Interactive visualization of classical Diffie-Hellman key exchange with color-mixing analogy and modular arithmetic steps.
Follow one complete exchange from public parameters through both matching secret calculations. Enter a prime modulus p, a base g, and separate private exponents for Alice and Bob. The visualizer shows each public value, then uses the received public value to derive the same result on both sides, alongside a color-mixing analogy. The common surprise is that Alice's and Bob's public values are meant to be exposed, while their private exponents and the resulting shared secret must remain confidential. Matching outputs demonstrate agreement, not authentication or production-grade security.
A concrete input and expected output from the current implementation.
Input
p = 23, g = 5, Alice private exponent a = 6, Bob private exponent b = 15
Expected output
Alice public value A = 5^6 mod 23 = 8. Bob public value B = 5^15 mod 23 = 19. Alice computes 19^6 mod 23 = 2, and Bob computes 8^15 mod 23 = 2. The shared secret is 2.
Each side combines the other side's public value with its own private exponent. Both calculations reduce to 5^(6*15) mod 23, so they produce the same residue, 2.
With modulus p and base g, Alice selects private exponent a and publishes A = g^a mod p. Bob selects b and publishes B = g^b mod p. The color track distinguishes the common starting value, each private contribution, and the values sent across the public channel. It is an analogy for the exchange, not another cryptographic calculation.
After exchanging A and B, Alice computes s = B^a mod p while Bob computes s = A^b mod p. Both equal g^(ab) mod p, so the displayed secrets match. The arithmetic steps help check modular powers, whose final residues can be small even when ordinary exponentiation would produce very large numbers.
Alice raises Bob's public value to a, producing (g^b)^a, while Bob raises Alice's public value to b, producing (g^a)^b. Exponent multiplication gives the same g^(ab) before reduction modulo p. The public values carry the needed mathematical contribution without directly transmitting a or b.
No. A small integer from this visualizer is an educational result, not a deployable key. A secure protocol must also address parameter selection, private-value generation, public-value validation, peer authentication, and key derivation. The visualizer verifies the core equality but does not turn hand-entered demonstration values into a secure communications protocol.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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