Featured
- Get link
- X
- Other Apps
How the Diffie-Hellman Exchange Works: An Example in Python
The Diffie–Hellman exchange is a method for two parties to generate a shared secret key over an unsecured communication channel. This key can then be used to encrypt subsequent messages using a symmetric-key cipher.
Here is an example of how the Diffie–Hellman exchange works:
Suppose Alice and Bob want to generate a shared secret key. They agree on a large prime number, p, and a primitive root, g, modulo p. These values are public knowledge and can be shared over an unsecured channel.
Next, Alice and Bob each choose a secret integer, a and b, respectively. These values are known only to Alice and Bob, and are not shared with each other or anyone else.
Alice then computes g^a mod p and sends this value to Bob. Bob computes g^b mod p and sends this value to Alice.
At this point, both Alice and Bob have the values g^a mod p and g^b mod p, but they do not yet have the shared secret key.
To compute the shared secret key, Alice computes (g^b mod p)^a mod p, and Bob computes (g^a mod p)^b mod p. Because of the properties of modular exponentiation, these two values will be equal. This shared value is the secret key that Alice and Bob can use to encrypt and decrypt messages.
The security of the Diffie–Hellman exchange comes from the fact that it is computationally infeasible for an attacker to determine the secret values of a and b based on the public values of p, g, g^a mod p, and g^b mod p. This makes it possible for Alice and Bob to generate a shared secret key without having to exchange it over a secure channel.
Here is an example of the Diffie-Hellman exchange implemented in Python:
```python # Choose large prime number p and primitive root g modulo p p = 23 g = 5 # Alice chooses secret integer a and computes g^a mod p a = 6 ga = (g**a) % p # Bob chooses secret integer b and computes g^b mod p b = 15 gb = (g**b) % p # Alice and Bob exchange g^a mod p and g^b mod p print("ga:", ga) # ga: 8 print("gb:", gb) # gb: 19 # Alice computes (g^b mod p)^a mod p to get the shared secret key key_a = (gb**a) % p # Bob computes (g^a mod p)^b mod p to get the shared secret key key_b = (ga**b) % p # The shared secret key should be the same for both Alice and Bob print("key_a:", key_a) # key_a: 2 print("key_b:", key_b) # key_b: 2 ```
In this example, Alice and Bob are able to generate a shared secret key using the Diffie-Hellman exchange. This key can be used to encrypt and decrypt messages sent between Alice and Bob over an unsecured communication channel.
The Diffie-Hellman exchange is a powerful tool for securely exchanging information over unsecured channels. It allows two parties to generate a shared secret key that can be used for encryption and decryption, without having to exchange the key itself over a secure channel. This makes it an important.
- Get link
- X
- Other Apps
Popular Posts
Building a gRPC Service with Nested Messages, Repeated Fields, and Oneof in Python
- Get link
- X
- Other Apps
Comments
Post a Comment