q = (x - 8) - (m % (x / 8)) where: x is the rate m i

To decrypt, we compute N = (c ** d mod n). N is the original message

To encrypt, we compute c = m ** e mod n where m is the message, c is encrypted message and n is the modulus