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.
-
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.
- Go version 1.21 or higher
May need this:
xcode-select --install
Clone the repository:
git clone https://github.com/fishfugu/elliptic.git
cd ellipticmake build-all
make test
AKA see example output and kick the tyres:
make test-drive
Usage: make <TARGETS>
BUILD
build-all Build the project - all necessary components
build-bigmath Build bigmath executable
build-finitefield Build finitefield executable
build-ecviz Build Elliptic Curve Data Viz Tool
RUN
run-bigmath Run bigmath binary after building it - ensuring latest build is executed - running tests first
run-finitefield Run finitefield binary after building it - ensuring latest build is executed - running tests first
run-ecviz Run Elliptic Curve Data Viz Tool (after doing a build)
TEST and CLEAN
test Run unit tests for all packages under pkg
clean Remove binaries and any temporary files
testdrive Run through all (appropriate) make file commands - just to take it for a test drive (check I haven't done stupidity)
HELPER
test-quiet Run unit tests for all packages under pkg - but quietly - quits at first error
test-verbose Run unit tests for all packages under pkg - in verbose mode
help Show this help
2D Plane Visualization with Cartesian Axes, Reflection Line, and Scale:
| 43
| *
| *
| *
| * * * 39
|
| *
| *
| 35
| *
| *
| *
| * * * 31
| *
|
|
| 27
| *
| * * *
| *
| * 23
| . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43/2
| *
| *
| * 19
| * * *
| *
|
| 15
|
| *
| * * *
| * 11
| *
| *
|
| * 7
| *
|
| * * *
| * 3
| *
| *
+ - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - - - / - * - 0
- Makefile tidy - organise / make headings for help
- Core algos for elliptic curve operations
- Arbitrarily large finite filed ops - use BigInt - but make simpler
- 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
- Visualization 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
testdriveoption
- Turn this interactive and make current code into
- 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
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.
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent