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For K-12 Students · Diffie-Hellman

Diffie-Hellman for a key exchange

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a key exchange live below — adjust the inputs and watch it respond, right in your browser.

Diffie-Hellman Key ExchangeLive

a shared secret over an open line

Alice

secret a = 6

sends A = g^a = 8

key = B^a = 2

Bob

secret b = 15

sends B = g^b = 19

key = A^b = 2

Eavesdropper sees g=5, p=23, A=8, B=19 — but cannot find the key 2

Controls

Presets

Generator g

Prime p

Alice's secret a

Bob's secret b

Diffie-Hellman lets two strangers agree on a secret key while an eavesdropper hears everything. Both share public numbers g and p, each picks a private exponent, and they exchange g raised to it. Raising the other's public value to your own secret yields the same shared key — yet recovering it from the public traffic requires solving the discrete logarithm, which is infeasible.

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Data Inspector

Alice sends A8

Bob sends B19

Shared secret2

Match?yes ✓

Governing equation

K = g^{ab} mod 23 = 2, A = g^{a} mod 23 = 8

Reading this result: Both sides arrive at the same key 2 because (g^a)^b and (g^b)^a are the same value mod 23 — yet an eavesdropper who sees g, p, A and B must still solve a discrete logarithm to recover it.

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More with Diffie-Hellman

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Diffie-Hellman for a key exchange" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.