Group

o1js / Modules / Group

Class: Group

An element of a Group.

Table of contents

Constructors

• constructor

Properties

• x
• y

Accessors

• generator
• zero

Methods

• add
• assertEquals
• equals
• isZero
• neg
• scale
• sub
• toFields
• toJSON
• add
• assertEqual
• check
• equal
• from
• fromFields
• fromJSON
• neg
• scale
• sizeInFields
• sub
• toAuxiliary
• toFields
• toJSON

Constructors

constructor

• new Group(«destructured»)

Coerces anything group-like to a Group.

Parameters

Name	Type
«destructured»	Object
› x	string | number | bigint | FieldVar | Field
› y	string | number | bigint | FieldVar | Field

Defined in

lib/group.ts:44

Properties

x

• x: Field

Defined in

lib/group.ts:15

---

y

• y: Field

Defined in

lib/group.ts:16

Accessors

generator

• Static get generator(): Group

The generator g of the Group.

Returns

Group

Defined in

lib/group.ts:21

---

zero

• Static get zero(): Group

Unique representation of the zero element of the Group (the identity element of addition in this Group).

Note: The zero element is represented as (0, 0).

// g + -g = 0
g.add(g.neg()).assertEquals(zero);
// g + 0 = g
g.add(zero).assertEquals(g);

Returns

Group

Defined in

lib/group.ts:37

Methods

add

▸ add(g): Group

Adds this Group element to another Group element.

let g1 = Group({ x: -1, y: 2})
let g2 = g1.add(g1)

Parameters

Name	Type
g	Group

Returns

Group

Defined in

lib/group.ts:91

---

assertEquals

▸ assertEquals(g, message?): void

Assert that this Group element equals another Group element. Throws an error if the assertion fails.

g1.assertEquals(g2);

Parameters

Name	Type
g	Group
message?	string

Returns

void

Defined in

lib/group.ts:213

---

equals

▸ equals(g): Bool

Check if this Group element equals another Group element. Returns a Bool.

g1.equals(g1); // Bool(true)

Parameters

Name	Type
g	Group

Returns

Bool

Defined in

lib/group.ts:229

---

isZero

▸ isZero(): Bool

Checks if this element is the zero element {x: 0, y: 0}.

Returns

Bool

Defined in

lib/group.ts:78

---

neg

▸ neg(): Group

Negates this Group. Under the hood, it simply negates the y coordinate and leaves the x coordinate as is.

Returns

Group

Defined in

lib/group.ts:177

---

scale

▸ scale(s): Group

Elliptic curve scalar multiplication. Scales the Group element n-times by itself, where n is the Scalar.

let s = Scalar(5);
let 5g = g.scale(s);

Parameters

Name	Type
s	number | bigint | Scalar

Returns

Group

Defined in

lib/group.ts:191

---

sub

▸ sub(g): Group

Subtracts another Group element from this one.

Parameters

Name	Type
g	Group

Returns

Group

Defined in

lib/group.ts:170

---

toFields

▸ toFields(): Field[]

Part of the Provable interface.

Returns an array containing this Group element as an array of Field elements.

Returns

Field[]

Defined in

lib/group.ts:256

---

toJSON

▸ toJSON(): Object

Serializes this Group element to a JSON object.

This operation does NOT affect the circuit and can't be used to prove anything about the representation of the element.

Returns

Object

Name	Type
x	string
y	string

Defined in

lib/group.ts:241

---

add

▸ Static add(g1, g2): Group

Parameters

Name	Type
g1	Group
g2	Group

Returns

Group

Deprecated

Please use the method .add on the instance instead

Adds a Group element to another one.

Defined in

lib/group.ts:275

---

assertEqual

▸ Static assertEqual(g1, g2): void

Parameters

Name	Type
g1	Group
g2	Group

Returns

void

Deprecated

Please use the method .assertEqual on the instance instead.

Assert that two Group elements are equal to another. Throws an error if the assertion fails.

Group.assertEquals(g1, g2);

Defined in

lib/group.ts:325

---

check

▸ Static check(g): unknown

Checks that a Group element is constraint properly by checking that the element is on the curve.

Parameters

Name	Type
g	Group

Returns

unknown

Defined in

lib/group.ts:406

---

equal

▸ Static equal(g1, g2): Bool

Parameters

Name	Type
g1	Group
g2	Group

Returns

Bool

Deprecated

Please use the method .equals on the instance instead.

Checks if a Group element is equal to another Group element. Returns a Bool.

Group.equal(g1, g2); // Bool(true)

Defined in

lib/group.ts:339

---

from

▸ Static from(x, y): Group

Coerces two x and y coordinates into a Group element.

Parameters

Name	Type
x	string | number | bigint | FieldVar | Field
y	string | number | bigint | FieldVar | Field

Returns

Group

Defined in

lib/group.ts:263

---

fromFields

▸ Static fromFields(«destructured»): Group

Part of the Provable interface.

Deserializes a Group element from a list of field elements.

Parameters

Name	Type
«destructured»	Field[]

Returns

Group

Defined in

lib/group.ts:366

---

fromJSON

▸ Static fromJSON(«destructured»): Group

Deserializes a JSON-like structure to a Group element.

This operation does NOT affect the circuit and can't be used to prove anything about the representation of the element.

Parameters

Name	Type
«destructured»	Object
› x	string | number | bigint | FieldVar | Field
› y	string | number | bigint | FieldVar | Field

Returns

Group

Defined in

lib/group.ts:393

---

neg

▸ Static neg(g): Group

Parameters

Name	Type
g	Group

Returns

Group

Deprecated

Please use the method .neg on the instance instead

Negates a Group element. Under the hood, it simply negates the y coordinate and leaves the x coordinate as is.

let gNeg = Group.neg(g);

Defined in

lib/group.ts:297

---

scale

▸ Static scale(g, s): Group

Parameters

Name	Type
g	Group
s	Scalar

Returns

Group

Deprecated

Please use the method .scale on the instance instead

Elliptic curve scalar multiplication. Scales a Group element n-times by itself, where n is the Scalar.

let s = Scalar(5);
let 5g = Group.scale(g, s);

Defined in

lib/group.ts:311

---

sizeInFields

▸ Static sizeInFields(): number

Part of the Provable interface.

Returns 2.

Returns

number

Defined in

lib/group.ts:375

---

sub

▸ Static sub(g1, g2): Group

Parameters

Name	Type
g1	Group
g2	Group

Returns

Group

Deprecated

Please use the method .sub on the instance instead

Subtracts a Group element from another one.

Defined in

lib/group.ts:284

---

toAuxiliary

▸ Static toAuxiliary(g?): never[]

Part of the Provable interface.

Returns an empty array.

Parameters

Name	Type
g?	Group

Returns

never[]

Defined in

lib/group.ts:357

---

toFields

▸ Static toFields(g): Field[]

Part of the Provable interface.

Returns an array containing a Group element as an array of Field elements.

Parameters

Name	Type
g	Group

Returns

Field[]

Defined in

lib/group.ts:348

---

toJSON

▸ Static toJSON(g): Object

Serializes a Group element to a JSON object.

This operation does NOT affect the circuit and can't be used to prove anything about the representation of the element.

Parameters

Name	Type
g	Group

Returns

Object

Name	Type
x	string
y	string

Defined in

lib/group.ts:384