crypts

A Bun-powered zero-dependency library for cryptography, for self-educational purposes mostly.

finite fields Finite Fields

• Prime Field defines a finite field of prime order.
• Binary Field defines a finite field of order 2 with Boolean values & Boolean algebra.
• Field Extension defines an extension of an existing field using an irreducible polynomial.

polynomials Polynomials

• Polynomials defines a polynomial with coefficients in a finite field.
• Lagrange Interpolation constructs a polynomial based on point evaluations.
• Shamir's Secret Sharing splits a given secret into $n$ shares such that with at least $k$ of them the secret can be reconstructed.

elliptic curves Elliptic Curves

• Short Weierstrass defines an elliptic curve in Short Weierstrass form with affine points, along with curve conversions.
• Montgomery defines an elliptic curve in Montgomery form with affine points, along with curve conversions.
• Twisted Edwards defines an elliptic curve in Twisted Edwards form with affine points, along with curve conversions.

numbers Numbers

• Miller-Rabin probabilistically & efficiently checks if a number is prime.
• Tonelli-Shanks finds the square root of a quadratic residue in a finite field.
• Legendre Symbol tells whether a number is quadratic residue or quadratic non-residue.

Usage

TODO

Testing

We prepare our test cases using SageMath, and then try to match the results obtained there using our implementations. To run all tests, do:

bun run test
bun t # alias

Tip

If you do not have Sage installed, but still would like to play around with the Sage code, fret not! We have prepared scripts for the Sagemath docker image:

bun sage:pull     # pulls the image
bun sage:cli      # opens Sage cli
bun sage:notebook # opens Jupyter Notebook

The containers will have volumes attached to the tests/data and tests/sage folders, so that the Sage code can directly write to the test data there.

Building

We use Bun as a builder, and dts-bundle-generator for types.

bun run build
bun b # alias

Examples

See several examples:

• secp256k1
• ed25519

Styling

Check the formatting and lint everything with the following commands:

bun format
bun lint
bun style # does both

Resources

This would not have been possible without the amazing resources out there:

• MoonMath Manual
• ZCash - Halo2 Background
• Risencrypto
• 2π
• Standford PBC Notes
• cliff0412