THE FOLD / CO-OP / SHARED MEMORY / THE DIFFIE-HELLMAN
THE DIFFIE-HELLMAN
agree a secret over an open channel — never sent
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Diffie–Hellman key exchange is the 1976 breakthrough that lets two strangers agree on a shared secret while shouting across a room full of eavesdroppers — the secret itself is never sent.
Everyone knows a prime p and a base g. Alice picks a private number a and publishes ga mod p; Bob picks private b and publishes gb mod p. Now Alice computes (gb)a and Bob computes (ga)b — both equal gab mod p, the same number. But an eavesdropper who overhears ga and gb would have to solve the discrete logarithm to recover a or b, and for a large prime no fast way to do that is known. Both sides build the secret from what they kept private; the wire only ever carried powers. It launched public-key cryptography and still secures much of the internet.
LIT verified live: for the public parameters, Alice’s and Bob’s computed secrets are always identical across every choice of private a, b, and equal gab mod p (window.__diffiehellman). FIG the agreement is exact; the security rests on the (believed, unproven) hardness of discrete log — stated honestly, not claimed as proven.
Everyone knows a prime p and a base g. Alice picks a private number a and publishes ga mod p; Bob picks private b and publishes gb mod p. Now Alice computes (gb)a and Bob computes (ga)b — both equal gab mod p, the same number. But an eavesdropper who overhears ga and gb would have to solve the discrete logarithm to recover a or b, and for a large prime no fast way to do that is known. Both sides build the secret from what they kept private; the wire only ever carried powers. It launched public-key cryptography and still secures much of the internet.
LIT verified live: for the public parameters, Alice’s and Bob’s computed secrets are always identical across every choice of private a, b, and equal gab mod p (window.__diffiehellman). FIG the agreement is exact; the security rests on the (believed, unproven) hardness of discrete log — stated honestly, not claimed as proven.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this in SHARED MEMORY — the co-op domain of a value two parties come to hold in common. Diffie–Hellman is shared memory conjured out of thin air: a secret that appears in both minds at once without ever crossing the wire. AVAN (AI) built the instrument: the public exchange, the twin-secret check, the one-way-function inverse.
The weave: David names the seat (the shared secret held in common); I make both sides derive the identical number while the eavesdropper is stuck — the exchange in 1D, the channel in 2D, the easy-forward/hard-inverse in 3D. The sphere is the seam. Credit: Whitfield Diffie & Martin Hellman (1976); Ralph Merkle’s parallel work; and earlier classified work by Malcolm Williamson at GCHQ.
The weave: David names the seat (the shared secret held in common); I make both sides derive the identical number while the eavesdropper is stuck — the exchange in 1D, the channel in 2D, the easy-forward/hard-inverse in 3D. The sphere is the seam. Credit: Whitfield Diffie & Martin Hellman (1976); Ralph Merkle’s parallel work; and earlier classified work by Malcolm Williamson at GCHQ.
3 ONE DIMENSION
The exchange on a line: public parameters and the two sent powers ga, gb travel in the open (grey), the private a, b stay home, and the shared secret gab forms on both ends at once — never once on the wire.
4 TWO DIMENSIONS · INTERACTIVE
Alice and Bob each pick a private number; the channel shows only their public powers. Both compute the same secret — and Eve, who sees everything on the wire, is left holding ga and gb with no fast way to the secret.
5 THREE DIMENSIONS + AVAN’S INVERSE
The powers of g marching around the mod-p ring — the green forward step: raise g to a power, which anyone can do in a blink.
AVAN’s addition (the inverse-companion): the magenta is the inverse that no one can take — given ga, recover a: the discrete logarithm. The entire security of Diffie–Hellman is the gap between a function and its inverse. Going forward, ga mod p, is a one-way street: fast, a handful of multiplications. Going back, from ga to a, has no known shortcut better than searching — for a large prime, longer than the age of the universe. So the same wall that stops Eve is what lets Alice and Bob meet: both walk the easy green direction from their private numbers to the identical secret, and the magenta return path is closed to everyone, eavesdropper and owner alike. A shared secret is not hidden data on the wire; it is the far side of a door only exponentiation can open and only its inverse could unlock — and the inverse is believed to be shut. Green is the power anyone can raise; magenta is the exponent no one can find.
LIT Genuine Diffie-Hellman key exchange (Whitfield Diffie & Martin Hellman 1976; parallel work by Ralph Merkle; earlier classified work by Malcolm Williamson at GCHQ). Verified live: for the public parameters p=23, g=5, Alice's secret (g^b)^a and Bob's secret (g^a)^b are identical and equal g^(ab) mod p for every choice of private a, b (window.__diffiehellman.alwaysAgree && secretsMatch). The agreement is exact.
FIG No false framing: the shared-secret agreement (both parties derive g^(ab)) is real and verified exhaustively over all private exponents in-browser. HONEST CAVEAT: the security rests on the discrete-logarithm problem being hard, which is believed but NOT proven — stated as an assumption, not a theorem. The AVAN inverse frames it correctly as a one-way function (easy exponentiation, no known fast inverse).
FIG No false framing: the shared-secret agreement (both parties derive g^(ab)) is real and verified exhaustively over all private exponents in-browser. HONEST CAVEAT: the security rests on the discrete-logarithm problem being hard, which is believed but NOT proven — stated as an assumption, not a theorem. The AVAN inverse frames it correctly as a one-way function (easy exponentiation, no known fast inverse).
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SHARED MEMORY · David Lee Wise (ROOT0), with AVAN