54 lines
1.7 KiB
Python
54 lines
1.7 KiB
Python
from elliptic import *
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from fractions import Fraction as frac
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from finitefield.finitefield import FiniteField
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import itertools
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def findPoints(curve, field):
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print('Finding all points over %s' % (curve))
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print('The ideal generator is %s' % (field.idealGenerator))
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degree = field.idealGenerator.degree()
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subfield = field.primeSubfield
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xs = [field(x) for x in itertools.product(range(subfield.p), repeat=degree)]
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ys = [field(x) for x in itertools.product(range(subfield.p), repeat=degree)]
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points = [Point(curve, x, y) for x in xs for y in ys if curve.testPoint(x, y)]
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return points
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FFd = FiniteField(67, 1) # F_67
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curve = EllipticCurve(a=FFd(2), b=FFd(3)) # Curve params
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G = Point(curve, FFd(2), FFd(22)) # G : pub key
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n_a = 4 # Private key of A (n_a < n)
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n_b = 4 # Private key of B (n_b < n)
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k = 2 # k is a random int the sender selects when encrypting (k < n)
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P_m = Point(curve, FFd(24), FFd(26)) # Point encoded plaintext msg
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print("\n\n\n=========\n\n\nEl Gamal\n\n\n=========\n\n\n")
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# Pvt key of A
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print("***************\nCalculating for A:\n***************\n")
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P_a = n_a*G
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print("\nPub key of A : ", P_a)
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# Pvt key of B
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print("\n***************\nCalculating for B:\n***************\n")
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P_b = n_b * G
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print("\nPub Key of B :", P_b)
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print("\nB is sending to A (Encrypting with A's pub key)\n")
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print("\n***************\nCiphertexts:\n***************\n\n C1=k*G; C2=P_m + k*P_a\n")
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C1 = k*G
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C2 = P_m + k*P_a
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print("\nC1 : {} \n".format(C1))
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print("\nC2 : {} \n".format(C2))
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print("\nC = [ {}, {} ]\n".format(C1, C2))
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print("\nA is decrypting\n")
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P_m_dec = C2 - C1*n_a
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print("\nDecrypted plaintext C2 - C1*n_a : {} \n".format(P_m_dec))
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