Searching for K nonce

[krashfire]

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

[1714497407]

1714497407

[stanner.austin]

Hi
This is my version if you have private key or may need to bf.

Code:

def Get_Nonce_K_With_Private_Key(r,s,z,x):
	if (x == 0 ):
		return 0;
	sinv = pow(s,N-2,N)
	t1 = (x*r) % N
	t2 = (z+t1) % N 
	myK = (sinv*t2) % N
	if (myK == 0 ):
		return 0;
	if ((myK*G).x.num == r):
		return myK
	return 0

But you can always do R == K * G to find out if you really found valid K or not.

Regards,

[COBRAS]

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=0x00fc5e2ab560be4649b85511940daf8302cf2e2e06bfd60a75c8bae5f832da289c
s=0x45c4c9d548699bbc5f3484a2d6d59ac07ea3328a1deb6b2bb9f2f8f0727be1de
z=0x6559f4e4b8d7824a641418b992f913411a1995fa35668c8c634b5a19a93a944c

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

great , I will try

[COBRAS]

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=0x00fc5e2ab560be4649b85511940daf8302cf2e2e06bfd60a75c8bae5f832da289c
s=0x45c4c9d548699bbc5f3484a2d6d59ac07ea3328a1deb6b2bb9f2f8f0727be1de
z=0x6559f4e4b8d7824a641418b992f913411a1995fa35668c8c634b5a19a93a944c

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

I take error:

line 12
SyntaxError: Non-ASCII character '\xc2' in file nonce9.sage.py on line 12, but no encoding declared; see http://python.org/dev/peps/pep-0263/ for details

[COBRAS]

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=0x00fc5e2ab560be4649b85511940daf8302cf2e2e06bfd60a75c8bae5f832da289c
s=0x45c4c9d548699bbc5f3484a2d6d59ac07ea3328a1deb6b2bb9f2f8f0727be1de
z=0x6559f4e4b8d7824a641418b992f913411a1995fa35668c8c634b5a19a93a944c

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

Krashfire,


 u1 = (modinv(s, n) * z) % n
    u2 = (modinv(s, n) * r) % n
    if K == (u1 * G + u2 * R):



u1, u2 are known. What a problem find u1*G +u2*R ?

u2 * R is a number? How you add number to point u1*G ?

br

[krashfire]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

bro, test your code at this test data, I try you scrypt from your orevious topic not found k !


this test data from ecdsa123:



r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


k = 6

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

[krashfire]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

im use this rsz bro:


r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


?

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

im use this rsz bro:


r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


?

I put this part:

k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break


and put to your code  of your presious thread, working.

('Found real k:', 87069027473077907962879272067307854440257155754636880132689937952837782290998, 6)
('Match found for u1 at i =', 0)
('!!!', 6, 4)


but ecdsa123 tell what nonce is 6, not  87069027473077907962879272067307854440257155754636880132689937952837782290998

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

little example how to  add your code to bsgs or kangaroo software:


r= 1157805759774926330395047584278303292417$
s= 1157844137307671538341935006214495221120$
z= 2

i = 0


while True:
    k = (z + i )%n # * modinv(s, n) % n #start range
    print("k",k)
    R = E.lift_x(Integer(r))
    K = k * ( modinv(s, n) * G) #( modinv(s, n) * G) - base point
    u1 = (modinv(s, n) * z) % n
    u2 = (modinv(s, n) * r) % n
#if k <=2**100:print("$$$",k,i)
    if K == (u1 * G + u2 * R): # in () is a pubkey
        print("&",k)
        print("yes!!!")
        print("Found real k:", k,i)
        break

    i = i +  r




('Found real k:', 115723009678374821119173625523542436186184050224879315428219959977314762717633, 69468345586495579823702855056698197545037187162025383734124577568490557018931





enjoy ))

[krashfire]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

im use this rsz bro:


r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


?

lol. of course that wont work. its not real rsz

[COBRAS]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

im use this rsz bro:


r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


?

lol. of course that wont work. its not real rsz

why this not work ?


replace base pooint and "i" in cangaroo and you take "i" were finder k,after put "i" to your formula....




this is work, jast enother way of using cangaroo and bsgs search

try with your real 6 weeks search rsz, and tall what time was need to find k with cuda bsgs or cuda kangaroo ?

thx

ps this is work, bro

[COBRAS]

@Krashfire,  do you have any new findings ?

[dexizer7799]

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
# Loop to search for k in hexadecimal
for i in range(0, n):
    k = (r * i + z) * modinv(s, n) % n
    R = E.lift_x(Integer(r))
    P = k * G
    print("K:", hex(P.xy()[0]))  # Print the x-coordinate of K in hexadecimal
    if hex(P.xy()[0]) == hex(r):
        print("Found real k:", hex(P.xy()[0]))  # Print the real k in hexadecimal
        break

i just updated the code in sagemath.

error again, I try remove error, same error:


k = ((r * i%n + z%n)%n * modinv(s, n) % n)%n
  File "sage/structure/element.pyx", line 1921, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13675)
  File "sage/structure/coerce.pyx", line 1167, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9612)
  File "sage/structure/element.pyx", line 1919, in sage.structure.element.Element.__mod__ (build/cythonized/sage/structure/element.c:13640)
  File "sage/structure/element.pyx", line 1954, in sage.structure.element.Element._mod_ (build/cythonized/sage/structure/element.c:13933)
TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

that's impossible. Have you insert your rsz? I did with 3 different sets of rsz. The signature verified. And the code works.

im use this rsz bro:


r= 115780575977492633039504758427830329241728645270042306223540962614150928364886
s= 115784413730767153834193500621449522112098284939719838943229029456606672741370
z= 2


?

lol. of course that wont work. its not real rsz

why this not work ?


replace base pooint and "i" in cangaroo and you take "i" were finder k,after put "i" to your formula....




this is work, jast enother way of using cangaroo and bsgs search

try with your real 6 weeks search rsz, and tall what time was need to find k with cuda bsgs or cuda kangaroo ?

thx

ps this is work, bro

Hi sir I want to try your code with these rsz

1:

r = 0x57a463b8ac30f2ed36767d5ccabf04fbe29c94b054b4309996f086556428c748
s = 0x5a4c7e96159688e8cd2525a3230ec5184597d6cfbaf037ca5815fa01097f67cc
z = 0xa37f38a2db651ba57f68ef4d0ac297e732d0eb3954bb85ac069569f9b372daa0

2:

r = 0x4f7f2657387cf1fef8152e2bbd39f153ee235e1f46294fded0d42dacbbe7ea
s = 0x430773be7ebda7fba5ed2f829e9b47a7f92d526905c250780f044ed860de0786
z = 0x76757e4b29801bbb747a125c0bb6752feeeabd84c58fe3dd71e94eed3839dfaa

Can you help me with script to find private keys from these rsz.

[jacky19790729]

Hi sir I want to try your code with these rsz
1:
r = 0x57a463b8ac30f2ed36767d5ccabf04fbe29c94b054b4309996f086556428c748
s = 0x5a4c7e96159688e8cd2525a3230ec5184597d6cfbaf037ca5815fa01097f67cc
z = 0xa37f38a2db651ba57f68ef4d0ac297e732d0eb3954bb85ac069569f9b372daa0
2:
r = 0x4f7f2657387cf1fef8152e2bbd39f153ee235e1f46294fded0d42dacbbe7ea
s = 0x430773be7ebda7fba5ed2f829e9b47a7f92d526905c250780f044ed860de0786
z = 0x76757e4b29801bbb747a125c0bb6752feeeabd84c58fe3dd71e94eed3839dfaa
Can you help me with script to find private keys from these rsz.

These 2 sets of r,s,z   use different public keys...the private keys must also be different..
1:
0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd036413e

2:
0x000000000000000000000000000000000000000000000001a838b13505b26867

[COBRAS]

Hi sir I want to try your code with these rsz
1:
r = 0x57a463b8ac30f2ed36767d5ccabf04fbe29c94b054b4309996f086556428c748
s = 0x5a4c7e96159688e8cd2525a3230ec5184597d6cfbaf037ca5815fa01097f67cc
z = 0xa37f38a2db651ba57f68ef4d0ac297e732d0eb3954bb85ac069569f9b372daa0
2:
r = 0x4f7f2657387cf1fef8152e2bbd39f153ee235e1f46294fded0d42dacbbe7ea
s = 0x430773be7ebda7fba5ed2f829e9b47a7f92d526905c250780f044ed860de0786
z = 0x76757e4b29801bbb747a125c0bb6752feeeabd84c58fe3dd71e94eed3839dfaa
Can you help me with script to find private keys from these rsz.

These 2 sets of r,s,z   use different public keys...the private keys must also be different..
1:
0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd036413e

2:
0x000000000000000000000000000000000000000000000001a838b13505b26867

oh f-k, you really find privkeys?

you use kangaroo multy gpu from GL or keyhunt ?


 

[jacky19790729]

oh f-k, you really find privkeys?
you use kangaroo multy gpu from GL or keyhunt ?
 

use Google .......so I find 2 private key from his 2 rsz
 

1:  
D:\python\bitcoin_rsz>python getz_input.py -txid a37f2f87bd371d621178605a79062010298c31fc884ed966a2041684eb8198f1

Starting Program...
======================================================================
[Input Index #: 0]
     R: 57a463b8ac30f2ed36767d5ccabf04fbe29c94b054b4309996f086556428c748
     S: 5a4c7e96159688e8cd2525a3230ec5184597d6cfbaf037ca5815fa01097f67cc
     Z: a37f38a2db651ba57f68ef4d0ac297e732d0eb3954bb85ac069569f9b372daa0
PubKey: 02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9

2:   puzzle #65
D:\python\bitcoin_rsz>python getz_input.py -txid 65c7e5cbff719ff7fd32645b777cb20b69db513f1cd6a064dfcc95b69ad77acc

Starting Program...
======================================================================
[Input Index #: 0]
     R: 4f7f2657387cf1fef8152e2bbd39f153ee235e1f46294fded0d42dacbbe7ea
     S: 430773be7ebda7fba5ed2f829e9b47a7f92d526905c250780f044ed860de0786
     Z: 76757e4b29801bbb747a125c0bb6752feeeabd84c58fe3dd71e94eed3839dfaa
PubKey: 0230210c23b1a047bc9bdbb13448e67deddc108946de6de639bcc75d47c0216b1b

[dexizer7799]

oh f-k, you really find privkeys?
you use kangaroo multy gpu from GL or keyhunt ?
 

use Google .......so I find 2 private key from his 2 rsz
 

1:  
D:\python\bitcoin_rsz>python getz_input.py -txid a37f2f87bd371d621178605a79062010298c31fc884ed966a2041684eb8198f1

Starting Program...
======================================================================
[Input Index #: 0]
     R: 57a463b8ac30f2ed36767d5ccabf04fbe29c94b054b4309996f086556428c748
     S: 5a4c7e96159688e8cd2525a3230ec5184597d6cfbaf037ca5815fa01097f67cc
     Z: a37f38a2db651ba57f68ef4d0ac297e732d0eb3954bb85ac069569f9b372daa0
PubKey: 02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9

2:   puzzle #65
D:\python\bitcoin_rsz>python getz_input.py -txid 65c7e5cbff719ff7fd32645b777cb20b69db513f1cd6a064dfcc95b69ad77acc

Starting Program...
======================================================================
[Input Index #: 0]
     R: 4f7f2657387cf1fef8152e2bbd39f153ee235e1f46294fded0d42dacbbe7ea
     S: 430773be7ebda7fba5ed2f829e9b47a7f92d526905c250780f044ed860de0786
     Z: 76757e4b29801bbb747a125c0bb6752feeeabd84c58fe3dd71e94eed3839dfaa
PubKey: 0230210c23b1a047bc9bdbb13448e67deddc108946de6de639bcc75d47c0216b1b

Ok but how can I find these rsz with this script very fast?