Diffie-Hellman Key Calculator

About this calculator

The Diffie-Hellman key exchange lets two parties agree on a shared secret over a public channel without ever transmitting the secret itself. Both sides agree on a public prime modulus p and generator g; each picks a private key (a and b) and computes a public key — A = g^a mod p and B = g^b mod p — which they exchange openly. Each side then raises the other's public key to their own private key: the shared secret is s = B^a mod p = A^b mod p = g^(ab) mod p, arriving at the same number without either private key ever crossing the wire.

Security rests on the discrete logarithm problem — computing a from g, p and A = g^a mod p is computationally infeasible for a large enough prime p, even though computing A from a is easy. Computer science students, security engineers, and protocol implementers use small-number examples like this to verify by hand how TLS, SSH, and other protocols establish a shared session key before any application data is sent.