Diffie-Hellman Key Exchange

cryptography

Definition

Diffie-Hellman Key Exchange

The Diffie-Hellman key exchange is a key exchange algorithm for two parties to agree on a shared secret key over an insecure channel. Its security relies on the hardness of the discrete logarithm problem.

Protocol

Let $p$ be a prime and $g$ a primitive root modulo $p$, agreed upon publicly.

1. Alice chooses a secret ${\mathrm{prv}}_A$ and sends ${\mathrm{pub}}_A$ to Bob

   $${\mathrm{pub}}_A=g^{{\mathrm{prv}}_A}\mathrm{mod}p$$

2. Bob chooses a secret ${\mathrm{prv}}_B$ and sends ${\mathrm{pub}}_B$ to Alice

   $${\mathrm{pub}}_B=g^{{\mathrm{prv}}_B}\mathrm{mod}p$$

3. Alice computes the shared secret $S$

   $$S={\mathrm{pub}}_B^{{\mathrm{prv}}_A}\mathrm{mod}p=g^{{\mathrm{prv}}_A\cdot {\mathrm{prv}}_B}\mathrm{mod}p$$

4. Bob computes the shared secret $S$

   $$S={\mathrm{pub}}_A^{{\mathrm{prv}}_B}\mathrm{mod}p=g^{{\mathrm{prv}}_A\cdot {\mathrm{prv}}_B}\mathrm{mod}p$$

¹

Man-in-the-Middle Attack

¹

Footnotes

1. 192.019 Introduction to Security ↩ ↩²