Blockchain – Elliptic Curve Digital Signature Algorithm (ECDSA)

By Ann Roberts On Nov 27, 2022

p = pow(2, 255) - 19

base = 15112221349535400772501151409588531511454012693041857206046113283949847762202, 46316835694926478169428394003475163141307993866256225615783033603165251855960

def findPositiveModulus(a, p):

if a < 0:

a = (a + p * int(abs(a)/p) + p) % p

return a

def textToInt(text):

encoded_text = text.encode('utf-8')

hex_text = encoded_text.hex()

int_text = int(hex_text, 16)

return int_text

def gcd(a, b):

while a != 0:

a, b = b % a, a

return b

def findModInverse(a, m):

if a < 0:

a = (a + m * int(abs(a)/m) + m) % m

if gcd(a, m) != 1:

return None

u1, u2, u3 = 1, 0, a

v1, v2, v3 = 0, 1, m

while v3 != 0:

q = u3 // v3

v1, v2, v3, u1, u2, u3 = (u1 - q * v1), (u2 - q * v2), (u3 - q * v3), v1, v2, v3

return u1 % m

def applyDoubleAndAddMethod(P, k, a, d, mod):

additionPoint = (P[0], P[1])

kAsBinary = bin(k)

kAsBinary = kAsBinary[2:len(kAsBinary)]

for i in range(1, len(kAsBinary)):

currentBit = kAsBinary[i: i+1]

additionPoint = pointAddition(additionPoint, additionPoint, a, d, mod)

if currentBit == '1':

additionPoint = pointAddition(additionPoint, P, a, d, mod)

return additionPoint

def pointAddition(P, Q, a, d, mod):

x1 = P[0]; y1 = P[1]

x2 = Q[0]; y2 = Q[1]

x3 = (((x1*y2 + y1*x2) % mod) * findModInverse(1+d*x1*x2*y1*y2, mod)) % mod

y3 = (((y1*y2 - a*x1*x2) % mod) * findModInverse(1- d*x1*x2*y1*y2, mod)) % mod

return x3, y3

a = -1; d = findPositiveModulus(-121665 * findModInverse(121666, p), p)

x0 = base[0]; y0 = base[1]

print("----------------------")

print("Key Generation: ")

import random

privateKey = random.getrandbits(256)

publicKey = applyDoubleAndAddMethod(base, privateKey, a, d, p)

print("public key: ", publicKey)

message = textToInt("Hello, world!")

def hashing(message):

import hashlib

return int(hashlib.sha512(str(message).encode("utf-8")).hexdigest(), 16)

r = hashing(hashing(message) + message) % p

R = applyDoubleAndAddMethod(base, r, a, d, p)

h = hashing(R[0] + publicKey[0] + message) % p

s = (r + h * privateKey)

print("----------------------")

print("Signing:")

print("message: ",message)

print("Signature (R, s)")

print("R: ",R)

print("s: ",s)

h = hashing(R[0] + publicKey[0] + message) % p

P1 = applyDoubleAndAddMethod(base, s, a, d, p)

P2 = pointAddition(R, applyDoubleAndAddMethod(publicKey, h, a, d, p), a, d, p)

print("----------------------")

print("Verification:")

print("P1: ",P1)

print("P2: ",P2)

print("----------------------")

print("result")

if P1[0] == P2[0] and P1[1] == P2[1]:

print("The Signature is valid")

else:

print("The Signature violation detected!")

p = pow(2, 255) - 19

base = 15112221349535400772501151409588531511454012693041857206046113283949847762202, 46316835694926478169428394003475163141307993866256225615783033603165251855960

def findPositiveModulus(a, p):

if a < 0:

a = (a + p * int(abs(a)/p) + p) % p

return a

def textToInt(text):

encoded_text = text.encode('utf-8')

hex_text = encoded_text.hex()

int_text = int(hex_text, 16)

return int_text

def gcd(a, b):

while a != 0:

a, b = b % a, a

return b

def findModInverse(a, m):

if a < 0:

a = (a + m * int(abs(a)/m) + m) % m

if gcd(a, m) != 1:

return None

u1, u2, u3 = 1, 0, a

v1, v2, v3 = 0, 1, m

while v3 != 0:

q = u3 // v3

v1, v2, v3, u1, u2, u3 = (u1 - q * v1), (u2 - q * v2), (u3 - q * v3), v1, v2, v3

return u1 % m

def applyDoubleAndAddMethod(P, k, a, d, mod):

additionPoint = (P[0], P[1])

kAsBinary = bin(k)

kAsBinary = kAsBinary[2:len(kAsBinary)]

for i in range(1, len(kAsBinary)):

currentBit = kAsBinary[i: i+1]

additionPoint = pointAddition(additionPoint, additionPoint, a, d, mod)

if currentBit == '1':

additionPoint = pointAddition(additionPoint, P, a, d, mod)

return additionPoint

def pointAddition(P, Q, a, d, mod):

x1 = P[0]; y1 = P[1]

x2 = Q[0]; y2 = Q[1]

x3 = (((x1*y2 + y1*x2) % mod) * findModInverse(1+d*x1*x2*y1*y2, mod)) % mod

y3 = (((y1*y2 - a*x1*x2) % mod) * findModInverse(1- d*x1*x2*y1*y2, mod)) % mod

return x3, y3

a = -1; d = findPositiveModulus(-121665 * findModInverse(121666, p), p)

x0 = base[0]; y0 = base[1]

print("----------------------")

print("Key Generation: ")

import random

privateKey = random.getrandbits(256)

publicKey = applyDoubleAndAddMethod(base, privateKey, a, d, p)

print("public key: ", publicKey)

message = textToInt("Hello, world!")

def hashing(message):

import hashlib

return int(hashlib.sha512(str(message).encode("utf-8")).hexdigest(), 16)

r = hashing(hashing(message) + message) % p

R = applyDoubleAndAddMethod(base, r, a, d, p)

h = hashing(R[0] + publicKey[0] + message) % p

s = (r + h * privateKey)

print("----------------------")

print("Signing:")

print("message: ",message)

print("Signature (R, s)")

print("R: ",R)

print("s: ",s)

h = hashing(R[0] + publicKey[0] + message) % p

P1 = applyDoubleAndAddMethod(base, s, a, d, p)

P2 = pointAddition(R, applyDoubleAndAddMethod(publicKey, h, a, d, p), a, d, p)

print("----------------------")

print("Verification:")

print("P1: ",P1)

print("P2: ",P2)

print("----------------------")

print("result")

if P1[0] == P2[0] and P1[1] == P2[1]:

print("The Signature is valid")

else:

print("The Signature violation detected!")

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