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A literate 📝 implementation of algebraic primitives for cryptography and algebraic applications ⚗️

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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

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.