Key Exchange

Key exchange in cryptography refers to the process of securely exchanging encryption keys between two parties to establish a shared secret key that can be used for secure communication. The objective of key exchange is to ensure that the shared key remains confidential and is not intercepted or tampered with by attackers.

In a secure key exchange, the two parties (usually referred to as Alice and Bob) follow a protocol that allows them to agree on a secret key without revealing it to others, even if the communication channel is unsecure or potentially compromised.

One of the most widely used key exchange protocols is the Diffie-Hellman key exchange algorithm. Here's how it works:

1. Initialization: Both Alice and Bob publicly agree on a large prime number (p) and a primitive root (g) modulo p. These parameters are used to define the key exchange group.
2. Private and Public Keys: Each party generates their private key. For example, Alice selects a random private key (a), and Bob selects a random private key (b).
3. Public Key Calculation: Based on their private keys and the agreed-upon parameters (p and g), both Alice and Bob calculate their public keys. Alice computes A = g^a mod p, and Bob computes B = g^b mod p.
4. Key Exchange: Alice and Bob exchange their public keys (A and B) over an unsecure communication channel.
5. Shared Secret: Both Alice and Bob then use the other party's public key and their own private key to calculate the shared secret. For Alice, the shared secret is S = B^a mod p, and for Bob, it is S = A^b mod p. The shared secret is the same for both parties and can be used as the symmetric encryption key for further communication.
6. Security: Even though the public keys (A and B) are exchanged over an insecure channel, an attacker who intercepts them would not be able to compute the shared secret without knowing Alice's or Bob's private key. This is because the discrete logarithm problem makes it computationally infeasible to determine the private key from the public key.