ForeignCurve

o1js / Modules / ForeignCurve

Class: ForeignCurve

Table of contents

Constructors

• constructor

Properties

• x
• y
• _Bigint
• _Field
• _Scalar
• _provable

Accessors

• Constructor
• modulus
• Bigint
• Field
• Scalar
• generator
• modulus
• provable

Methods

• add
• addSafe
• assertInSubgroup
• assertOnCurve
• double
• isConstant
• negate
• scale
• toBigint
• assertInSubgroup
• assertOnCurve
• check
• from

Constructors

constructor

• new ForeignCurve(g)

Create a new ForeignCurve from an object representing the (affine) x and y coordinates.

Parameters

Name	Type
g	Object
g.x	number | bigint | Field3 | AlmostForeignField
g.y	number | bigint | Field3 | AlmostForeignField

Example

let x = new ForeignCurve({ x: 1n, y: 1n });

Important: By design, there is no way for a ForeignCurve to represent the zero point.

Warning: This fails for a constant input which does not represent an actual point on the curve.

Defined in

lib/foreign-curve.ts:45

Properties

x

• x: AlmostForeignField

Defined in

lib/foreign-curve.ts:30

---

y

• y: AlmostForeignField

Defined in

lib/foreign-curve.ts:31

---

_Bigint

▪ Static Optional _Bigint: Object

Type declaration

Name	Type
Field	{ M: bigint = twoadicity; modulus: bigint = p; sizeInBits: number ; t: bigint = oddFactor; twoadicRoot: bigint ; add: (x: bigint, y: bigint) => bigint ; div: (x: bigint, y: bigint) => undefined | bigint ; dot: (x: bigint[], y: bigint[]) => bigint ; equal: (x: bigint, y: bigint) => boolean ; fromBigint: (x: bigint) => bigint ; fromNumber: (x: number) => bigint ; inverse: (x: bigint) => undefined | bigint ; isEven: (x: bigint) => boolean ; isSquare: (x: bigint) => boolean ; leftShift: (x: bigint, bits: number, maxBitSize: number) => bigint ; mod: (x: bigint) => bigint ; mul: (x: bigint, y: bigint) => bigint ; negate: (x: bigint) => bigint ; not: (x: bigint, bits: number) => bigint ; power: (x: bigint, n: bigint) => bigint ; random: () => bigint ; rightShift: (x: bigint, bits: number) => bigint ; rot: (x: bigint, bits: bigint, direction: "left" | "right", maxBits: bigint) => bigint ; sqrt: (x: bigint) => undefined | bigint ; square: (x: bigint) => bigint ; sub: (x: bigint, y: bigint) => bigint }
Field.M	bigint
Field.modulus	bigint
Field.sizeInBits	number
Field.t	bigint
Field.twoadicRoot	bigint
Field.add	[object Object]
Field.div	[object Object]
Field.dot	[object Object]
Field.equal	[object Object]
Field.fromBigint	[object Object]
Field.fromNumber	[object Object]
Field.inverse	[object Object]
Field.isEven	[object Object]
Field.isSquare	[object Object]
Field.leftShift	[object Object]
Field.mod	[object Object]
Field.mul	[object Object]
Field.negate	[object Object]
Field.not	[object Object]
Field.power	[object Object]
Field.random	[object Object]
Field.rightShift	[object Object]
Field.rot	[object Object]
Field.sqrt	[object Object]
Field.square	[object Object]
Field.sub	[object Object]
Scalar	{ M: bigint = twoadicity; modulus: bigint = p; sizeInBits: number ; t: bigint = oddFactor; twoadicRoot: bigint ; add: (x: bigint, y: bigint) => bigint ; div: (x: bigint, y: bigint) => undefined | bigint ; dot: (x: bigint[], y: bigint[]) => bigint ; equal: (x: bigint, y: bigint) => boolean ; fromBigint: (x: bigint) => bigint ; fromNumber: (x: number) => bigint ; inverse: (x: bigint) => undefined | bigint ; isEven: (x: bigint) => boolean ; isSquare: (x: bigint) => boolean ; leftShift: (x: bigint, bits: number, maxBitSize: number) => bigint ; mod: (x: bigint) => bigint ; mul: (x: bigint, y: bigint) => bigint ; negate: (x: bigint) => bigint ; not: (x: bigint, bits: number) => bigint ; power: (x: bigint, n: bigint) => bigint ; random: () => bigint ; rightShift: (x: bigint, bits: number) => bigint ; rot: (x: bigint, bits: bigint, direction: "left" | "right", maxBits: bigint) => bigint ; sqrt: (x: bigint) => undefined | bigint ; square: (x: bigint) => bigint ; sub: (x: bigint, y: bigint) => bigint }
Scalar.M	bigint
Scalar.modulus	bigint
Scalar.sizeInBits	number
Scalar.t	bigint
Scalar.twoadicRoot	bigint
Scalar.add	[object Object]
Scalar.div	[object Object]
Scalar.dot	[object Object]
Scalar.equal	[object Object]
Scalar.fromBigint	[object Object]
Scalar.fromNumber	[object Object]
Scalar.inverse	[object Object]
Scalar.isEven	[object Object]
Scalar.isSquare	[object Object]
Scalar.leftShift	[object Object]
Scalar.mod	[object Object]
Scalar.mul	[object Object]
Scalar.negate	[object Object]
Scalar.not	[object Object]
Scalar.power	[object Object]
Scalar.random	[object Object]
Scalar.rightShift	[object Object]
Scalar.rot	[object Object]
Scalar.sqrt	[object Object]
Scalar.square	[object Object]
Scalar.sub	[object Object]
a	bigint
b	bigint
cofactor	undefined | bigint
hasCofactor	boolean
hasEndomorphism	boolean
modulus	bigint
name	string
one	{ infinity: boolean = false; x: bigint ; y: bigint }
one.infinity	boolean
one.x	bigint
one.y	bigint
order	bigint
zero	GroupAffine
get Endo()	{ base: bigint = endoBase; decomposeMaxBits: number = glvData.maxBits; scalar: bigint = endoScalar; decompose: (s: bigint) => readonly [{ abs: bigint ; isNegative: boolean ; value: bigint = s0 }, { abs: bigint ; isNegative: boolean ; value: bigint = s1 }] ; endomorphism: (P: GroupAffine) => { x: bigint ; y: bigint = P.y } ; scale: (g: GroupAffine, s: bigint) => GroupAffine ; scaleProjective: (g: GroupProjective, s: bigint) => { x: bigint ; y: bigint ; z: bigint } }
add	(g: GroupAffine, h: GroupAffine) => GroupAffine
double	(g: GroupAffine) => GroupAffine
equal	(g: GroupAffine, h: GroupAffine) => boolean
from	(g: { x: bigint ; y: bigint }) => GroupAffine
fromNonzero	(g: { x: bigint ; y: bigint }) => GroupAffine
isInSubgroup	(g: GroupAffine) => boolean
isOnCurve	(g: GroupAffine) => boolean
negate	(g: GroupAffine) => GroupAffine
scale	(g: GroupAffine, s: bigint | boolean[]) => GroupAffine
sub	(g: GroupAffine, h: GroupAffine) => GroupAffine

Defined in

lib/foreign-curve.ts:240

---

_Field

▪ Static Optional _Field: typeof AlmostForeignField

Defined in

lib/foreign-curve.ts:241

---

_Scalar

▪ Static Optional _Scalar: typeof AlmostForeignField

Defined in

lib/foreign-curve.ts:242

---

_provable

▪ Static Optional _provable: ProvablePureExtended\<ForeignCurve, { x: string ; y: string }>

Defined in

lib/foreign-curve.ts:243

Accessors

Constructor

• get Constructor(): typeof ForeignCurve

Returns

typeof ForeignCurve

Defined in

lib/foreign-curve.ts:237

---

modulus

• get modulus(): bigint

The size of the curve's base field.

Returns

bigint

Defined in

lib/foreign-curve.ts:81

---

Bigint

• Static get Bigint(): Object

Curve arithmetic on JS bigints.

Returns

Object

Name	Type
Field	{ M: bigint = twoadicity; modulus: bigint = p; sizeInBits: number ; t: bigint = oddFactor; twoadicRoot: bigint ; add: (x: bigint, y: bigint) => bigint ; div: (x: bigint, y: bigint) => undefined | bigint ; dot: (x: bigint[], y: bigint[]) => bigint ; equal: (x: bigint, y: bigint) => boolean ; fromBigint: (x: bigint) => bigint ; fromNumber: (x: number) => bigint ; inverse: (x: bigint) => undefined | bigint ; isEven: (x: bigint) => boolean ; isSquare: (x: bigint) => boolean ; leftShift: (x: bigint, bits: number, maxBitSize: number) => bigint ; mod: (x: bigint) => bigint ; mul: (x: bigint, y: bigint) => bigint ; negate: (x: bigint) => bigint ; not: (x: bigint, bits: number) => bigint ; power: (x: bigint, n: bigint) => bigint ; random: () => bigint ; rightShift: (x: bigint, bits: number) => bigint ; rot: (x: bigint, bits: bigint, direction: "left" | "right", maxBits: bigint) => bigint ; sqrt: (x: bigint) => undefined | bigint ; square: (x: bigint) => bigint ; sub: (x: bigint, y: bigint) => bigint }
Field.M	bigint
Field.modulus	bigint
Field.sizeInBits	number
Field.t	bigint
Field.twoadicRoot	bigint
Field.add	[object Object]
Field.div	[object Object]
Field.dot	[object Object]
Field.equal	[object Object]
Field.fromBigint	[object Object]
Field.fromNumber	[object Object]
Field.inverse	[object Object]
Field.isEven	[object Object]
Field.isSquare	[object Object]
Field.leftShift	[object Object]
Field.mod	[object Object]
Field.mul	[object Object]
Field.negate	[object Object]
Field.not	[object Object]
Field.power	[object Object]
Field.random	[object Object]
Field.rightShift	[object Object]
Field.rot	[object Object]
Field.sqrt	[object Object]
Field.square	[object Object]
Field.sub	[object Object]
Scalar	{ M: bigint = twoadicity; modulus: bigint = p; sizeInBits: number ; t: bigint = oddFactor; twoadicRoot: bigint ; add: (x: bigint, y: bigint) => bigint ; div: (x: bigint, y: bigint) => undefined | bigint ; dot: (x: bigint[], y: bigint[]) => bigint ; equal: (x: bigint, y: bigint) => boolean ; fromBigint: (x: bigint) => bigint ; fromNumber: (x: number) => bigint ; inverse: (x: bigint) => undefined | bigint ; isEven: (x: bigint) => boolean ; isSquare: (x: bigint) => boolean ; leftShift: (x: bigint, bits: number, maxBitSize: number) => bigint ; mod: (x: bigint) => bigint ; mul: (x: bigint, y: bigint) => bigint ; negate: (x: bigint) => bigint ; not: (x: bigint, bits: number) => bigint ; power: (x: bigint, n: bigint) => bigint ; random: () => bigint ; rightShift: (x: bigint, bits: number) => bigint ; rot: (x: bigint, bits: bigint, direction: "left" | "right", maxBits: bigint) => bigint ; sqrt: (x: bigint) => undefined | bigint ; square: (x: bigint) => bigint ; sub: (x: bigint, y: bigint) => bigint }
Scalar.M	bigint
Scalar.modulus	bigint
Scalar.sizeInBits	number
Scalar.t	bigint
Scalar.twoadicRoot	bigint
Scalar.add	[object Object]
Scalar.div	[object Object]
Scalar.dot	[object Object]
Scalar.equal	[object Object]
Scalar.fromBigint	[object Object]
Scalar.fromNumber	[object Object]
Scalar.inverse	[object Object]
Scalar.isEven	[object Object]
Scalar.isSquare	[object Object]
Scalar.leftShift	[object Object]
Scalar.mod	[object Object]
Scalar.mul	[object Object]
Scalar.negate	[object Object]
Scalar.not	[object Object]
Scalar.power	[object Object]
Scalar.random	[object Object]
Scalar.rightShift	[object Object]
Scalar.rot	[object Object]
Scalar.sqrt	[object Object]
Scalar.square	[object Object]
Scalar.sub	[object Object]
a	bigint
b	bigint
cofactor	undefined | bigint
hasCofactor	boolean
hasEndomorphism	boolean
modulus	bigint
name	string
one	{ infinity: boolean = false; x: bigint ; y: bigint }
one.infinity	boolean
one.x	bigint
one.y	bigint
order	bigint
zero	GroupAffine
get Endo()	{ base: bigint = endoBase; decomposeMaxBits: number = glvData.maxBits; scalar: bigint = endoScalar; decompose: (s: bigint) => readonly [{ abs: bigint ; isNegative: boolean ; value: bigint = s0 }, { abs: bigint ; isNegative: boolean ; value: bigint = s1 }] ; endomorphism: (P: GroupAffine) => { x: bigint ; y: bigint = P.y } ; scale: (g: GroupAffine, s: bigint) => GroupAffine ; scaleProjective: (g: GroupProjective, s: bigint) => { x: bigint ; y: bigint ; z: bigint } }
add	(g: GroupAffine, h: GroupAffine) => GroupAffine
double	(g: GroupAffine) => GroupAffine
equal	(g: GroupAffine, h: GroupAffine) => boolean
from	(g: { x: bigint ; y: bigint }) => GroupAffine
fromNonzero	(g: { x: bigint ; y: bigint }) => GroupAffine
isInSubgroup	(g: GroupAffine) => boolean
isOnCurve	(g: GroupAffine) => boolean
negate	(g: GroupAffine) => GroupAffine
scale	(g: GroupAffine, s: bigint | boolean[]) => GroupAffine
sub	(g: GroupAffine, h: GroupAffine) => GroupAffine

Defined in

lib/foreign-curve.ts:251

---

Field

• Static get Field(): typeof AlmostForeignField

The base field of this curve as a ForeignField.

Returns

typeof AlmostForeignField

Defined in

lib/foreign-curve.ts:258

---

Scalar

• Static get Scalar(): typeof AlmostForeignField

The scalar field of this curve as a ForeignField.

Returns

typeof AlmostForeignField

Defined in

lib/foreign-curve.ts:265

---

generator

• Static get generator(): ForeignCurve

The constant generator point.

Returns

ForeignCurve

Defined in

lib/foreign-curve.ts:69

---

modulus

• Static get modulus(): bigint

The size of the curve's base field.

Returns

bigint

Defined in

lib/foreign-curve.ts:75

---

provable

• Static get provable(): ProvablePureExtended\<ForeignCurve, { x: string ; y: string }>

Provable<ForeignCurve>

Returns

ProvablePureExtended\<ForeignCurve, { x: string ; y: string }>

Defined in

lib/foreign-curve.ts:272

Methods

add

▸ add(h): ForeignCurve

Elliptic curve addition.

let r = p.add(q); // r = p + q

Important: this is incomplete addition and does not handle the degenerate cases:

• Inputs are equal, g = h (where you would use double). In this case, the result of this method is garbage and can be manipulated arbitrarily by a malicious prover.
• Inputs are inverses of each other, g = -h, so that the result would be the zero point. In this case, the proof fails.

If you want guaranteed soundness regardless of the input, use addSafe instead.

Parameters

Name	Type
h	ForeignCurve | FlexiblePoint

Returns

ForeignCurve

Throws

if the inputs are inverses of each other.

Defined in

lib/foreign-curve.ts:121

---

addSafe

▸ addSafe(h): ForeignCurve

Safe elliptic curve addition.

This is the same as add, but additionally proves that the inputs are not equal. Therefore, the method is guaranteed to either fail or return a valid addition result.

Beware: this is more expensive than add, and is still incomplete in that it does not succeed on equal or inverse inputs.

Parameters

Name	Type
h	ForeignCurve | FlexiblePoint

Returns

ForeignCurve

Throws

if the inputs are equal or inverses of each other.

Defined in

lib/foreign-curve.ts:139

---

assertInSubgroup

▸ assertInSubgroup(): void

Assert that this point lies in the subgroup defined by order*P = 0.

Note: this is a no-op if the curve has cofactor equal to 1. Otherwise it performs the full scalar multiplication order*P and is expensive.

Returns

void

Defined in

lib/foreign-curve.ts:219

---

assertOnCurve

▸ assertOnCurve(): void

Assert that this point lies on the elliptic curve, which means it satisfies the equation y^2 = x^3 + ax + b

Returns

void

Defined in

lib/foreign-curve.ts:203

---

double

▸ double(): ForeignCurve

Elliptic curve doubling.

Returns

ForeignCurve

Example

let r = p.double(); // r = 2 * p

Defined in

lib/foreign-curve.ts:158

---

isConstant

▸ isConstant(): boolean

Checks whether this curve point is constant.

See FieldVar to understand constants vs variables.

Returns

boolean

Defined in

lib/foreign-curve.ts:90

---

negate

▸ negate(): ForeignCurve

Elliptic curve negation.

Returns

ForeignCurve

Example

let r = p.negate(); // r = -p

Defined in

lib/foreign-curve.ts:172

---

scale

▸ scale(scalar): ForeignCurve

Elliptic curve scalar multiplication, where the scalar is represented as a ForeignField element.

Important: this proves that the result of the scalar multiplication is not the zero point.

Parameters

Name	Type
scalar	number | bigint | AlmostForeignField

Returns

ForeignCurve

Throws

if the scalar multiplication results in the zero point; for example, if the scalar is zero.

Example

let r = p.scale(s); // r = s * p

Defined in

lib/foreign-curve.ts:188

---

toBigint

▸ toBigint(): GroupAffine

Convert this curve point to a point with bigint coordinates.

Returns

GroupAffine

Defined in

lib/foreign-curve.ts:97

---

assertInSubgroup

▸ Static assertInSubgroup(g): void

Parameters

Name	Type
g	ForeignCurve

Returns

void

Defined in

lib/foreign-curve.ts:207

---

assertOnCurve

▸ Static assertOnCurve(g): void

Parameters

Name	Type
g	ForeignCurve

Returns

void

Defined in

lib/foreign-curve.ts:195

---

check

▸ Static check(g): void

Check that this is a valid element of the target subgroup of the curve:

• Check that the coordinates are valid field elements
• Use () to check that the point lies on the curve
• If the curve has cofactor unequal to 1, use ().

Parameters

Name	Type
g	ForeignCurve

Returns

void

Defined in

lib/foreign-curve.ts:229

---

from

▸ Static from(g): ForeignCurve

Coerce the input to a ForeignCurve.

Parameters

Name	Type
g	ForeignCurve | FlexiblePoint

Returns

ForeignCurve

Defined in

lib/foreign-curve.ts:61