How can I get diff from two rsz
this is script need to get diff and get right private key without knowing K nonce
# -*- coding: utf-8 -*-
"""
@author: iceland
@credit: KV
"""
import random
import secp256k1 as ice
G = ice.scalar_multiplication(1)
N = ice.N
# ==============================================================================
def countTotalBits(num):
# convert number into it's binary and
# remove first two characters .
binary = bin(num)[2:]
return len(binary)
def inv(a):
return pow(a, N - 2, N)
def valid_rsz(r, s, z, pub_point):
RP1 = ice.pub2upub('02' + hex(r)[2:].zfill(64))
RP2 = ice.pub2upub('03' + hex(r)[2:].zfill(64))
sdr = (s * inv(r)) % N
zdr = (z * inv(r)) % N
FF1 = ice.point_subtraction( ice.point_multiplication(RP1, sdr),
ice.scalar_multiplication(zdr) )
FF2 = ice.point_subtraction( ice.point_multiplication(RP2, sdr),
ice.scalar_multiplication(zdr) )
if FF1 == pub_point or FF2 == pub_point:
return True
else:
return False
def getk1(r1, s1, z1, r2, s2, z2, m):
nr = (s2 * m * r1 + z1 * r2 - z2 * r1) % N
dr = (s1 * r2 - s2 * r1) % N
return (nr * inv(dr)) % N
def getpvk(r1, s1, z1, r2, s2, z2, m):
x1 = (s2 * z1 - s1 * z2 + m * s1 * s2) % N
xi = inv((s1 * r2 - s2 * r1) % N)
x = (x1 * xi) % N
return x
def getx(Q):
return int(Q[1:33].hex(), 16)
# ==============================================================================
pvk = random.SystemRandom().randint(2 ** 129, 2 ** 130)
print('=' * 72)
print(' True Privatekey = ', hex(pvk))
print('=' * 72)
Q = ice.scalar_multiplication(pvk)
k1 = random.SystemRandom().randint(1, 2 ** 256)
P1 = ice.scalar_multiplication(k1)
r1 = getx(P1)
z1 = random.SystemRandom().randint(1, 2 ** 256)
s1 = (inv(k1) * (z1 + r1 * pvk)) % N
k2 = random.SystemRandom().randint(1, 2 ** 256)
P2 = ice.scalar_multiplication(k2)
r2 = getx(P2)
z2 = random.SystemRandom().randint(1, 2 ** 256)
s2 = (inv(k2) * (z2 + r2 * pvk)) % N
#diff = (k2 - k1) % N
diff = 0
# ==============================================================================
print(f'k1: {hex(k1)}\nr1: {hex(r1)}\ns1: {hex(s1)}\nz1: {hex(z1)}')
if valid_rsz(r1, s1, z1, Q): print(' Tx1 Correct: rsz Validated the Pubkey')
print('=' * 72)
print(f'k2: {hex(k2)}\nr2: {hex(r2)}\ns2: {hex(s2)}\nz2: {hex(z2)}')
if valid_rsz(r2, s2, z2, Q): print(' Tx2 Correct: rsz Validated the Pubkey')
# ==============================================================================
# Generation Complete. Now let's start to solve it using 2 rsz and diff.
# ==============================================================================
print('=' * 72)
print(' Starting to solve rsz using difference of k between 2 Tx')
k = getk1(r1, s1, z1, r2, s2, z2, diff)
x = getpvk(r1, s1, z1, r2, s2, z2, diff)
print(f' Extracted Privatekey = {hex(x)}')
if getx(ice.scalar_multiplication(k)) == r1 or getx(ice.scalar_multiplication(k)) == r2:
print(f'==== Nonce Found using 2 rsz diff = {hex(k)}')
print('Original PVK', int(pvk), countTotalBits(int(pvk)))
print('Extracted PVK', int(x), countTotalBits(int(x)))
