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Subrahand.py
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Subrahand.py
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import subprocess
import os
# https://stackoverflow.com/questions/58755669/how-to-get-an-elliptic-curve-public-key-from-a-private-key
class ECPoint:
gmpy2 = None
# import gmpy2
import random
class InvError(Exception):
def __init__(self, *pargs):
self.value = pargs
@classmethod
def Int(cls, x):
return int(x) if cls.gmpy2 is None else cls.gmpy2.mpz(x)
@classmethod
def std_point(cls, t):
if t == 'secp256k1':
# https://en.bitcoin.it/wiki/Secp256k1
# https://www.secg.org/sec2-v2.pdf
p = 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFC2F
a = 0
b = 7
x = 0x79BE667E_F9DCBBAC_55A06295_CE870B07_029BFCDB_2DCE28D9_59F2815B_16F81798
y = 0x483ADA77_26A3C465_5DA4FBFC_0E1108A8_FD17B448_A6855419_9C47D08F_FB10D4B8
q = 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_BAAEDCE6_AF48A03B_BFD25E8C_D0364141
elif t == 'secp256r1':
# https://www.secg.org/sec2-v2.pdf
p = 0xFFFFFFFF_00000001_00000000_00000000_00000000_FFFFFFFF_FFFFFFFF_FFFFFFFF
a = 0xFFFFFFFF_00000001_00000000_00000000_00000000_FFFFFFFF_FFFFFFFF_FFFFFFFC
b = 0x5AC635D8_AA3A93E7_B3EBBD55_769886BC_651D06B0_CC53B0F6_3BCE3C3E_27D2604B
x = 0x6B17D1F2_E12C4247_F8BCE6E5_63A440F2_77037D81_2DEB33A0_F4A13945_D898C296
y = 0x4FE342E2_FE1A7F9B_8EE7EB4A_7C0F9E16_2BCE3357_6B315ECE_CBB64068_37BF51F5
q = 0xFFFFFFFF_00000000_FFFFFFFF_FFFFFFFF_BCE6FAAD_A7179E84_F3B9CAC2_FC632551
elif t == 'secp384r1':
# https://www.secg.org/sec2-v2.pdf
p = 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_00000000_00000000_FFFFFFFF
a = 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFE_FFFFFFFF_00000000_00000000_FFFFFFFC
b = 0xB3312FA7_E23EE7E4_988E056B_E3F82D19_181D9C6E_FE814112_0314088F_5013875A_C656398D_8A2ED19D_2A85C8ED_D3EC2AEF
x = 0xAA87CA22_BE8B0537_8EB1C71E_F320AD74_6E1D3B62_8BA79B98_59F741E0_82542A38_5502F25D_BF55296C_3A545E38_72760AB7
y = 0x3617DE4A_96262C6F_5D9E98BF_9292DC29_F8F41DBD_289A147C_E9DA3113_B5F0B8C0_0A60B1CE_1D7E819D_7A431D7C_90EA0E5F
q = 0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_C7634D81_F4372DDF_581A0DB2_48B0A77A_ECEC196A_CCC52973
elif t == 'secp521r1':
# https://www.secg.org/sec2-v2.pdf
p = 2 ** 521 - 1
a = 2 ** 521 - 4
b = 0x0051_953EB961_8E1C9A1F_929A21A0_B68540EE_A2DA725B_99B315F3_B8B48991_8EF109E1_56193951_EC7E937B_1652C0BD_3BB1BF07_3573DF88_3D2C34F1_EF451FD4_6B503F00
x = 0x00C6_858E06B7_0404E9CD_9E3ECB66_2395B442_9C648139_053FB521_F828AF60_6B4D3DBA_A14B5E77_EFE75928_FE1DC127_A2FFA8DE_3348B3C1_856A429B_F97E7E31_C2E5BD66
y = 0x0118_39296A78_9A3BC004_5C8A5FB4_2C7D1BD9_98F54449_579B4468_17AFBD17_273E662C_97EE7299_5EF42640_C550B901_3FAD0761_353C7086_A272C240_88BE9476_9FD16650
q = 0x01FF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFA_51868783_BF2F966B_7FCC0148_F709A5D0_3BB5C9B8_899C47AE_BB6FB71E_91386409
else:
assert False
return ECPoint(a, b, p, x, y, q=q)
def __init__(self, A, B, N, x, y, *, q=0, prepare=True):
if prepare:
N = self.Int(N)
A, B, x, y, q = [self.Int(e) % N for e in [A, B, x, y, q]]
assert (4 * A ** 3 + 27 * B ** 2) % N != 0
assert (y ** 2 - x ** 3 - A * x - B) % N == 0, (hex(N), hex((y ** 2 - x ** 3 - A * x) % N))
assert N % 4 == 3
assert y == pow(x ** 3 + A * x + B, (N + 1) // 4, N)
self.A, self.B, self.N, self.x, self.y, self.q = A, B, N, x, y, q
def __add__(self, other):
A, B, N = self.A, self.B, self.N
Px, Py, Qx, Qy = self.x, self.y, other.x, other.y
if Px == Qx and Py == Qy:
s = ((Px * Px * 3 + A) * self.inv(Py * 2, N)) % N
else:
s = ((Py - Qy) * self.inv(Px - Qx, N)) % N
x = (s * s - Px - Qx) % N
y = (s * (Px - x) - Py) % N
return ECPoint(A, B, N, x, y, prepare=False)
def __rmul__(self, other):
assert other >= 1
if other == 1:
return self
other = self.Int(other - 1)
r = self
while True:
if other & 1:
r = r + self
if other == 1:
return r
other >>= 1
self = self + self
@classmethod
def inv(cls, a, n):
a %= n
if cls.gmpy2 is None:
try:
return pow(a, -1, n)
except ValueError:
import math
raise cls.InvError(math.gcd(a, n), a, n)
else:
g, s, t = cls.gmpy2.gcdext(a, n)
if g != 1:
raise cls.InvError(g, a, n)
return s % n
def __repr__(self):
return str(dict(x=self.x, y=self.y, A=self.A, B=self.B, N=self.N, q=self.q))
def __eq__(self, other):
for i, (a, b) in enumerate([(self.x, other.x), (self.y, other.y), (self.A, other.A),
(self.B, other.B), (self.N, other.N), (self.q, other.q)]):
if a != b:
return False
return True
def get_pub(priv_key):
bp = ECPoint.std_point('secp256k1')
pub = priv_key * bp
return pub.x, pub.y
def main():
import hashlib
priv_key = int(hashlib.sha3_256(b"Led Zeppelin - No Quarter").hexdigest(), 16)
print('priv key :', hex(priv_key))
pubx, puby = get_pub(priv_key)
print('pub key x:', hex(pubx))
print('pub key y:', hex(puby))
main()
def subtract(x,n):
#print("./mel.exe -p %s -s -n 4 -r 0:%x -o test.txt"%(x,n))
#FNULL = open(os.devnull, 'w')
d =subprocess.run(["mel.exe", "-p", "%s"%(x),"-s" ,"-n", "4", "-r", "0:%x"%(n)], capture_output=True, text=True).stdout
print("D=",d)
d = d.split("\n")[-4].split()[0]
"""
with open("test.txt") as f:
d = f.readlines()
w = d[-1].split()[0]
print(d,w)
pubx, puby = get_pub(int(w,16))
print('pub key x:', hex(pubx))
print('pub key y:', hex(puby))
return w
os.remove("test.txt")
"""
print("d=",d,"\n")
pubx, puby = get_pub(int(d, 16))
print('pub key x:', hex(pubx))
print('pub key y:', hex(puby))
input()
return d
def getSubtrahand(x,a,b,PubKey0,PubKey1):
mid = (a+b)//2
if mid<=a:
return mid
pubkeyNew = subtract(x,mid)
print("\n \n Mid ", mid, a, b, pubkeyNew,PubKey0, PubKey1)
x1,y1 = get_pub(int(pubkeyNew,16))
print("%x, %x"%(x1,y1))
input()
if pubkeyNew[-len(PubKey0):]<PubKey0:
return getSubtrahand(x,a,mid,PubKey0,PubKey1)
elif pubkeyNew[-len(PubKey1):]>PubKey1:
return getSubtrahand(x,mid,b,PubKey0,PubKey1)
return mid
START = 0x0000000000000000000000000000000200000000000000000000000000000000
END = 0x00000000000000000000000000000003FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
START_NEW = 0x0000000000000000000000000000000000000000000000000000000000000001
END_NEW = 1000000
start = 0x0000000000000000000000000000000300000000000000000000000000000001
# 1020847100762815390390123822295304634369
# public 5HpHagT65TZzG1PH3CSu649jkvD5x9fGYxstEap59ucLQcH1pxj
# private 03CF62F121200F56C503DC6CEC1AA862E03B6B85D84D9D4026F093A254D62DC72B
# dec 441179842594957130278973409334323152175017054977628378887208019926257543005995
PubKey0 = "0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798" # Public key of START_NEW
PubKey1 = "02CE9FF4C0B094BA34B93EC9CD0164CCCC308EB4D5F600FAA06D29BD8CAADB6A0F" # Public key of END_NEW
PubKey0 = "0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
PubKey1 = "038282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508"
# example input
#x = "03CF62F121200F56C503DC6CEC1AA862E03B6B85D84D9D4026F093A254D62DC72B" #
x= "03EA1CC79FF6BE554FB04333AE959958C71CB54E7A8403258CB9B7781394B416C9"
for i in range(1,11):
print(subtract(x,int(x,16) + i))
n = getSubtrahand(x,START,END,PubKey0,PubKey1)
print("\n n=", n)
# n= 680564733841876926926749214863536422912 == 0x200000000000000