Key exchange algorithms are essential cryptographic tools used to establish secure communication channels between two parties. These algorithms enable the parties to agree upon a shared secret key that can be used for secure communication. Various key exchange algorithms such as Diffie-Hellman, RSA, and Elliptic Curve Cryptography offer different levels of security and efficiency, and the choice of algorithm depends on the specific needs of the application. Regardless of the algorithm chosen, the key exchange process must ensure that the secret key remains confidential and protected from interception.
The Diffie-Hellman algorithm is a widely used key exchange algorithm in cryptography, named after its inventors, Whitfield Diffie and Martin Hellman. It enables two parties to establish a shared secret key over an insecure communication channel.
Let me explain the key exchange process of the Diffie-Hellman algorithm in more detail:
- First, the two parties, Alice and Bob, agree on two public values: a prime number, p, and a generator, g. These values are agreed upon ahead of time and are assumed to be known to both parties.
- Alice chooses a secret value, a, which is a randomly selected integer between 1 and p-1. She then computes A = g^a mod p, where “^” denotes exponentiation. The value A is known as Alice’s public key.
- Bob also chooses a secret value, b, which is a randomly selected integer between 1 and p-1. He then computes B = g^b mod p. The value B is known as Bob’s public key.
- Alice sends her public key, A, to Bob, and Bob sends his public key, B, to Alice.
- Alice then computes the shared secret key, K, using the formula K = B^a mod p. This means that Alice takes Bob’s public key, B, raises it to the power of her secret value, a, and takes the result modulo p to obtain the shared secret key, K.
- Bob also computes the shared secret key, K, using the formula K = A^b mod p. This means that Bob takes Alice’s public key, A, raises it to the power of his secret value, b, and takes the result modulo p to obtain the shared secret key, K.
Now both Alice and Bob have the same shared secret key, K, which they can use to encrypt and decrypt messages using a symmetric encryption algorithm.
It is important to note that the values of a and b are kept secret and are never shared with anyone else. Also, even though A and B are exchanged publicly, they do not reveal any information about a or b that can be used to compute the shared secret key, K, without solving the discrete logarithm problem, which is believed to be computationally difficult.
# Input: Prime number p, generator g, secret integers a and b
# Output: Shared secret key K
# Alice's computation
A = g^a mod p # Compute Alice's public key
# Bob's computation
B = g^b mod p # Compute Bob's public key
# Key exchange
# Alice sends A to Bob, Bob sends B to Alice
# Shared secret computation
K1 = B^a mod p # Alice computes shared secret key
K2 = A^b mod p # Bob computes shared secret key