Bn254 Curve

[MauroToscano]

Add BN254 to Lambdaworks (ethereum altbn128)

• Add the finite field used by the curve, using MontgomeryBackend
• Add the curve
• Add the degree 2 extensión finite field
• Add the twist
• Add the pairing

References:

Pairing friendly elliptic curves
Succinct Non-Interactive Zero Knowledge
for a von Neumann Architecture
Bn 254 for the rest of us
Bn 254 Gnark Docs
Bn 254 Gnark Implementation
Bn 254 Arkworks Docs

Constants:

Fr:

$21888242871839275222246405745257275088696311157297823662689037894645226208583$ ->
$0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47$

Fp:

$21888242871839275222246405745257275088696311157297823662689037894645226208583$ ->
$0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47$

Curve equation:

$Y²=X³+3$ -> $a = 0, b = 3$

Twist:

$Y² = X³+3/(u+9)$

$G1 = (1,2)$
$G2 = ([10857046999023057135944570762232829481370756359578518086990519993285655852781,11559732032986387107991004021392285783925812861821192530917403151452391805634] , [8495653923123431417604973247489272438418190587263600148770280649306958101930,4082367875863433681332203403145435568316851327593401208105741076214120093531]$

[dbejarano820]

I'll look into this one as I progress through the Sparkling Water bootcamp

[skaunov]

Does anybody doing the last part of this one?

Am looking into it.

[diegokingston]

Solved