Curve implementations

This repository contains implementations of some popular elliptic curves. The curve API implemented here matches the curve traits defined here in the arkworks-rs/algebra repository.

BLS12-381 and embedded curves

• ark-bls12-381: Implements the BLS12-381 pairing-friendly curve
• ark-ed-on-bls12-381: Implements a Twisted Edwards curve atop the scalar field of BLS12-381
• ark-ed-on-bls12-381-bandersnatch: Implements Bandersnatch, another Twisted Edwards curve atop the scalar field of BLS12-381

BLS12-377 and related curves

• ark-bls12-377: Implements the BLS12-377 pairing-friendly curve

• ark-ed-on-bls12-377: Implements a Twisted Edwards curve atop the scalar field of BLS12-377

• ark-bw6-761: Implements the BW6-761 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377

• ark-ed-on-bw6-761: Implements a Twisted Edwards curve atop the scalar field of BW6-761

• ark-cp6-782: Implements the CP6-782 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377

• ark-ed-on-cp6-782: Implements a Twisted Edwards curve atop the scalar field of CP6-782. This is the same curve as in ark-ed-on-bw6-761

BN254 and related curves

• ark-bn254: Implements the BN254 pairing-friendly curve
• ark-ed-on-bn254: Implements a Twisted Edwards curve atop the scalar field of BN254

MNT-298 cycle of curves and related curves

• ark-mnt4-298: Implements the MNT4-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-298
• ark-mnt6-298: Implements the MNT6-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-298
• ark-ed-on-mnt4-298: Implements a Twisted Edwards curve atop the scalar field of MNT4-298

MNT-753 cycle of curves and related curves

• ark-mnt4-753: Implements the MNT4-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-753
• ark-mnt6-753: Implements the MNT6-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-753
• ark-ed-on-mnt4-753: Implements a Twisted Edwards curve atop the scalar field of MNT4-753

Pasta cycle of curves

• ark-pallas: Implements Pallas, a prime-order curve that forms an amicable pair with Vesta
• ark-vesta: Implements Vesta, a prime-order curve that forms an amicable pair with Pallas

lib.rs:

This library implements the curve25519 Montgomery curve.

Curve information:

• Base field: q = 57896044618658097711785492504343953926634992332820282019728792003956564819949
• Scalar field: r = 7237005577332262213973186563042994240857116359379907606001950938285454250989
• Curve equation: B * y^2 = x^3 + A * x^2 + x, where
  • A = 486662
  • B = 1