Elliptic Curve Toolbox

Tools for analysis / manipulation of elliptic curves. Provides utilities for experimentation, and educational exploration of elliptic curve theory.

All partly inspired by my work over here: Recent course output - SCI395, with UNE. I'll be updating this site and this repo in tandem, as I go, and as I get to different parts of the investigation / analysis.

Current Features

• Big Integer Arithmetic: Perform arithmetic operations on arbitrarily large integers with precise results.

• Finite Field Calculation: Prime number finite field operations. Calculating points on an elliptic curve (in the Weierstrass form) defined on a prime integer finite field. Visualise prime integer finite field points, on an elliptic curve.

Getting Started

Prerequisites

• Go version 1.21 or higher

May need this:

xcode-select --install

Installation

Clone the repository:

git clone https://github.com/fishfugu/elliptic.git
cd elliptic

See make options

make

Build the project

make build-all

Recommended way to run each binary

_ bigmath _ (just for basic teating really)

make run-bigmath

_ finitefield _ (just for basic testing really)

make run-finitefield

_ ecviz _

make run-ecviz

_ ellipticcurvecli _

make run-cli

for "with text visualise" option:

make build-cli
./bin/ellipticcurvecli -visualise

Run tests

make test

Take it all for a test drive

AKA see example output and kick the tyres:

make test-drive

Text Visualisation Example

2D Plane Visualization with Cartesian Axes, Reflection Line, and Scale:
|                                                                                        43
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|         *
|           * *                                             *                            39
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|     *
| *
|                                                                                        35
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|                       *
|   *           *                                                 *                      31
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|                                                                                        27
|                                           *
|                     *     *       *
|                                                                             *
|                                                                               *        23
| . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43/2
|                             *
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|                     *     *       *
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|                                                                                        15
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|   *           *                                                 *
|                       *                                                                11
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| *                                                                                      7
|     *
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|           * *                                             *
|         *                                                                              3
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+ - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - * -  0

TODO

• Makefile tidy - organise / make headings for help
• Core algos for elliptic curve operations - [x] Arbitrarily large finite filed ops - use BigInt - but make simpler - [x] Find Prime - [ ] Work out how many checks is "good enough" - [ ] Check that use of BigInt versus own reimplement is consistent / sane - [ ] Investigate what "multiplying points" and "multiplicative inverse of points" means (extend lit review work: SCI395 Course Material )
• Functions for operations within finite fields
  • Calculate points on an EC in prime finite field
  • Make ECs into types to hand around (immutable)
  • Implement adding points and multplying points in field by real nums
• Visualisation tools for elliptic curves
  • Basic text vis output
  • Debug the text vis output - scale / reflection line is wrong
  • Improve tick marks / scale numbers under x-axis
  • Vis adding and multplying numbers (see implementation above)
  • Turn vis into a window with real drawings thingy
  • Annimate doubling / adding / rings of points - text and / or proper drawing
• Additional command line tools for other utilities
  • Turn this interactive and make current code into test-drive target
• Comprehensive unit tests for elliptic curve functionalities
  • Do "random" test of more complex finite field calcs - rondomly selected in loop,small numbers without bigint, double checked / compared to function output

Contributing

Welcome contributions from anyone. Fork repo / submit PR.

Open to questions and input on where to go next - as I'd like to make this whole thing useful to others too.