actuallyachraf/algebra

A literate :pencil: implementation of algebraic primitives for cryptography and algebraic applications :alembic:

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.

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
• Guide To Elliptic Curve Cryptography
• Pairings For Begineers
• Pairings For Cryptographers
• Implementing Pairing Based Cryptography
• Modern Computer Algebra

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.