Group

Defined in: lib/provable/group.ts:16

An element of a Group.

Constructors

Constructor

new Group(__namedParameters: {
  x: string | number | bigint | FieldVar | Field;
  y: string | number | bigint | FieldVar | Field;
}): Group;

Defined in: lib/provable/group.ts:46

Coerces anything group-like to a Group.

Parameters

__namedParameters

x

string | number | bigint | FieldVar | Field

y

string | number | bigint | FieldVar | Field

Returns

Group

Properties

x

x: Field;

Defined in: lib/provable/group.ts:17

---

y

y: Field;

Defined in: lib/provable/group.ts:18

Accessors

generator

Get Signature

get static generator(): Group;

Defined in: lib/provable/group.ts:23

The generator g of the Group.

Returns

Group

---

zero

Get Signature

get static zero(): Group;

Defined in: lib/provable/group.ts:39

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

Methods

add()

add(g: Group): Group;

Defined in: lib/provable/group.ts:89

Adds this Group element to another Group element.

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

Parameters

g

Group

Returns

Group

---

addNonZero()

addNonZero(g2: Group, allowZeroOutput: boolean): Group;

Defined in: lib/provable/group.ts:128

Lower-level variant of add which doesn't handle the case where one of the operands is zero, and asserts that the output is non-zero.

Optionally, zero outputs can be allowed by setting allowZeroOutput to true.

Warning: If one of the inputs is zero, the result will be garbage and the proof useless. This case has to be prevented or handled separately by the caller of this method.

Parameters

g2

Group

allowZeroOutput

boolean = false

Returns

Group

---

assertEquals()

assertEquals(g: Group, message?: string): void;

Defined in: lib/provable/group.ts:189

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

g1.assertEquals(g2);

Parameters

g

Group

message?

string

Returns

void

---

equals()

equals(g: Group): Bool;

Defined in: lib/provable/group.ts:205

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

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

Parameters

g

Group

Returns

Bool

---

isZero()

isZero(): Bool;

Defined in: lib/provable/group.ts:76

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

Returns

Bool

---

neg()

neg(): Group;

Defined in: lib/provable/group.ts:154

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

Returns

Group

---

scale()

scale(s: number | bigint | Field | Scalar): Group;

Defined in: lib/provable/group.ts:168

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

s

number | bigint | Field | Scalar

Returns

Group

---

sub()

sub(g: Group): Group;

Defined in: lib/provable/group.ts:147

Subtracts another Group element from this one.

Parameters

g

Group

Returns

Group

---

toFields()

toFields(): Field[];

Defined in: lib/provable/group.ts:240

Part of the Provable interface.

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

Returns

Field[]

---

toJSON()

toJSON(): {
  x: string;
  y: string;
};

Defined in: lib/provable/group.ts:225

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

{
  x: string;
  y: string;
}

x

x: string;

y

y: string;

---

check()

static check(g: Group): unknown;

Defined in: lib/provable/group.ts:317

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

Parameters

g

Group

Returns

unknown

---

empty()

static empty(): Group;

Defined in: lib/provable/group.ts:341

Returns

Group

---

from()

static from(x: string | number | bigint | FieldVar | Field, y: string | number | bigint | FieldVar | Field): Group;

Defined in: lib/provable/group.ts:247

Coerces two x and y coordinates into a Group element.

Parameters

x

string | number | bigint | FieldVar | Field

y

string | number | bigint | FieldVar | Field

Returns

Group

---

fromFields()

static fromFields(__namedParameters: Field[]): Group;

Defined in: lib/provable/group.ts:277

Part of the Provable interface.

Deserializes a Group element from a list of field elements.

Parameters

__namedParameters

Field[]

Returns

Group

---

fromJSON()

static fromJSON(__namedParameters: {
  x: string | number | bigint | FieldVar | Field;
  y: string | number | bigint | FieldVar | Field;
}): Group;

Defined in: lib/provable/group.ts:304

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

__namedParameters

x

string | number | bigint | FieldVar | Field

y

string | number | bigint | FieldVar | Field

Returns

Group

---

fromValue()

static fromValue(g: 
  | Group
  | {
  x: number | bigint | Field;
  y: number | bigint | Field;
}): Group;

Defined in: lib/provable/group.ts:216

Parameters

g

Group | { x: number | bigint | Field; y: number | bigint | Field; }

Returns

Group

---

sizeInFields()

static sizeInFields(): number;

Defined in: lib/provable/group.ts:286

Part of the Provable interface.

Returns 2.

Returns

number

---

toAuxiliary()

static toAuxiliary(g?: Group): never[];

Defined in: lib/provable/group.ts:268

Part of the Provable interface.

Returns an empty array.

Parameters

g?

Group

Returns

never[]

---

toFields()

static toFields(g: Group): Field[];

Defined in: lib/provable/group.ts:259

Part of the Provable interface.

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

Parameters

g

Group

Returns

Field[]

---

toInput()

static toInput(x: Group): {
  fields: Field[];
};

Defined in: lib/provable/group.ts:335

Parameters

x

Group

Returns

{
  fields: Field[];
}

fields

fields: Field[];

---

toJSON()

static toJSON(g: Group): {
  x: string;
  y: string;
};

Defined in: lib/provable/group.ts:295

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

g

Group

Returns

{
  x: string;
  y: string;
}

x

x: string;

y

y: string;

---

toValue()

static toValue(__namedParameters: Group): {
  x: bigint;
  y: bigint;
};

Defined in: lib/provable/group.ts:212

Parameters

__namedParameters

Group

Returns

{
  x: bigint;
  y: bigint;
}

x

x: bigint;

y

y: bigint;