generator

from sage.all import *
from Crypto.Util.number import *
import random
import time
random.seed(time.time())

p = random_prime(2**8 - 1, False, 2**7)
a, b = random.randint(2, p), random.randint(2, p)

print(f"p = {p}\na = {a}\nb = {b}")

F = GF(p)
elements = []
for i in range(p):
    Y = F((((b ** 2) * (a ** 2 - i ** 2)) % p * pow(a ** 2, -1, p)) % p)
    if Y.is_square():
        elements.append((i, Mod(Y, p).sqrt()))

def point_addition(px, py, qx, qy):
    rx = F((pow(a, -1, p) * (px * qx - py * qy * (a ** 2) * (pow(b ** 2, - 1, p)))) % p )
    ry = F((pow(a, -1, p) * (px * qy + py * qx)) % p)
    return (rx, ry)

def scalar_multiplication(px, py, k):
    rx = a
    ry = 0
    while k:
        if k % 2:
            rx, ry = point_addition(rx, ry, px, py)
        px, py = point_addition(px, py, px, py)
        k >>= 1
    return rx, ry

print(2 * len(elements) - 2)

for element in elements:
    print(element, end = " ")
    for i in range(1, 2 * len(elements)):
        if scalar_multiplication(element[0], element[1], i) == (a, 0):
            print(i)
            break