What is the Diffie–Hellman key exchange?

Diffie–Hellman is a key exchange protocol that allows two parties to agree on a shared secret over an insecure channel. They choose a public prime p and a base g, then each party picks a private integer, sends a corresponding public value, and both compute the same shared secret using modular exponentiation.

Is this calculator cryptographically secure?

No. This calculator is an educational tool that uses small integers and simple JavaScript arithmetic. It is not suitable for real-world security. Production systems use very large parameters and carefully vetted implementations.

Why do we need a prime modulus in Diffie–Hellman?

Using a large prime modulus p and an appropriate generator g ensures that the multiplicative group modulo p has desirable algebraic properties. This makes the discrete logarithm problem hard, which underpins the security of the protocol.

Can I use negative or non-integer values?

No. The protocol is defined over integers modulo a prime p. This calculator accepts only integer values and treats the private keys modulo p-1 for convenience.

Diffie–Hellman Key Exchange Calculator

Interactive Diffie–Hellman key exchange calculator. Choose a small prime and generator, set Alice and Bob's private keys, and see how the shared secret is derived step-by-step. Educational use only, not for real cryptography.

Full original guide (expanded)

Diffie–Hellman Key Exchange Calculator

Simulate the Diffie–Hellman exchange with small integers to see how public values produce the same shared secret.

Inputs

Use small integers for learning. This is not suitable for real cryptography.

Prime modulus (p) Generator (g) Alice private key (a) Bob private key (b)

Results

Alice public value

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Bob public value

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Shared secret (Alice)

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Shared secret (Bob)

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How the exchange works

Alice publishes A = g^a mod p, Bob publishes B = g^b mod p.
Alice computes s = B^a mod p, Bob computes s = A^b mod p.
Both results match, creating a shared secret without sharing private keys.

Audit: Needs review

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.
Note: This page needs review to confirm formulas and sources.

No formulas provided in audit spec.

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verification pending · Last code update: 2026-01-19

Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft

Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog

0.1.0-draft — 2026-01-19: Initial draft (review required).