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