Bitpolito Cryptography Simulator

An interactive Bitcoin secp256k1 elliptic curve asymmetric cryptography simulator designed with soft neumorphic floating aesthetics, and an interactive 2D graph with finite field modulo ($p$) and continuous ($\mathbb{R}$) point stepping.

📐 Mathematical Foundation (Bitcoin secp256k1)

Authentic, zero-dependency BigInt point arithmetic on the Bitcoin curve:

$$y^2 \equiv x^3 + 7 \pmod p$$

Where:

• Field Prime ($p$): $2^{256} - 2^{32} - 977 = \text{0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F}$
• Generator Point ($G$):
  • $G_x = \text{0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798}$
  • $G_y = \text{0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8}$

Key Generation

1. Private Key ($d$): Random 256-bit scalar ($1 \le d < n$).
2. Public Key ($Q$): Point scalar multiplication $Q = d \cdot G$.

💻 Local Execution

# Serve locally via Python
python3 -m http.server 8080

# Open in browser
http://localhost:8080

BitPolitoAsymmetricCryptoGraphy