1# Curve implementations
 2
 3This repository contains implementations of some popular elliptic curves. The curve API implemented here matches the curve traits defined [here](https://github.com/arkworks-rs/algebra/blob/master/ec/src/lib.rs) in the [arkworks-rs/algebra](https://github.com/arkworks-rs/algebra) repository.
 4
 5### BLS12-381 and embedded curves
 6* [`ark-bls12-381`](bls12_381): Implements the BLS12-381 pairing-friendly curve
 7* [`ark-ed-on-bls12-381`](ed_on_bls12_381): Implements a Twisted Edwards curve atop the scalar field of BLS12-381
 8* [`ark-ed-on-bls12-381-bandersnatch`](ed_on_bls12_381_bandersnatch): Implements Bandersnatch, another Twisted Edwards curve atop the scalar field of BLS12-381
 9
10### BLS12-377 and related curves
11* [`ark-bls12-377`](bls12_377): Implements the BLS12-377 pairing-friendly curve
12* [`ark-ed-on-bls12-377`](ed_on_bls12_377): Implements a Twisted Edwards curve atop the scalar field of BLS12-377
13
14* [`ark-bw6-761`](bw6_761): Implements the BW6-761 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
15* [`ark-ed-on-bw6-761`](ed_on_bw6_761): Implements a Twisted Edwards curve atop the scalar field of BW6-761
16
17* [`ark-cp6-782`](cp6_782): Implements the CP6-782 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
18* [`ark-ed-on-cp6-782`](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`
19
20### BN254 and related curves
21* [`ark-bn254`](bn254): Implements the BN254 pairing-friendly curve
22* [`ark-ed-on-bn254`](ed_on_bn254): Implements a Twisted Edwards curve atop the scalar field of BN254
23* [`ark-grumpkin`](grumpkin): Implements the Grumpkin curve. A curve that forms a cycle with bn254.
24
25### MNT-298 cycle of curves and related curves
26* [`ark-mnt4-298`](mnt4_298): Implements the MNT4-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-298
27* [`ark-mnt6-298`](mnt6_298): Implements the MNT6-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-298
28* [`ark-ed-on-mnt4-298`](ed_on_mnt4_298): Implements a Twisted Edwards curve atop the scalar field of MNT4-298
29
30### MNT-753 cycle of curves and related curves
31* [`ark-mnt4-753`](mnt4_753): Implements the MNT4-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-753
32* [`ark-mnt6-753`](mnt6_753): Implements the MNT6-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-753
33* [`ark-ed-on-mnt4-753`](ed_on_mnt4_753): Implements a Twisted Edwards curve atop the scalar field of MNT4-753
34
35### [Pasta](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/) cycle of curves
36* [`ark-pallas`](pallas): Implements Pallas, a prime-order curve that forms an amicable pair with Vesta
37* [`ark-vesta`](vesta): Implements Vesta, a prime-order curve that forms an amicable pair with Pallas