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diegokingston committed Aug 23, 2024
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Expand Up @@ -135,7 +135,7 @@ Pairings are an important calculation for BLS signatures and the KZG polynomial
2. Non-degeneracy
Not all elliptic curves have efficiently computable pairings. If the curve is pairing-friendly, we can implement the trait `IsPairing`. Examples of pairing-friendly curves are BLS12-381, BLS12-377, BN254. Curves such as Pallas, Vesta, secp256k1 are not pairing-friendly. For an explanation of pairings, see our [blogpost](https://blog.lambdaclass.com/how-we-implemented-the-bn254-ate-pairing-in-lambdaworks/).

The pairing function takes pairs of points $(a , b)$, where $a \in G_1$ (formed by coordinates $x,y$ taking values on the base field $\mathbb{F_p}$) and $b \in G_2$ (formed by coordinates $x,y$ taking values in $\mathbb{F}_{ p^2 }$, a quadratic extension of the base field) and outputs an element in the $r$-th roots of unity of $\mathbb{F}_{ p^k }$. To use the pairing, provide a slice of pairs and call the function `compute_batch`. For example,
The pairing function takes pairs of points $(a , b)$, where $a \in G_1$ (formed by coordinates $x,y$ taking values on the base field ${F_p}$) and $b \in G_2$ (formed by coordinates $x,y$ taking values in ${F}_{ p^2 }$, a quadratic extension of the base field) and outputs an element in the $r$-th roots of unity of ${F}_{ p^k }$. To use the pairing, provide a slice of pairs and call the function `compute_batch`. For example,
```rust
let p = BN254Curve::generator();
let q = BN254TwistCurve::generator();
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