Elliptic Curve

About

Every UI panel, canvas, and API call here is focused on making elliptic-curve cryptography approachable without sacrificing rigor. You explore curves, run demonstrations, encrypt/decrypt data, and inspect the full history from a single dashboard.

Curve Exploration Workflow

• Initialization: Select a preset curve or enter custom a, b, and prime p. The system calculates the full finite field group (including the point at infinity) so you can map the geometry.
• Visualization: Two synchronized canvases plot all points with optional labels, color-coded highlights, and click-to-select behaviour so you can interrogate the group law visually.
• Point Operations: The addition and scalar multiplication panels guide you through the algebraic steps, show animated point movement, and keep transcripts ready to copy as JSON/LaTeX.
• Real/Finite Comparison: The ℝ tab mirrors the workflow over the reals, while the finite field tab stays true to modular arithmetic, letting you contrast the geometry.

Demonstrations & Learning

• Diffie-Hellman: Run a live handshake using the current curve, watch Alice/Bob compute shared secrets, and scrub through animated steps with the slider, auto-scroll, and canvas highlights.
• Discrete Logarithm: Select a scalar k, optionally prefer Baby-step Giant-step, and the demo exhausts attempts with metadata, time estimates, and a human-friendly summary.
• Tutorial player: Contextual tutorials are available from the menu, each explaining curve initialization, point addition, and other core concepts with inline animations.
• Interactive explanations: Expandable cards describe associativity, identity, inverses, smoothness, and why ECC is hard—each tied to animations inside the visualization area.

Encryption & History

• Encryption workflow: Generate ephemeral keys, encrypt text or uploaded files, and follow the step-by-step animation that draws R/S points, ciphertext batches, and shared secrets.
• Decryption workflow: Paste or drop ciphertext, decrypt with the stored private key, and see how the shared secret reassembles the plaintext; a guided "show steps" view mirrors the same animation.
• History database: Every curve initialization, parameter change, point addition/multiplication, encryption, and decryption is logged into the SQLite history table. You can export operations, replay demonstrations, and copy JSON summaries directly from the sliding history panel.

Advanced Utilities

• Point classification: Use the advanced API to identify generators, torsion points, and their orders—perfect for understanding subgroup structure.
• Preset management: The dropdown keeps curated educational curves and lets you save custom presets with descriptions for future work.
• Exports: Generate test vectors, download point lists as CSV/JSON, or copy curve parameters/test results with a single click.
• Theme & shortcuts: Toggle dark/light mode with the floating menu icon, use keyboard helpers, and watch toasts confirm actions.

Why Elliptic Curves?

These curves form a compact, high-security group where the discrete logarithm problem remains hard. This interface makes every layer—from the algebra to encrypted messages and tutorials—visible so you can both experiment and explain ECC confidently.