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Curve Visualizer

Explore the mathematics behind blockchain signatures

ECDSA - Weierstrass Curve

The secp256k1 curve y² = x³ + 7 secures Ethereum and Bitcoin. Click points on the curve to explore point addition - the fundamental operation behind every digital signature.

The Curve : y² = x³ + 7ℝ (real numbers)
Gy² = x³ + 7

Real-number visualization. Blockchain uses this over a finite field - the geometry is identical.

Point Addition

Click two points on the curve. A chord connects them, intersects at a third point, then reflects to give P + Q.

PClick on the curve to place P
QPlace P first

Three cases in Weierstrass addition:

P + QDifferent points - chord through P and Q
P + PPoint doubling - tangent line at P
P + OIdentity - point at infinity
ECDSA vs Ed25519
CurveWeierstrassTwisted Edwards
Equationy²=x³+7-x²+y²=1+dx²y²
Prime~2²⁵⁶2²⁵⁵−19
NonceRandom ⚠Deterministic ✓
Edge cases3 formulas1 unified
Sig size65 B (ETH) / 64 B (Schnorr)64 B
Cofactorh = 1 (no clamping)h = 8 (clamping required)
Pub key33 B32 B
Used byETH, BTCSOL, NEAR

Why Bonding Curves Matter in Web3

Bonding curves power some of the most innovative mechanisms in crypto, from Uniswap's constant product AMM to token launch platforms like pump.fun. They enable continuous token issuance without traditional fundraising, create instant liquidity for new tokens, and establish transparent pricing rules encoded in smart contracts. Understanding curve mechanics is essential for evaluating DeFi protocols and token economics.

Frequently Asked Questions

See these algorithms used across real chains?

Try the Multi-Chain Signature Tool to sign and verify messages with ECDSA and Ed25519