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Version: 2.15.0

ForeignCurveNotNeeded

Defined in: lib/provable/crypto/foreign-curve.ts:402

@see: ForeignCurve

Extends​

Constructors​

Constructor​

new ForeignCurveNotNeeded(g: {
  x:   | number
     | bigint
     | Field3
     | AlmostForeignField;
  y:   | number
     | bigint
     | Field3
     | AlmostForeignField;
}): ForeignCurveNotNeeded;

Defined in: lib/provable/crypto/foreign-curve.ts:403

Parameters​

g​
x​

| number | bigint | Field3 | AlmostForeignField

y​

| number | bigint | Field3 | AlmostForeignField

Returns​

ForeignCurveNotNeeded

Overrides​

ForeignCurve.constructor

Properties​

x​

x: AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:31

Inherited from​

ForeignCurve.x

y​

y: AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:32

Inherited from​

ForeignCurve.y

_Bigint?​

static optional _Bigint?: {
};

Defined in: lib/provable/crypto/foreign-curve.ts:360

Inherited from​

ForeignCurve._Bigint

_Field?​

static optional _Field?: typeof AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:361

Inherited from​

ForeignCurve._Field

_provable?​

static optional _provable?: ProvablePureExtended<ForeignCurve, {
  x: bigint;
  y: bigint;
}, {
  x: string;
  y: string;
}>;

Defined in: lib/provable/crypto/foreign-curve.ts:363

Inherited from​

ForeignCurve._provable

_Scalar?​

static optional _Scalar?: typeof AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:362

Inherited from​

ForeignCurve._Scalar

Accessors​

Constructor​

Get Signature​

get Constructor(): typeof ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:357

Returns​

typeof ForeignCurve

Inherited from​

ForeignCurve.Constructor

modulus​

Get Signature​

get modulus(): bigint;

Defined in: lib/provable/crypto/foreign-curve.ts:200

The size of the curve's base field.

Returns​

bigint

Inherited from​

ForeignCurve.modulus

Bigint​

Get Signature​

get static Bigint(): {
};

Defined in: lib/provable/crypto/foreign-curve.ts:372

Curve arithmetic on JS bigints.

Returns​
{
}

Inherited from​

ForeignCurve.Bigint

Field​

Get Signature​

get static Field(): typeof AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:379

The base field of this curve as a ForeignField.

Returns​

typeof AlmostForeignField

Inherited from​

ForeignCurve.Field

generator​

Get Signature​

get static generator(): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:188

The constant generator point.

Returns​

ForeignCurve

Inherited from​

ForeignCurve.generator

modulus​

Get Signature​

get static modulus(): bigint;

Defined in: lib/provable/crypto/foreign-curve.ts:194

The size of the curve's base field.

Returns​

bigint

Inherited from​

ForeignCurve.modulus

provable​

Get Signature​

get static provable(): ProvablePureExtended<ForeignCurve, {
  x: bigint;
  y: bigint;
}, {
  x: string;
  y: string;
}>;

Defined in: lib/provable/crypto/foreign-curve.ts:393

Provable<ForeignCurve>

Returns​

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

Inherited from​

ForeignCurve.provable

Scalar​

Get Signature​

get static Scalar(): typeof AlmostForeignField;

Defined in: lib/provable/crypto/foreign-curve.ts:386

The scalar field of this curve as a ForeignField.

Returns​

typeof AlmostForeignField

Inherited from​

ForeignCurve.Scalar

Methods​

add()​

add(h: 
  | ForeignCurve
  | FlexiblePoint): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:241

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​

h​

| ForeignCurve | FlexiblePoint

Returns​

ForeignCurve

Throws​

if the inputs are inverses of each other.

Inherited from​

ForeignCurve.add

addSafe()​

addSafe(h: 
  | ForeignCurve
  | FlexiblePoint): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:259

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​

h​

| ForeignCurve | FlexiblePoint

Returns​

ForeignCurve

Throws​

if the inputs are equal or inverses of each other.

Inherited from​

ForeignCurve.addSafe

assertInSubgroup()​

assertInSubgroup(): void;

Defined in: lib/provable/crypto/foreign-curve.ts:339

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

Inherited from​

ForeignCurve.assertInSubgroup

assertOnCurve()​

assertOnCurve(): void;

Defined in: lib/provable/crypto/foreign-curve.ts:323

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

Returns​

void

Inherited from​

ForeignCurve.assertOnCurve

double()​

double(): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:278

Elliptic curve doubling.

Returns​

ForeignCurve

Example​

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

Inherited from​

ForeignCurve.double

negate()​

negate(): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:292

Elliptic curve negation.

Returns​

ForeignCurve

Example​

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

Inherited from​

ForeignCurve.negate

scale()​

scale(scalar: 
  | number
  | bigint
  | AlmostForeignField): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:308

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​

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

Inherited from​

ForeignCurve.scale

toBigint()​

toBigint(): GroupAffine;

Defined in: lib/provable/crypto/foreign-curve.ts:217

Convert this curve point to a point with bigint coordinates.

Returns​

GroupAffine

Inherited from​

ForeignCurve.toBigint

assertInSubgroup()​

static assertInSubgroup(g: ForeignCurve): void;

Defined in: lib/provable/crypto/foreign-curve.ts:327

Parameters​

g​

ForeignCurve

Returns​

void

Inherited from​

ForeignCurve.assertInSubgroup

assertOnCurve()​

static assertOnCurve(g: ForeignCurve): void;

Defined in: lib/provable/crypto/foreign-curve.ts:315

Parameters​

g​

ForeignCurve

Returns​

void

Inherited from​

ForeignCurve.assertOnCurve

check()​

static check(g: ForeignCurveNotNeeded): void;

Defined in: lib/provable/crypto/foreign-curve.ts:410

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​

g​

ForeignCurveNotNeeded

Returns​

void

Overrides​

ForeignCurve.check

from()​

static from(g: 
  | ForeignCurve
  | FlexiblePoint): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:64

Coerce the input to a ForeignCurve.

Parameters​

g​

| ForeignCurve | FlexiblePoint

Returns​

ForeignCurve

Inherited from​

ForeignCurve.from

fromEthers()​

static fromEthers(hex: string): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:142

Create a new ForeignCurve instance from an Ethereum public key in hex format, which may be either compressed or uncompressed. This method is designed to handle the parsing of public keys as used by the ethers.js library.

The input should represent the affine x and y coordinates of the point, in hexadecimal format. Compressed keys are 33 bytes long and begin with 0x02 or 0x03, while uncompressed keys are 65 bytes long and begin with 0x04.

Warning: This method is specifically designed for use with the Secp256k1 curve. Using it with other curves may result in incorrect behavior or errors. Ensure that the curve setup matches Secp256k1, as shown in the example, to avoid unintended issues.

Parameters​

hex​

string

The public key as a hexadecimal string (without the "0x" prefix).

Returns​

ForeignCurve

A new instance of the curve representing the given public key.

Example​

import { Wallet, Signature, getBytes } from 'ethers';

class Secp256k1 extends createForeignCurve(Crypto.CurveParams.Secp256k1) {}

const wallet = Wallet.createRandom();

const publicKey = Secp256k1.fromEthers(wallet.publicKey.slice(2));

Inherited from​

ForeignCurve.fromEthers

fromHex()​

static fromHex(hex: string): ForeignCurve;

Defined in: lib/provable/crypto/foreign-curve.ts:91

Parses a hexadecimal string representing an uncompressed elliptic curve point and coerces it into a ForeignCurve point.

The method extracts the x and y coordinates from the provided hex string and verifies that the resulting point lies on the curve.

Note: This method only supports uncompressed elliptic curve points, which are 65 bytes in total (1-byte prefix + 32 bytes for x + 32 bytes for y).

Parameters​

hex​

string

The hexadecimal string representing the uncompressed elliptic curve point.

Returns​

ForeignCurve

  • A point on the foreign curve, parsed from the given hexadecimal string.

Throws​

  • Throws an error if the input is not a valid public key.

Example​

class Secp256k1 extends createForeignCurve(Crypto.CurveParams.Secp256k1) {}

const publicKeyHex = '04f8b8db25c619d0c66b2dc9e97ecbafafae...'; // Example hex string for uncompressed point
const point = Secp256k1.fromHex(publicKeyHex);

Important: This method is only designed to handle uncompressed elliptic curve points in hex format.

Inherited from​

ForeignCurve.fromHex