> ## Documentation Index
> Fetch the complete documentation index at: https://voltaire.tevm.sh/llms.txt
> Use this file to discover all available pages before exploring further.

# G1

> Auto-generated API documentation

[**@tevm/voltaire**](../../../index.mdx)

***

[@tevm/voltaire](../../../index.mdx) / [crypto/Bls12381](../index.mdx) / G1

# G1

## Functions

### add()

> **add**(`p1`, `p2`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/add.js:14](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/add.js#L14)

Add two G1 points using Jacobian coordinates
Algorithm: [https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-2007-bl](https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-2007-bl)

#### Parameters

##### p1

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

First point

##### p2

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Second point

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### double()

> **double**(`point`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/double.js:12](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/double.js#L12)

Double a G1 point using Jacobian coordinates
Algorithm: [https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl](https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl)

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to double

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### equal()

> **equal**(`p1`, `p2`): `boolean`

Defined in: [src/crypto/Bls12381/G1/equal.js:12](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/equal.js#L12)

Check if two G1 points are equal
In Jacobian coordinates: P1 = P2 iff X1*Z2^2 = X2*Z1^2 and Y1*Z2^3 = Y2*Z1^3

#### Parameters

##### p1

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

First point

##### p2

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Second point

#### Returns

`boolean`

***

### fromAffine()

> **fromAffine**(`x`, `y`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/fromAffine.js:10](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/fromAffine.js#L10)

Create G1 point from affine coordinates

#### Parameters

##### x

`bigint`

x-coordinate

##### y

`bigint`

y-coordinate

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### generator()

> **generator**(): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/generator.js:8](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/generator.js#L8)

Return the generator point for G1

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### infinity()

> **infinity**(): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/infinity.js:6](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/infinity.js#L6)

Return the point at infinity (identity element) for G1

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### isOnCurve()

> **isOnCurve**(`point`): `boolean`

Defined in: [src/crypto/Bls12381/G1/isOnCurve.js:13](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/isOnCurve.js#L13)

Check if a G1 point is on the curve y^2 = x^3 + 4
In Jacobian projective coordinates where (X, Y, Z) represents (X/Z^2, Y/Z^3):
Y^2 = X^3 + b\*Z^6

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to check

#### Returns

`boolean`

***

### isZero()

> **isZero**(`point`): `boolean`

Defined in: [src/crypto/Bls12381/G1/isZero.js:7](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/isZero.js#L7)

Check if a G1 point is the point at infinity

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to check

#### Returns

`boolean`

***

### mul()

> **mul**(`point`, `scalar`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/mul.js:14](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/mul.js#L14)

Scalar multiplication of G1 point using double-and-add

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to multiply

##### scalar

`bigint`

Scalar multiplier

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### negate()

> **negate**(`point`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/negate.js:10](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/negate.js#L10)

Negate a G1 point (reflect over x-axis)

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to negate

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

***

### toAffine()

> **toAffine**(`point`): [`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Defined in: [src/crypto/Bls12381/G1/toAffine.js:12](https://github.com/evmts/voltaire/blob/bd6ec34405c15ad8cd51d11579d495dc53813482/src/crypto/Bls12381/G1/toAffine.js#L12)

Convert G1 point from projective to affine coordinates
Affine: (x/z^2, y/z^3, 1)

#### Parameters

##### point

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)

Point to convert

#### Returns

[`Bls12381G1PointType`](../../../index/index.mdx#bls12381g1pointtype)