Ephemeral Diffie-Hellman

cryptography

Definition

Ephemeral Diffie-Hellman

Ephemeral Diffie-Hellman (DHE or EDH) is a variant of the Diffie-Hellman key exchange in which each party generates a fresh, temporary private key for every session rather than reusing a long-term static key.

Let $G$ be a cyclic group of prime order $q$ with generator $g$. For each session:

1. Alice chooses $a\in {\mathbb{Z}}_q$ uniformly at random, computes $A=g^a$, and sends $A$ to Bob.
2. Bob chooses $b\in {\mathbb{Z}}_q$ uniformly at random, computes $B=g^b$, and sends $B$ to Alice.
3. Both derive the shared secret $K=g^{ab}$ via

$$K=B^a=(g^b{)}^a=g^{ab}=(g^a{)}^b=A^b.$$

The private exponents $a$ and $b$ are discarded after the session ends.