Cryptography Questions Long
The Diffie-Hellman key exchange is a cryptographic protocol that allows two parties to establish a shared secret key over an insecure communication channel. It was developed by Whitfield Diffie and Martin Hellman in 1976 and is widely used in various secure communication protocols.
The key exchange process involves the following steps:
1. Setup: Both parties, let's call them Alice and Bob, agree on a large prime number, p, and a primitive root modulo p, g. These values are publicly known and can be shared openly.
2. Key Generation: Alice and Bob independently choose their secret values, a and b, respectively. These values are kept private and not shared with anyone.
3. Public Key Exchange: Alice calculates A = g^a mod p and sends this value to Bob. Similarly, Bob calculates B = g^b mod p and sends it to Alice. These values are exchanged over the insecure channel.
4. Shared Secret Calculation: Alice and Bob use the received values to calculate the shared secret key. Alice computes s = B^a mod p, while Bob computes s = A^b mod p. Both calculations result in the same shared secret key, which can be used for symmetric encryption or other cryptographic purposes.
The security of the Diffie-Hellman key exchange relies on the computational difficulty of calculating discrete logarithms. While it is relatively easy to compute A or B given the values of a or b, it is computationally infeasible to determine the secret values a or b from A or B. This property ensures that even if an attacker intercepts the public values, they cannot derive the shared secret key without knowing the private values.
However, it is important to note that the Diffie-Hellman key exchange alone does not provide authentication or protection against man-in-the-middle attacks. Additional measures, such as digital signatures or certificates, are required to ensure the authenticity and integrity of the exchanged public values.