61 lines
1.5 KiB
Python
61 lines
1.5 KiB
Python
|
from math import ceil, sqrt
|
||
|
|
|
||
|
|
def bsgs(p, g, h):
|
||
|
|
##Berechne d in h = g^d mod p
|
||
|
|
|
||
|
|
N = ceil(sqrt(p - 1)) # phi(p) is p-1 if p is prime
|
||
|
|
|
||
|
|
# Baby step: compute a look-up table of g^i values for i = 0, 1, ..., N
|
||
|
|
lookup_table = {pow(g, i, p): i for i in range(N)}
|
||
|
|
|
||
|
|
# Precompute via Fermat's Little Theorem
|
||
|
|
c = pow(g, N * (p - 2), p)
|
||
|
|
|
||
|
|
# Giant step: Search for an equivalence in the lookup_table
|
||
|
|
for j in range(N):
|
||
|
|
y = (h * pow(c, j, p)) % p
|
||
|
|
if y in lookup_table:
|
||
|
|
return j * N + lookup_table[y]
|
||
|
|
|
||
|
|
# Solution not found
|
||
|
|
return None
|
||
|
|
|
||
|
|
|
||
|
|
def main():
|
||
|
|
|
||
|
|
p = 27893
|
||
|
|
g = 3729
|
||
|
|
alpha = 11819
|
||
|
|
beta = 1531
|
||
|
|
|
||
|
|
# Find the discrete logarithm a such that g^a = alpha mod p
|
||
|
|
a = bsgs(p, g, alpha)
|
||
|
|
print(f"a = {a}")
|
||
|
|
|
||
|
|
# Validate the result
|
||
|
|
if a is None:
|
||
|
|
print("No solution found for a")
|
||
|
|
else:
|
||
|
|
# Recompute the shared secret key: K = beta^a mod p
|
||
|
|
K = pow(beta, a, p)
|
||
|
|
print(f"Shared secret key K = {K}")
|
||
|
|
|
||
|
|
# Find the discrete logarithm b such that g^b = beta mod p
|
||
|
|
b = bsgs(p, g, beta)
|
||
|
|
print(f"b = {b}")
|
||
|
|
|
||
|
|
# Validate the result
|
||
|
|
if b is None:
|
||
|
|
print("No solution found for b")
|
||
|
|
else:
|
||
|
|
# Recompute the shared secret key: K = alpha^b mod p
|
||
|
|
K2 = pow(alpha, b, p)
|
||
|
|
if K2 == K:
|
||
|
|
print("b is correct")
|
||
|
|
else:
|
||
|
|
print("b is not correct")
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
main()
|