https://github.com/dexcompiler/curves
Elliptic curve operations over finite fields
https://github.com/dexcompiler/curves
cryptography csharp elliptic-curve-cryptography finite-fields high-performance prime-numbers
Last synced: 20 days ago
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Elliptic curve operations over finite fields
- Host: GitHub
- URL: https://github.com/dexcompiler/curves
- Owner: dexcompiler
- Created: 2025-02-24T04:22:17.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2025-02-24T06:30:31.000Z (over 1 year ago)
- Last Synced: 2026-05-23T22:06:49.590Z (about 1 month ago)
- Topics: cryptography, csharp, elliptic-curve-cryptography, finite-fields, high-performance, prime-numbers
- Language: C#
- Homepage:
- Size: 9.77 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Elliptic Curve Implementation
A C# implementation of elliptic curve arithmetic operations over finite fields, primarily focused on the mathematical fundamentals that underpin elliptic curve cryptography (ECC).
## Overview
This project provides a generic implementation of elliptic curves using the Weierstrass form: y² = x³ + ax + b over a finite field of prime characteristic p. It includes core operations like:
- Point addition
- Point doubling
- Scalar multiplication
- Point validation
- Point negation
## Usage Example
```csharp
// Create an elliptic curve y² = x³ + 2x + 3 (mod 17)
var curve = new EllipticCurve(
a: 2,
b: 3,
prime: 17,
basePoint: new Point(3, 6),
order: 19
);
// Verify if a point lies on the curve
var point = new Point(3, 6);
bool isValid = curve.IsOnCurve(point); // true
// Perform point addition
var sum = EllipticCurve.Add(curve, point1, point2);
// Scalar multiplication
var result = EllipticCurve.ScalarMultiply(curve, point, k);
```
## Features
- **Generic Implementation**: Supports different curve types through the `IEllipticCurve` interface
- **Core Operations**:
- Point addition and doubling
- Scalar multiplication using double-and-add algorithm
- Point validation
- Point negation
- **Mathematical Utilities**:
- Modular arithmetic operations
- Extended Euclidean algorithm for modular inverse
- **Test Coverage**: Comprehensive test suite verifying curve operations
## Mathematical Background
The implementation uses the standard formulas for elliptic curve arithmetic:
- **Point Addition**: When P₁ = (x₁, y₁) ≠ ±P₂ = (x₂, y₂):
- λ = (y₂ - y₁)/(x₂ - x₁)
- x₃ = λ² - x₁ - x₂
- y₃ = λ(x₁ - x₃) - y₁
- **Point Doubling**: When P = (x, y) and P is doubled:
- λ = (3x² + a)/(2y)
- x₃ = λ² - 2x
- y₃ = λ(x - x₃) - y
All operations are performed modulo the prime characteristic p.
## Security Note
This implementation is primarily for educational purposes and demonstrates the mathematical concepts behind ECC. For production cryptographic purposes, use established cryptographic libraries.
## License
MIT