HomeCybersecuritySchnorr Signatures: 2D Exponentiation Ladder & Hash Avalanche

Schnorr Signatures: 2D Exponentiation Ladder & Hash Avalanche

Interactive 2D counterpart to the 3D modular-ring Schnorr signature simulator: a genuine square-and-multiply exponentiation ladder plots every step of the real BigInt modular arithmetic, alongside a byte-level SHA-256 avalanche heatmap that shows exactly why a single tampered character breaks a Fiat-Shamir signature — both computed independently from scratch, not reprojected from the 3D scene.

Cybersecurity2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version
2d-zero-knowledge-proof-schnorr-protocol ↗ Open standalone

This is a genuine, independently-computed 2D counterpart to the 3D modular-ring Fiat–Shamir Schnorr signature simulator. Instead of plotting group elements as angles on a rotating ring, it renders the real left-to-right square-and-multiply algorithm as a bit-by-bit ladder for every modular exponentiation the protocol performs, and separately visualizes the byte-level diffusion of the real SHA-256 hash (via the browser's Web Crypto API) that turns the commitment and message into the Fiat–Shamir challenge. Sign a message to trace the commitment's exponentiation ladder, then verify it: the independently recomputed g^s and t·y^c' ladders converge to the same final value only when the signature is valid, and the avalanche grid below shows exactly why tampering with even one character of the message breaks that match — a single flipped character changes roughly half the bits of every byte of the hash. Every number here — the modular exponentiation trace and the hash digest — is computed from scratch in this page, verified against a plain modpow implementation and against the theoretical ~50% avalanche rate before shipping.

⚙ Under the hood

A genuine 2D counterpart to the 3D modular-ring Schnorr signature simulator: plots the real bit-by-bit square-and-multiply exponentiation ladder for every modular exponentiation in the Fiat-Shamir signature scheme, plus a byte-level SHA-256 avalanche heatmap showing why tampering with one character breaks verification.

cryptographydigital-signaturesschnorrfiat-shamirhash-functionzero-knowledgemodular-exponentiationavalanche-effect

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

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