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DH

The document contains a Python script that generates a random prime number and finds a primitive root for it. It simulates a key exchange process between two parties, A and B, using the generated prime and primitive root to compute their private and public keys, as well as a shared secret. The script includes assertions to ensure the shared secrets computed by both parties are equal.

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mayurgbari52076
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5 views1 page

DH

The document contains a Python script that generates a random prime number and finds a primitive root for it. It simulates a key exchange process between two parties, A and B, using the generated prime and primitive root to compute their private and public keys, as well as a shared secret. The script includes assertions to ensure the shared secrets computed by both parties are equal.

Uploaded by

mayurgbari52076
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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import random

def is_prime(num):
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True

def generate_prime():
while True:
num = random.randint(0, 100)
if is_prime(num):
return num

n = generate_prime()
print("Generated Prime (n):", n)

def find_primitive_root(n):
for g in range(2, n):
values = set()
for i in range(1, n):
values.add(pow(g, i, n)) # Compute g^i % n
if len(values) == n - 1: # If all numbers from 1 to n-1 are covered
return g
return None

g = find_primitive_root(n)
print("Primitive Root (g):", g)

# n = 19
# g = 7

a = random.randint(1, n-1) #Xa


A = (g ** a) % n

b = random.randint(1, n-1) #Xb


B = (g ** b) % n

secret_a = (B ** a) % n
secret_b = (A ** b) % n

print(f"A Private Key: {a}")


print(f"B Private Key: {b}")
print(f"A Public Key: {A}")
print(f"B Public Key: {B}")
print(f"A Shared Secret: {secret_a}")
print(f"B Shared Secret: {secret_b}")

assert secret_a == secret_b, "Key exchange failed!"

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