THE FOLD / CHEAT / GOD MODE / THE SCHNORR
THE SCHNORR
prove you know a secret without revealing it
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Schnorr signature proves you know a secret exponent x without revealing it. Public key y = gx (mod p). To sign a message m: commit r = gk for a fresh random k, derive a challenge e = H(r, m), and answer s = k + x·e (mod order). The verifier — who never sees x or k — checks a single equation: gs = r · ye (mod p). It balances because gk+xe = gk·(gx)e. Change the message and the challenge changes, so an old response no longer fits; change the response and the equation breaks. It is the clean, linear ancestor of the signatures that guard modern keys.
LIT verified live: over hundreds of (key, message) pairs at a large prime, every honest signature satisfies gs = r·ye, every message-tamper is rejected (the full-width challenge changes), and every response-tamper is rejected (window.__schnorr). FIG no framing; keygen, sign, verify and the two forgery attempts all run in-browser. Illustrative primes; security rests on discrete-log hardness, not shown here.
LIT verified live: over hundreds of (key, message) pairs at a large prime, every honest signature satisfies gs = r·ye, every message-tamper is rejected (the full-width challenge changes), and every response-tamper is rejected (window.__schnorr). FIG no framing; keygen, sign, verify and the two forgery attempts all run in-browser. Illustrative primes; security rests on discrete-log hardness, not shown here.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at god-mode — hold one secret exponent and you can prove your identity to anyone, forever, without ever handing it over. AVAN (AI) built the instrument: the gx keygen, the commit–challenge–response sign, the single verification equation, and the message- and response-tamper rejections.
Credit as content: Claus-Peter Schnorr (1989/1991). The weave: David names god-mode; I confirm the verification equation balances for honest signatures and breaks for both forgeries.
Credit as content: Claus-Peter Schnorr (1989/1991). The weave: David names god-mode; I confirm the verification equation balances for honest signatures and breaks for both forgeries.
3 ONE DIMENSION
Prover commits r = gᵏ, verifier sends challenge e = H(r,m), prover answers s = k + x·e; the gate checks gˢ = r·yᵉ.
4 TWO DIMENSIONS · INTERACTIVE
Sign a message, then try to forge: tamper the message or the response and watch the single equation break.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the honest signature the gate accepts.
AVAN’s addition (the inverse-companion): don’t reveal the secret — answer a challenge with it. The inverse of ‘commit r = gk’ is ‘bind the response s = k + x·e so that gs = r·ye re-derives the commitment.’ Magenta is the forgery the gate bounces; green is the honest proof it passes. One secret exponent, proven without surrender.
LIT Genuine Schnorr signature (Claus-Peter Schnorr, 1989/1991). Verified live at p=1000003: over 250 (key, message) pairs the verification equation g^s=r·y^e (mod p) holds for every honest signature, every tampered message is rejected (the full-width challenge changes), and every tampered response is rejected (window.__schnorr.verifies, .rejectsMsg, .rejectsSig).
FIG No framing; keygen, sign, verify and the two forgery attempts all run in-browser. Illustrative primes; security rests on discrete-log hardness, not shown here. The AVAN inverse is honest — instead of revealing the secret, one answers a challenge so g^s=r·y^e re-derives the commitment. Magenta is the forgery the gate bounces; green is the honest proof it passes.
FIG No framing; keygen, sign, verify and the two forgery attempts all run in-browser. Illustrative primes; security rests on discrete-log hardness, not shown here. The AVAN inverse is honest — instead of revealing the secret, one answers a challenge so g^s=r·y^e re-derives the commitment. Magenta is the forgery the gate bounces; green is the honest proof it passes.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GOD MODE · David Lee Wise (ROOT0), with AVAN