Exercises for lab 3 on EC

ec-exercise1.py

import math
import libnum


def func(a, x, y, p=37):
    return ((3 * x ** 2 + a) * libnum.invmod((2 * y), p)) % p


def pp(x1, a, b, p=37):
    y = libnum.sqrtmod_prime_power((math.pow(x1, 3) + a * x1 + b) % p, p, 1)

    y = list(y)

    if not y:
        return

    # for each in y[0:]:
    s = func(a, x1, y[0])

    x2 = (s ** 2 - 2 * x1) % p

    y2 = (s * (x1 - x2) - y[0]) % p
    print(x2, y2)
    

def main():
    a = 0
    b = 7
    p = 37
    x = 6
    pp(x, a, b, p)


if __name__ == '__main__':
    main()

ec-exercise2.py

import math
import libnum


def generate_100(a, b, p=37, r=100):
    k = 0
    for each in range(p):

        if k > r:
            return

        y = libnum.sqrtmod_prime_power((int(math.pow(each, 3)) + a * each + b) % p, p, 1)

        try:
            for another in y:
                k += 1
                print('(' + str(each) + ', ' + str(another) + ')', end=' ')
        except ValueError as e:
            pass


def main():
    a = 5
    b = 7
    p = 101
    generate_100(a, b, p=p)


if __name__ == '__main__':
    main()

# (1, 66) (1, 35) (2, 5) (2, 96) (3, 7) (3, 94) (5, 37) (5, 64) (7, 48) (7, 53) (8, 16) (8, 85) (10, 42) (10, 59) (11, 79) (11, 22) (12, 52) (12, 49) (13, 59) (13, 42) (15, 86) (15, 15) (17, 37) (17, 64) (18, 24) (18, 77) (21, 92) (21, 9) (23, 88) (23, 13) (24, 35) (24, 66) (25, 1) (25, 100) (28, 92) (28, 9) (32, 98) (32, 3) (33, 31) (33, 70) (35, 58) (35, 43) (36, 79) (36, 22) (38, 78) (38, 23) (41, 7) (41, 94) (42, 26) (42, 75) (50, 57) (50, 44) (52, 92) (52, 9) (54, 79) (54, 22) (57, 94) (57, 7) (59, 34) (59, 67) (61, 12) (61, 89) (66, 36) (66, 65) (67, 78) (67, 23) (69, 56) (69, 45) (70, 19) (70, 82) (72, 97) (72, 4) (75, 73) (75, 28) (76, 35) (76, 66) (77, 1) (77, 100) (78, 42) (78, 59) (79, 37) (79, 64) (81, 54) (81, 47) (82, 27) (82, 74) (86, 71) (86, 30) (87, 83) (87, 18) (88, 88) (88, 13) (89, 80) (89, 21) (91, 88) (91, 13) (94, 72) (94, 29) (95, 8) (95, 93) (97, 78) (97, 23) 

ec-exercise3.py

import math
import libnum
import numpy as np
import matplotlib.pyplot as plt


def generate_100(a, b, p=37, r=100):
    k = 0

    x, _y = [], []

    for each in range(p):

        if k > r:
            break

        y = libnum.sqrtmod_prime_power((int(math.pow(each, 3)) + a * each + b) % p, p, 1)

        try:
            for another in y:
                k += 1
                x.append(each)
                _y.append(another)
        except ValueError as e:
            pass

    return x, _y


def main():
    a = 5
    b = 7
    p = 101

    x, y = generate_100(a, b, p=p)

    fig = plt.figure()

    ax = fig.add_subplot(111)

    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_title('ECC Points')

    ax.scatter(x, y, color='r')
    plt.show()


if __name__ == '__main__':
    main()