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 BLS12_377 curve generated in [BCGMMW20, “Zexe”]. The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree 12, defined over a 377-bit (prime) field. The main feature of this curve is that both the scalar field and the base field are highly 2-adic. (This is in contrast to the BLS12_381 curve for which only the scalar field is highly 2-adic.)

Curve information:

• Base field: q = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
• Scalar field: r = 8444461749428370424248824938781546531375899335154063827935233455917409239041
• valuation(q - 1, 2) = 46
• valuation(r - 1, 2) = 47
• G1 curve equation: y^2 = x^3 + 1
• G2 curve equation: y^2 = x^3 + B, where
  • B = Fq2(0, 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906)