Category:Diffie-Hellman-Merkle Key Exchange
This category contains results about Diffie-Hellman-Merkle Key Exchange.
Definitions specific to this category can be found in Definitions/Diffie-Hellman-Merkle Key Exchange.
The Diffie-Hellman-Merkle key exchange is a safe method of exchanging a key.
Suppose Alice and Bob with to communicate securely.
They decide to use the order $p - 1$ cyclic group $G$ of multiplication modulo $p$ consisting of the non-zero elements of a finite field of order $p$
They choose a generator $g$ of $G$.
Alice chooses an integer $a$ and calculates $A = g^a$ modulo $p$.
Bob chooses an integer $b$ and calculates $B = g^b$ modulo $p$.
Both can calculate the key $g^{a b}$ modulo $p$:
- $K = B^a$, calculated by Alice
and:
- $K = A^b$, calculated by bob.
An eavesdropper may know $p$, $g$, $A$ and $B$ but cannot calculate $K$ without solving the discrete logarithm problem.
If $p$ is large, the discrete logarithm problem is very difficult to solve.
So $K$ can be used as the basis of a private key for Alice and Bob.
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