Quote from: COBRAS on Today at 10:44:04 AM

Quote from: bnm2610906 on Today at 09:29:45 AM

Quote from: krashfire on April 12, 2024, 08:49:21 AM

I had made a little change in my code. im just hoping i could receive some advice on whether my method here is more efficient or sound?

i got really lucky because i was told that 6 weeks was really fast. but.. i am hoping to go faster.

so my question is,

please take a look at my code in sagemath, and see what i might have miss out or can improve to make it much better?

and while im here, i was told the u1 value some sort of give a "hint" on the k nonce. i realise that it just really is the real mod n of k nonce only but its not k nonce itself,

please check my code to see where i can improve. thank you.

Code:

import random
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141

E = EllipticCurve(GF(p), [0, 7])

G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)) # Base point

r=0x
s=0x
z=0x

def egcd(a, b):

   if a == 0:

   return (b, 0, 1)

   else:

   g, y, x = egcd(b % a, a)

   return (g, x - (b // a) * y, y)
def modinv(a, m):

   g, x, y = egcd(a, m)

   if g != 1:

   raise Exception('modular inverse does not exist')

   else:

   return x % m
def make_public(r,s,z):
   R = E.lift_x(Integer(r))
   w = int(modinv(s, n))
   u1 = int((z * w) % n)
   u2 = int((r * w) % n)
   #R=u1*G + u2*public_key
   #pub= R*modinv(u2,n) - u1*modinv(u2,n)%n
   u_n2=modinv(u2,n)%n
   u_n1=- u1*modinv(u2,n)%n

   pub=u_n1*G + u_n2*R
   pub2=u_n1*G + u_n2*(-R)
   return pub,pub2

def verify(r, s,z,public_key):
   w = int(modinv(s, n))
   u1 = int((z * w) % n)
   u2 = int((r * w) % n)
   D=u1*G + u2*public_key
   x,y=D.xy()
   x=int(x)

   if (r % n) == (x % n):
   print( "signature matches")

   else:
   print("invalid signature")

def calc_u(r,s,z):
   mod_s= modinv(s,n)%n
   u1=mod_s*z%n
   u2=mod_s*r%n
   print("u1==",u1,"n-u1=",n-u1)
   print("u2==",u2,"n-u2=",n-u2)
   return u1,u2
u1, u2 = calc_u(r,s,z)

pub1,pub2=make_public(r,s,z)
print("public_key1",pub1)
print("pub1_x=",hex(pub1.xy()[0]))
print("public_key2",pub2)
print("pub2_x=",hex(pub2.xy()[0]))
verify(r,s,z,pub1)
verify(r,s,z,pub2)
print()

# Find the real mod n for k and K nonce

for i in range(1, n):
   k = (r * i + z) * modinv(s, n) % n
   R = E.lift_x(Integer(r))
   K = k * G
   u1 = (modinv(s, n) * z) % n
   u2 = (modinv(s, n) * r) % n
   if K == (u1 * G + u2 * R):
   print("Found real k:", k)
   break

Traceback (most recent call last):
File "/content/SageMath/crack_weak_ECDSA_nonces_with_LLL.py", line 9, in <module>
E = EllipticCurve(GF(p), [0, 7])
NameError: name 'EllipticCurve' is not defined

It's strange. Yesterday was still running fine, but today after restarting the cloud code, why did it end up like this?

this is a SAGEMATH code, not python

and needs put r,s,z data to:

r=0x
s=0x
z=0x

G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)) # Base point

I'd like to ask if I start with this line of code, and if so, which range value does it look like?