Classical Cryptography Simulator

Elliptic Curve Arithmetic

Interactive exploration of elliptic curve operations including point addition, point doubling, and scalar multiplication. Visualize curves and understand the mathematical foundations.

Elliptic Curve Visualization
Interactive graph of elliptic curve with point operations

Curve Equation:

y² = x³ + -1x + 1
Point Operations
Perform elliptic curve arithmetic operations
Elliptic Curve Properties
Mathematical foundations of elliptic curves

Group Structure

Points on an elliptic curve form an abelian group under point addition

Point at Infinity

Serves as the identity element (O) in the group

Geometric Interpretation

Point addition corresponds to chord-and-tangent method

Operation Rules
Mathematical formulas for elliptic curve operations

Point Addition

λ = (y₂ - y₁) / (x₂ - x₁)
x₃ = λ² - x₁ - x₂
y₃ = λ(x₁ - x₃) - y₁

Point Doubling

λ = (3x₁² + a) / (2y₁)
x₃ = λ² - 2x₁
y₃ = λ(x₁ - x₃) - y₁