https://github.com/actuallyachraf/algebra
A literate :pencil: implementation of algebraic primitives for cryptography and algebraic applications :alembic:
https://github.com/actuallyachraf/algebra
algebra bulletproofs cryptography elliptic-curve-arithmetic elliptic-curve-cryptography finite-fields learning-by-doing pairings polynomials primitives schnorr-signatures
Last synced: 4 months ago
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A literate :pencil: implementation of algebraic primitives for cryptography and algebraic applications :alembic:
- Host: GitHub
- URL: https://github.com/actuallyachraf/algebra
- Owner: actuallyachraf
- Created: 2019-09-06T18:39:33.000Z (almost 7 years ago)
- Default Branch: master
- Last Pushed: 2023-02-25T01:30:56.000Z (over 3 years ago)
- Last Synced: 2025-08-15T11:52:41.325Z (10 months ago)
- Topics: algebra, bulletproofs, cryptography, elliptic-curve-arithmetic, elliptic-curve-cryptography, finite-fields, learning-by-doing, pairings, polynomials, primitives, schnorr-signatures
- Language: Go
- Homepage:
- Size: 56.6 KB
- Stars: 3
- Watchers: 2
- Forks: 0
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
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README
# Algebra
This is a small library I write as a parallel of studying algebra
and number theory related to cryptography it's not suitable for production usage
and I doubt it ever will.
It aims to be literate.
It's a **WIP** and might take time to be finished.
## DO NOT USE FOR ANYTHING BUT LEARNING
## Packages
### Cryptography Implementations
- ```crypto/schnorr``` package implements Vanilla EC-Schnorr.
- ```crypto/bp``` package implements [Bulletproofs](https://eprint.iacr.org/2017/1066).
### Algebraic Tools Implementations
- ```bf``` package implements binary fields.
- ```ec``` package implements elliptic curve primitives and
a few cryptographic curves.
- ```nt``` package implements number theoretic algorithms and primitives using
arbitrary precision arithmetic.
- ```ff``` package implements generic finite fields and field elements.
- ```group``` package implements some custom groups such as Zp,GF(2),GF(8)...
- ```poly``` package implements polynomials over rings.
- ```pairing``` package implements bilinear pairings.
## References
- [Handbook Of Applied Cryptography](http://cacr.uwaterloo.ca/hac/)
- [Guide To Elliptic Curve Cryptography](http://cacr.uwaterloo.ca/ecc/)
- [Pairings For Begineers](http://www.craigcostello.com.au/pairings/PairingsForBeginners.pdf)
- [Pairings For Cryptographers](https://eprint.iacr.org/2006/165)
- [Implementing Pairing Based Cryptography](https://crypto.stanford.edu/pbc/thesis.pdf)
- [Modern Computer Algebra](https://www.cambridge.org/core/books/modern-computer-algebra/DB3563D4013401734851CF683D2F03F0)
## WIP
- ~~Implement operations on arbitrary precision integers and tests.~~
- ~~Implement finite field elements.~~
- Optimized version instead of wrapping bigint
- ~~Implement polynomial ops.~~
- Optimized FFT instead of naive Eval/Mul algorithms
- ~~Implement elliptic curves.~~
- Add projective coordinates support
- Support typed curves (Weirstrass,Edwards)
- Implement optimized formulas for Weirstrass curves
- Implement binary fields.
- Implement number theoretic transform.
- Implement groups for char 2 fields.
- Implement pairings.