Understanding Diffie-Hellman

Diffie-Hellman is an asymmetric encryption algorithm that allows the secure exchange of a secret key over a public channel. This method ensures that two parties can establish a shared secret even if the communication channel is insecure.

Key Points

Asymmetric Encryption: Diffie-Hellman uses a pair of keys (public and private) for encryption and decryption.
Public Channel: The algorithm allows the exchange of a secret over an insecure public channel.
Prime Number Requirement: The algorithm requires a prime number q and a generator g that satisfies certain conditions.

How It Works

Step-by-Step Process

Agree on Parameters: Alice and Bob agree on a prime number q and a generator g. For example, q = 29 and g = 3.
Alice's Calculation:
- Alice chooses a random number a smaller than q.
- She calculates A = (g^a) mod q.
- Alice sends A to Bob while keeping a secret.
- Example: Alice picks a = 13, calculates A = 3^13 % 29 = 19, and sends 19 to Bob.
Bob's Calculation:
- Bob chooses a random number b smaller than q.
- He calculates B = (g^b) mod q.
- Bob sends B to Alice while keeping b secret.
- Example: Bob picks b = 15, calculates B = 3^15 % 29 = 26, and sends 26 to Alice.
Shared Secret Calculation:
- Alice receives B and calculates the shared secret key = B^a mod q.
- Bob receives A and calculates the shared secret key = A^b mod q.
- Example: Both Alice and Bob calculate the shared secret key = 10.

Example Calculation

Step	Alice	Bob
Choose `a`	`a = 13`
Calculate `A`	`A = 3^13 % 29 = 19`
Send `A`	`19`
Choose `b`		`b = 15`
Calculate `B`		`B = 3^15 % 29 = 26`
Send `B`		`26`
Receive `B`	`B = 26`
Calculate Key	`key = 26^13 % 29 = 10`
Receive `A`		`A = 19`
Calculate Key		`key = 19^15 % 29 = 10`

Security Considerations

Man-in-the-Middle (MitM) Attack: The Diffie-Hellman key exchange is vulnerable to MitM attacks, where an attacker intercepts and relays messages between Alice and Bob, pretending to be the other party.

Learn More

For a more detailed explanation, watch this YouTube video.