Ahhh, Joes? Jules? Sup.
Try this, I just messed up when trying to divide each target by different scalar, so I can't tell whether this is dividing 1 target by odd and the other target by even values or not, if you could try it with scalar mod n instead of points, do try and also share it with us, I have no time to do it right now.
Code:
import gmpy2 as mpz
from gmpy2 import powmod
# Define the EllipticCurve class
class EllipticCurve:
def __init__(self, a, b, p):
self.a = mpz.mpz(a)
self.b = mpz.mpz(b)
self.p = mpz.mpz(p)
def contains(self, point):
x, y = point.x, point.y
return (y * y) % self.p == (x * x * x + self.a * x + self.b) % self.p
def __str__(self):
return f"y^2 = x^3 + {self.a}x + {self.b} mod {self.p}"
# Define the Point class
class Point:
def __init__(self, x, y, curve):
self.x = mpz.mpz(x)
self.y = mpz.mpz(y)
self.curve = curve
def __eq__(self, other):
return self.x == other.x and self.y == other.y and self.curve == other.curve
def __ne__(self, other):
return not self == other
def __add__(self, other):
if self.curve != other.curve:
raise ValueError("Cannot add points on different curves")
# Case when one point is zero
if self == Point.infinity(self.curve):
return other
if other == Point.infinity(self.curve):
return self
if self.x == other.x and self.y != other.y:
return Point.infinity(self.curve)
p = self.curve.p
s = 0
if self == other:
s = ((3 * self.x * self.x + self.curve.a) * powmod(2 * self.y, -1, p)) % p
else:
s = ((other.y - self.y) * powmod(other.x - self.x, -1, p)) % p
x = (s * s - self.x - other.x) % p
y = (s * (self.x - x) - self.y) % p
return Point(x, y, self.curve)
def __sub__(self, other):
if self.curve != other.curve:
raise ValueError("Cannot subtract points on different curves")
# Case when one point is zero
if self == Point.infinity(self.curve):
return other
if other == Point.infinity(self.curve):
return self
return self + Point(other.x, (-other.y) % self.curve.p, self.curve)
def __mul__(self, n):
if not isinstance(n, int):
raise ValueError("Multiplication is defined for integers only")
n = n % (self.curve.p - 1)
res = Point.infinity(self.curve)
addend = self
while n:
if n & 1:
res += addend
addend += addend
n >>= 1
return res
def __str__(self):
return f"({self.x}, {self.y}) on {self.curve}"
@staticmethod
def from_hex(s, curve):
if len(s) == 66 and s.startswith("02") or s.startswith("03"):
compressed = True
elif len(s) == 130 and s.startswith("04"):
compressed = False
else:
raise ValueError("Hex string is not a valid compressed or uncompressed point")
if compressed:
is_odd = s.startswith("03")
x = mpz.mpz(s[2:], 16)
# Calculate y-coordinate from x and parity bit
y_square = (x * x * x + curve.a * x + curve.b) % curve.p
y = powmod(y_square, (curve.p + 1) // 4, curve.p)
if is_odd != (y & 1):
y = -y % curve.p
return Point(x, y, curve)
else:
s_bytes = bytes.fromhex(s)
uncompressed = s_bytes[0] == 4
if not uncompressed:
raise ValueError("Only uncompressed or compressed points are supported")
num_bytes = len(s_bytes) // 2
x_bytes = s_bytes[1 : num_bytes + 1]
y_bytes = s_bytes[num_bytes + 1 :]
x = mpz.mpz(int.from_bytes(x_bytes, byteorder="big"))
y = mpz.mpz(int.from_bytes(y_bytes, byteorder="big"))
return Point(x, y, curve)
def to_hex(self, compressed=True):
if self.x is None and self.y is None:
return "00"
elif compressed:
prefix = "03" if self.y & 1 else "02"
return prefix + hex(self.x)[2:].zfill(64)
else:
x_hex = hex(self.x)[2:].zfill(64)
y_hex = hex(self.y)[2:].zfill(64)
return "04" + x_hex + y_hex
@staticmethod
def infinity(curve):
return Point(-1, -1, curve)
# Define the ec_mul function
def ec_mul(point, scalar, base_point):
result = Point.infinity(point.curve)
addend = point
while scalar:
if scalar & 1:
result += addend
addend += addend
scalar >>= 1
return result
# Define the ec_operations function
def ec_operations(start_range, end_range, target_1, target_2, curve, divide_1_by_odd=True, divide_1_by_even=True, divide_2_by_odd=True, divide_2_by_even=True):
# Define parameters for secp256k1 curve
n = mpz.mpz("0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141")
G = Point(
mpz.mpz("0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"),
mpz.mpz("0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"),
curve
)
for i in range(start_range + (start_range%2), end_range, 3):
# divide target 1 by odd or even numbers
if i%2 == 0 and not divide_1_by_even:
continue
elif i%2 == 1 and not divide_1_by_odd:
continue
try:
# calculate inverse modulo of i
i_inv = powmod(i, n-2, n)
# divide the targets by i modulo n
result_1 = ec_mul(target_1, i_inv, G)
result_2 = ec_mul(target_2, i_inv, G)
# divide target 2 by odd or even numbers
if i%2 == 0 and not divide_2_by_even:
continue
elif i%2 == 1 and not divide_2_by_odd:
continue
# subtract the results
sub_result = result_2 - result_1
# write the results to separate files
print(f"{i}-{sub_result.to_hex()}")
except ZeroDivisionError:
pass
if __name__ == "__main__":
# Set the targets and range for the operations
curve = EllipticCurve(
mpz.mpz(0),
mpz.mpz(7),
mpz.mpz("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F")
)
target_1 = Point.from_hex("037564539e85d56f8537d6619e1f5c5aa78d2a3de0889d1d4ee8dbcb5729b62026", curve)
target_2 = Point.from_hex("03633cbe3ec02b9401c5effa144c5b4d22f87940259634858fc7e59b1c09937852", curve)
start_range = 0
end_range = 256
ec_operations(start_range, end_range, target_2, target_1, curve)
Haters gonna keep hatin', bitches gonna keep bitchin. Beware of the old lady ahead, her whining kills.😉
