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

• 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 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.

• 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.

• 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.

TODO

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

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

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

bun run build
bun b # alias

See several examples:

• secp256k1
• ed25519

Check the formatting and lint everything with the following commands:

bun format
bun lint
bun style # does both

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

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