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ScalarField

ForeignField representing the scalar field of Pallas and the base field of Vesta

Extends​

  • UnreducedForeignField<this>

Constructors​

new ScalarField()​

new ScalarField(x: 
  | string
  | number
  | bigint
  | Field3
  | ForeignField): ScalarField

Create a new ForeignField from a bigint, number, string or another ForeignField.

Parameters​

• x: | string | number | bigint | Field3 | ForeignField

Returns​

ScalarField

Inherited from​

createForeignField(Fq.modulus).constructor

Example​

let x = new ForeignField(5);

Note: Inputs must be range checked if they originate from a different field with a different modulus or if they are not constants.

  • When constructing from another ForeignField instance, ensure the modulus matches. If not, check the modulus using Gadgets.ForeignField.assertLessThan() and handle appropriately.
  • When constructing from a Field3 array, ensure all elements are valid Field elements and range checked.
  • Ensure constants are correctly reduced to the modulus of the field.

Source​

lib/provable/foreign-field.ts:101

Properties​

type​

type: "Unreduced" | "AlmostReduced" | "FullyReduced" = 'Unreduced';

Inherited from​

createForeignField(Fq.modulus).type

Source​

lib/provable/foreign-field.ts:469

value​

value: Field3;

The internal representation of a foreign field element, as a tuple of 3 limbs.

Inherited from​

createForeignField(Fq.modulus).value

Source​

lib/provable/foreign-field.ts:49

_Bigint​

static _Bigint: undefined | {} = undefined;

Inherited from​

createForeignField(Fq.modulus)._Bigint

Source​

lib/provable/foreign-field.ts:27

_modulus​

static _modulus: undefined | bigint = undefined;

Inherited from​

createForeignField(Fq.modulus)._modulus

Source​

lib/provable/foreign-field.ts:28

_provable​

static _provable: undefined | ProvablePureExtended<UnreducedForeignField, bigint, string> = undefined;

Inherited from​

createForeignField(Fq.modulus)._provable

Source​

lib/provable/foreign-field.ts:471

_variants​

static _variants: undefined | {
  "almostReduced": typeof AlmostForeignField;
  "canonical": typeof CanonicalForeignField;
  "unreduced": typeof UnreducedForeignField;
 } = undefined;

Sibling classes that represent different ranges of field elements.

Inherited from​

createForeignField(Fq.modulus)._variants

Source​

lib/provable/foreign-field.ts:58

Accessors​

Constructor​

get Constructor(): typeof ForeignField

Returns​

typeof ForeignField

Source​

lib/provable/foreign-field.ts:51

modulus​

get modulus(): bigint

Returns​

bigint

Source​

lib/provable/foreign-field.ts:39

AlmostReduced​

get static AlmostReduced(): typeof AlmostForeignField

Constructor for field elements that are "almost reduced", i.e. lie in the range [0, 2^ceil(log2(p))).

Returns​

typeof AlmostForeignField

Source​

lib/provable/foreign-field.ts:76

Bigint​

get static Bigint(): {}

Returns​

{}

Source​

lib/provable/foreign-field.ts:31

Canonical​

get static Canonical(): typeof CanonicalForeignField

Constructor for field elements that are fully reduced, i.e. lie in the range [0, p).

Returns​

typeof CanonicalForeignField

Source​

lib/provable/foreign-field.ts:83

Unreduced​

get static Unreduced(): typeof UnreducedForeignField

Constructor for unreduced field elements.

Returns​

typeof UnreducedForeignField

Source​

lib/provable/foreign-field.ts:69

modulus​

get static modulus(): bigint

Returns​

bigint

Source​

lib/provable/foreign-field.ts:35

provable​

get static provable(): ProvablePureExtended<UnreducedForeignField, bigint, string>

Returns​

ProvablePureExtended<UnreducedForeignField, bigint, string>

Source​

lib/provable/foreign-field.ts:474

sizeInBits​

get static sizeInBits(): number

Returns​

number

Source​

lib/provable/foreign-field.ts:42

Methods​

add()​

add(y: number | bigint | ForeignField): UnreducedForeignField

Finite field addition

Parameters​

• y: number | bigint | ForeignField

Returns​

UnreducedForeignField

Inherited from​

createForeignField(Fq.modulus).add

Example​

x.add(2); // x + 2 mod p

Source​

lib/provable/foreign-field.ts:218

assertAlmostReduced()​

assertAlmostReduced(): AlmostForeignField

Assert that this field element lies in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.

Returns the field element as a AlmostForeignField.

For a more efficient version of this for multiple field elements, see assertAlmostReduced.

Note: this does not ensure that the field elements is in the canonical range [0, p). To assert that stronger property, there is assertCanonical. You should typically use assertAlmostReduced though, because it is cheaper to prove and sufficient for ensuring validity of all our non-native field arithmetic methods.

Returns​

AlmostForeignField

Inherited from​

createForeignField(Fq.modulus).assertAlmostReduced

Source​

lib/provable/foreign-field.ts:173

assertCanonical()​

assertCanonical(): CanonicalForeignField

Assert that this field element is fully reduced, i.e. lies in the range [0, p), where p is the foreign field modulus.

Returns the field element as a CanonicalForeignField.

Returns​

CanonicalForeignField

Inherited from​

createForeignField(Fq.modulus).assertCanonical

Source​

lib/provable/foreign-field.ts:204

assertEquals()​

assertEquals(y, message)​

assertEquals(y: number | bigint | CanonicalForeignField, message?: string): CanonicalForeignField

Assert equality with a ForeignField-like value

Parameters​

• y: number | bigint | CanonicalForeignField

• message?: string

Returns​

CanonicalForeignField

Inherited from​

createForeignField(Fq.modulus).assertEquals

Example​
x.assertEquals(0, "x is zero");

Since asserting equality can also serve as a range check, this method returns x with the appropriate type:

Example​
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Source​

lib/provable/foreign-field.ts:296

assertEquals(y, message)​

assertEquals(y: AlmostForeignField, message?: string): AlmostForeignField
Parameters​

• y: AlmostForeignField

• message?: string

Returns​

AlmostForeignField

Inherited from​

createForeignField(Fq.modulus).assertEquals

Source​

lib/provable/foreign-field.ts:300

assertEquals(y, message)​

assertEquals(y: ForeignField, message?: string): ForeignField
Parameters​

• y: ForeignField

• message?: string

Returns​

ForeignField

Inherited from​

createForeignField(Fq.modulus).assertEquals

Source​

lib/provable/foreign-field.ts:301

assertLessThan()​

assertLessThan(c: number | bigint, message?: string): void

Assert that this field element is less than a constant c: x < c.

The constant must satisfy 0 <= c < 2^264, otherwise an error is thrown.

Parameters​

• c: number | bigint

• message?: string

Returns​

void

Inherited from​

createForeignField(Fq.modulus).assertLessThan

Example​

x.assertLessThan(10);

Source​

lib/provable/foreign-field.ts:339

isConstant()​

isConstant(): boolean

Checks whether this field element is a constant.

See FieldVar to understand constants vs variables.

Returns​

boolean

Inherited from​

createForeignField(Fq.modulus).isConstant

Source​

lib/provable/foreign-field.ts:136

neg()​

neg(): AlmostForeignField

Finite field negation

Returns​

AlmostForeignField

Inherited from​

createForeignField(Fq.modulus).neg

Example​

x.neg(); // -x mod p = p - x

Source​

lib/provable/foreign-field.ts:229

sub()​

sub(y: number | bigint | ForeignField): UnreducedForeignField

Finite field subtraction

Parameters​

• y: number | bigint | ForeignField

Returns​

UnreducedForeignField

Inherited from​

createForeignField(Fq.modulus).sub

Example​

x.sub(1); // x - 1 mod p

Source​

lib/provable/foreign-field.ts:244

toBigInt()​

toBigInt(): bigint

Convert this field element to a bigint.

Returns​

bigint

Inherited from​

createForeignField(Fq.modulus).toBigInt

Source​

lib/provable/foreign-field.ts:156

toBits()​

toBits(length?: number): Bool[]

Unpack a field element to its bits, as a Bool[] array.

This method is provable!

Parameters​

• length?: number

Returns​

Bool[]

Inherited from​

createForeignField(Fq.modulus).toBits

Source​

lib/provable/foreign-field.ts:358

toConstant()​

toConstant(): ForeignField

Convert this field element to a constant.

See FieldVar to understand constants vs variables.

Warning: This function is only useful in Provable.witness or Provable.asProver blocks, that is, in situations where the prover computes a value outside provable code.

Returns​

ForeignField

Inherited from​

createForeignField(Fq.modulus).toConstant

Source​

lib/provable/foreign-field.ts:148

toFields()​

toFields(): Field[]

Instance version of Provable<ForeignField>.toFields, see Provable.toFields

Returns​

Field[]

Inherited from​

createForeignField(Fq.modulus).toFields

Source​

lib/provable/foreign-field.ts:406

toScalar()​

toScalar(): Scalar

Provable method to convert a ScalarField into a Scalar

Returns​

Scalar

Source​

lib/provable/scalar-field.ts:16

assertAlmostReduced()​

static assertAlmostReduced<T>(...xs: T): [...{ [i in string | number | symbol]: AlmostForeignField }[]]

Assert that one or more field elements lie in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.

This is most efficient than when checking a multiple of 3 field elements at once.

Type parameters​

• T extends Tuple<ForeignField>

Parameters​

• ...xs: T

Returns​

[...{ [i in string | number | symbol]: AlmostForeignField }[]]

Inherited from​

createForeignField(Fq.modulus).assertAlmostReduced

Source​

lib/provable/foreign-field.ts:187

check()​

static check(x: ForeignField): void

Parameters​

• x: ForeignField

Returns​

void

Inherited from​

createForeignField(Fq.modulus).check

Source​

lib/provable/foreign-field.ts:479

from()​

from(x)​

static from(x: string | number | bigint): CanonicalForeignField

Coerce the input to a ForeignField.

Parameters​

• x: string | number | bigint

Returns​

CanonicalForeignField

Inherited from​

createForeignField(Fq.modulus).from

Source​

lib/provable/foreign-field.ts:124

from(x)​

static from(x: string | number | bigint | ForeignField): ForeignField
Parameters​

• x: string | number | bigint | ForeignField

Returns​

ForeignField

Inherited from​

createForeignField(Fq.modulus).from

Source​

lib/provable/foreign-field.ts:125

fromBits()​

static fromBits(bits: Bool[]): AlmostForeignField

Create a field element from its bits, as a Bool[] array.

This method is provable!

Parameters​

• bits: Bool[]

Returns​

AlmostForeignField

Inherited from​

createForeignField(Fq.modulus).fromBits

Source​

lib/provable/foreign-field.ts:388

fromScalar()​

static fromScalar(s: Scalar): ScalarField

Converts this Scalar into a ScalarField

Parameters​

• s: Scalar

Returns​

ScalarField

Source​

lib/provable/scalar-field.ts:34

random()​

static random(): CanonicalForeignField

Returns​

CanonicalForeignField

Inherited from​

createForeignField(Fq.modulus).random

Source​

lib/provable/foreign-field.ts:399

sum()​

static sum(xs: (number | bigint | ForeignField)[], operations: (-1 | 1)[]): UnreducedForeignField

Sum (or difference) of multiple finite field elements.

Parameters​

• xs: (number | bigint | ForeignField)[]

• operations: (-1 | 1)[]

Returns​

UnreducedForeignField

Inherited from​

createForeignField(Fq.modulus).sum

Example​

let z = ForeignField.sum([3, 2, 1], [-1, 1]); // 3 - 2 + 1
z.assertEquals(2);

This method expects a list of ForeignField-like values, x0,...,xn, and a list of "operations" op1,...,opn where every op is 1 or -1 (plus or minus), and returns

x0 + op1*x1 + ... + opn*xn

where the sum is computed in finite field arithmetic.

Important: For more than two summands, this is significantly more efficient than chaining calls to ForeignField.add and ForeignField.sub.

Source​

lib/provable/foreign-field.ts:269

toScalar()​

static toScalar(field: ForeignField): Scalar

Parameters​

• field: ForeignField

Returns​

Scalar

Source​

lib/provable/scalar-field.ts:20