Group

o1js / Modules / Group

Class: Group

An element of a Group.

Table of contents

Constructors

• constructor

Properties

• x
• y

Accessors

• generator
• zero

Methods

• #isConstant
• #toProjective
• #toTuple
• add
• assertEquals
• equals
• isZero
• neg
• scale
• sub
• toFields
• toJSON
• #fromAffine
• #fromProjective
• 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:47

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

#isConstant

▸ Private #isConstant(): boolean

Returns

boolean

Defined in

lib/group.ts:99

---

#toProjective

▸ Private #toProjective(): Object

Returns

Object

Name	Type
x	bigint
y	bigint
z	bigint

Defined in

lib/group.ts:103

---

#toTuple

▸ Private #toTuple(): [0, FieldVar, FieldVar]

Returns

[0, FieldVar, FieldVar]

Defined in

lib/group.ts:95

---

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:127

---

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:261

---

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:277

---

isZero

▸ isZero(): Bool

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

Returns

Bool

Defined in

lib/group.ts:114

---

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:225

---

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:239

---

sub

▸ sub(g): Group

Subtracts another Group element from this one.

Parameters

Name	Type
g	Group

Returns

Group

Defined in

lib/group.ts:218

---

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:304

---

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:289

---

#fromAffine

▸ Static Private #fromAffine(«destructured»): Group

Parameters

Name	Type
«destructured»	Object
› infinity	boolean
› x	bigint
› y	bigint

Returns

Group

Defined in

lib/group.ts:79

---

#fromProjective

▸ Static Private #fromProjective(«destructured»): Group

Parameters

Name	Type
«destructured»	Object
› x	bigint
› y	bigint
› z	bigint

Returns

Group

Defined in

lib/group.ts:91

---

add

▸ Static add(g1, g2): Group

Deprecated

Please use the method .add on the instance instead

Adds a Group element to another one.

Parameters

Name	Type
g1	Group
g2	Group

Returns

Group

Defined in

lib/group.ts:323

---

assertEqual

▸ Static assertEqual(g1, g2): 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);

Parameters

Name	Type
g1	Group
g2	Group

Returns

void

Defined in

lib/group.ts:373

---

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:454

---

equal

▸ Static equal(g1, g2): 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)

Parameters

Name	Type
g1	Group
g2	Group

Returns

Bool

Defined in

lib/group.ts:387

---

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:311

---

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:414

---

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:441

---

neg

▸ Static neg(g): 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);

Parameters

Name	Type
g	Group

Returns

Group

Defined in

lib/group.ts:345

---

scale

▸ Static scale(g, s): 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);

Parameters

Name	Type
g	Group
s	Scalar

Returns

Group

Defined in

lib/group.ts:359

---

sizeInFields

▸ Static sizeInFields(): number

Part of the Provable interface.

Returns 2.

Returns

number

Defined in

lib/group.ts:423

---

sub

▸ Static sub(g1, g2): Group

Deprecated

Please use the method .sub on the instance instead

Subtracts a Group element from another one.

Parameters

Name	Type
g1	Group
g2	Group

Returns

Group

Defined in

lib/group.ts:332

---

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:405

---

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:396

---

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:432