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Nullifier

Nullifiers are used as a public commitment to a specific anonymous account, to forbid actions like double spending, or allow a consistent identity between anonymous actions.

RFC: https://github.com/o1-labs/o1js/issues/756

Paper: https://eprint.iacr.org/2022/1255.pdf

Extends​

  • { "private": { "c": Field; "g_r": Group; "h_m_pk_r": Group; }; "public": { "nullifier": Group; "s": Scalar; }; "publicKey": Group; }

Constructors​

new Nullifier()​

new Nullifier(value: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }): Nullifier

Parameters​

• value

• value.private= undefined

• value.private.c: Field= Field

• value.private.g_r: Group= Group

• value.private.h_m_pk_r: Group= Group

• value.public= undefined

• value.public.nullifier: Group= Group

• value.public.s: Scalar= Scalar

• value.publicKey: Group= Group

Returns​

Nullifier

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).constructor

Source​

lib/provable/types/struct.ts:148

Properties​

private​

private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};

c​

c: Field = Field;

g_r​

g_r: Group = Group;

h_m_pk_r​

h_m_pk_r: Group = Group;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).private

Source​

lib/provable/crypto/nullifier.ts:26

public​

public: {
  "nullifier": Group;
  "s": Scalar;
};

nullifier​

nullifier: Group = Group;

s​

s: Scalar = Scalar;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).public

Source​

lib/provable/crypto/nullifier.ts:22

publicKey​

publicKey: Group = Group;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).publicKey

Source​

lib/provable/crypto/nullifier.ts:21

_isStruct​

static _isStruct: true;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, })._isStruct

Source​

lib/provable/types/struct.ts:148

check()​

static check: (value: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => void;

Add assertions to the proof to check if value is a valid member of type T. This function does not return anything, instead it creates any number of assertions to prove that value is a valid member of the type T.

For instance, calling check function on the type Bool asserts that the value of the element is either 1 or 0.

Parameters​

• value

the element of type T to put assertions on.

• value.private= undefined

• value.private.c: Field= Field

• value.private.g_r: Group= Group

• value.private.h_m_pk_r: Group= Group

• value.public= undefined

• value.public.nullifier: Group= Group

• value.public.s: Scalar= Scalar

• value.publicKey: Group= Group

Returns​

void

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).check

Source​

lib/provable/types/provable-intf.ts:76

empty()​

static empty: () => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Returns​

{
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
}
private​
private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};
private.c​
c: Field = Field;
private.g_r​
g_r: Group = Group;
private.h_m_pk_r​
h_m_pk_r: Group = Group;
public​
public: {
  "nullifier": Group;
  "s": Scalar;
};
public.nullifier​
nullifier: Group = Group;
public.s​
s: Scalar = Scalar;
publicKey​
publicKey: Group = Group;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).empty

Source​

lib/provable/types/struct.ts:158

fromFields()​

static fromFields: (fields: Field[]) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Parameters​

• fields: Field[]

Returns​

{
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
}
private​
private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};
private.c​
c: Field = Field;
private.g_r​
g_r: Group = Group;
private.h_m_pk_r​
h_m_pk_r: Group = Group;
public​
public: {
  "nullifier": Group;
  "s": Scalar;
};
public.nullifier​
nullifier: Group = Group;
public.s​
s: Scalar = Scalar;
publicKey​
publicKey: Group = Group;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).fromFields

Source​

lib/provable/types/provable-intf.ts:115

fromValue​

static fromValue: (x: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 } | {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 } & (value: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Convert provable type from a normal JS type.

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).fromValue

Source​

lib/provable/types/provable-intf.ts:86

toAuxiliary()​

static toAuxiliary: (value?: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => any[];

A function that takes value (optional), an element of type T, as argument and returns an array of any type that make up the "auxiliary" (non-provable) data of value.

Parameters​

• value?

the element of type T to generate the auxiliary data array from, optional. If not provided, a default value for auxiliary data is returned.

• value.private?= undefined

• value.private.c?: Field= Field

• value.private.g_r?: Group= Group

• value.private.h_m_pk_r?: Group= Group

• value.public?= undefined

• value.public.nullifier?: Group= Group

• value.public.s?: Scalar= Scalar

• value.publicKey?: Group= Group

Returns​

any[]

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toAuxiliary

Source​

lib/provable/types/provable-intf.ts:47

toCanonical()?​

static optional toCanonical: (x: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Optional method which transforms a provable type into its canonical representation.

This is needed for types that have multiple representations of the same underlying value, and might even not have perfect completeness for some of those representations.

An example is the ForeignField class, which allows non-native field elements to exist in unreduced form. The unreduced form is not perfectly complete, for example, addition of two unreduced field elements can cause a prover error.

Specific protocols need to be able to protect themselves against incomplete operations at all costs. For example, when using actions and reducer, the reducer must be able to produce a proof regardless of the input action. toCanonical() converts any input into a safe form and enables us to handle cases like this generically.

Note: For most types, this method is the identity function. The identity function will also be used when the toCanonical() is not present on a type.

Parameters​

• x

• x.private= undefined

• x.private.c: Field= Field

• x.private.g_r: Group= Group

• x.private.h_m_pk_r: Group= Group

• x.public= undefined

• x.public.nullifier: Group= Group

• x.public.s: Scalar= Scalar

• x.publicKey: Group= Group

Returns​

{
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
}
private​
private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};
private.c​
c: Field = Field;
private.g_r​
g_r: Group = Group;
private.h_m_pk_r​
h_m_pk_r: Group = Group;
public​
public: {
  "nullifier": Group;
  "s": Scalar;
};
public.nullifier​
nullifier: Group = Group;
public.s​
s: Scalar = Scalar;
publicKey​
publicKey: Group = Group;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toCanonical

Source​

lib/provable/types/provable-intf.ts:104

toFields()​

static toFields: (value: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => Field[];

A function that takes value, an element of type T, as argument and returns an array of Field elements that make up the provable data of value.

Parameters​

• value

the element of type T to generate the Field array from.

• value.private= undefined

• value.private.c: Field= Field

• value.private.g_r: Group= Group

• value.private.h_m_pk_r: Group= Group

• value.public= undefined

• value.public.nullifier: Group= Group

• value.public.s: Scalar= Scalar

• value.publicKey: Group= Group

Returns​

Field[]

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toFields

Source​

lib/provable/types/provable-intf.ts:36

toInput()​

static toInput: (x: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "fields": Field[];
  "packed": [Field, number][];
};

Parameters​

• x

• x.private= undefined

• x.private.c: Field= Field

• x.private.g_r: Group= Group

• x.private.h_m_pk_r: Group= Group

• x.public= undefined

• x.public.nullifier: Group= Group

• x.public.s: Scalar= Scalar

• x.publicKey: Group= Group

Returns​

{
  "fields": Field[];
  "packed": [Field, number][];
}
fields?​
optional fields: Field[];
packed?​
optional packed: [Field, number][];

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toInput

Source​

lib/provable/types/struct.ts:152

toJSON()​

static toJSON: (x: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Parameters​

• x

• x.private= undefined

• x.private.c: Field= Field

• x.private.g_r: Group= Group

• x.private.h_m_pk_r: Group= Group

• x.public= undefined

• x.public.nullifier: Group= Group

• x.public.s: Scalar= Scalar

• x.publicKey: Group= Group

Returns​

{
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
}
private​
private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};
private.c​
c: string = Field;
private.g_r​
g_r: {
  "x": string;
  "y": string;
 } = Group;
private.g_r.x​
x: string;
private.g_r.y​
y: string;
private.h_m_pk_r​
h_m_pk_r: {
  "x": string;
  "y": string;
 } = Group;
private.h_m_pk_r.x​
x: string;
private.h_m_pk_r.y​
y: string;
public​
public: {
  "nullifier": Group;
  "s": Scalar;
};
public.nullifier​
nullifier: {
  "x": string;
  "y": string;
 } = Group;
public.nullifier.x​
x: string;
public.nullifier.y​
y: string;
public.s​
s: string = Scalar;
publicKey​
publicKey: {
  "x": string;
  "y": string;
 } = Group;
publicKey.x​
x: string;
publicKey.y​
y: string;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toJSON

Source​

lib/provable/types/struct.ts:156

toValue()​

static toValue: (x: {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
 }) => {
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
};

Convert provable type to a normal JS type.

Parameters​

• x

• x.private= undefined

• x.private.c: Field= Field

• x.private.g_r: Group= Group

• x.private.h_m_pk_r: Group= Group

• x.public= undefined

• x.public.nullifier: Group= Group

• x.public.s: Scalar= Scalar

• x.publicKey: Group= Group

Returns​

{
  "private": {
     "c": Field;
     "g_r": Group;
     "h_m_pk_r": Group;
    };
  "public": {
     "nullifier": Group;
     "s": Scalar;
    };
  "publicKey": Group;
}
private​
private: {
  "c": Field;
  "g_r": Group;
  "h_m_pk_r": Group;
};
private.c​
c: bigint = Field;
private.g_r​
g_r: {
  "x": bigint;
  "y": bigint;
 } = Group;
private.g_r.x​
x: bigint;
private.g_r.y​
y: bigint;
private.h_m_pk_r​
h_m_pk_r: {
  "x": bigint;
  "y": bigint;
 } = Group;
private.h_m_pk_r.x​
x: bigint;
private.h_m_pk_r.y​
y: bigint;
public​
public: {
  "nullifier": Group;
  "s": Scalar;
};
public.nullifier​
nullifier: {
  "x": bigint;
  "y": bigint;
 } = Group;
public.nullifier.x​
x: bigint;
public.nullifier.y​
y: bigint;
public.s​
s: bigint = Scalar;
publicKey​
publicKey: {
  "x": bigint;
  "y": bigint;
 } = Group;
publicKey.x​
x: bigint;
publicKey.y​
y: bigint;

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).toValue

Source​

lib/provable/types/provable-intf.ts:81

Methods​

assertUnused()​

assertUnused(witness: MerkleMapWitness, root: Field): void

Checks if the Nullifier has been used before.

Parameters​

• witness: MerkleMapWitness

• root: Field

Returns​

void

Example​

// asserts that the nullifier has not been used before, throws an error otherwise
nullifier.assertUnused();

Source​

lib/provable/crypto/nullifier.ts:128

getPublicKey()​

getPublicKey(): PublicKey

Returns the PublicKey that is associated with this Nullifier.

Returns​

PublicKey

Example​

let pk = nullifier.getPublicKey();

Source​

lib/provable/crypto/nullifier.ts:157

isUnused()​

isUnused(witness: MerkleMapWitness, root: Field): Bool

Returns the state of the Nullifier.

Parameters​

• witness: MerkleMapWitness

• root: Field

Returns​

Bool

Example​

// returns a Bool based on whether or not the nullifier has been used before
let isUnused = nullifier.isUnused();

Source​

lib/provable/crypto/nullifier.ts:108

key()​

key(): Field

The key of the nullifier, which belongs to a unique message and a public key. Used as an index in Merkle trees.

Returns​

Field

Example​

// returns the key of the nullifier which can be used as index in a Merkle tree/map
let key = nullifier.key();

Source​

lib/provable/crypto/nullifier.ts:95

setUsed()​

setUsed(witness: MerkleMapWitness): Field

Sets the Nullifier, returns the new Merkle root.

Parameters​

• witness: MerkleMapWitness

Returns​

Field

Example​

// calculates the new root of the Merkle tree in which the nullifier is set to used
let newRoot = nullifier.setUsed(witness);

Source​

lib/provable/crypto/nullifier.ts:143

verify()​

verify(message: Field[]): void

Verifies that the Nullifier belongs to a specific message. Throws an error if the Nullifier is incorrect.

Parameters​

• message: Field[]

Returns​

void

Example​

let nullifierMessage = [voteId, ...otherData];
// throws an error if the nullifier is invalid or doesn't belong to this specific message
nullifier.verify(nullifierMessage);

Source​

lib/provable/crypto/nullifier.ts:47

createTestNullifier()​

static createTestNullifier(message: Field[], sk: PrivateKey): Nullifier

Note: This is not the recommended way to create a Nullifier in production. Please use mina-signer to create Nullifiers. Also, this function cannot be run within provable code to avoid unintended creations of Nullifiers - a Nullifier should never be created inside proveable code (e.g. a smart contract) directly, but rather created inside the users wallet (or other secure enclaves, so the private key never leaves that enclave).

PLUME: An ECDSA Nullifier Scheme for Unique Pseudonymity within Zero Knowledge Proofs https://eprint.iacr.org/2022/1255.pdf chapter 3 page 14

Parameters​

• message: Field[]

• sk: PrivateKey

Returns​

Nullifier

Source​

lib/provable/crypto/nullifier.ts:170

fromJSON()​

static fromJSON(json: Nullifier): Nullifier

Parameters​

• json: Nullifier

Returns​

Nullifier

Overrides​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).fromJSON

Source​

lib/provable/crypto/nullifier.ts:32

sizeInFields()​

static sizeInFields(): number

Return the size of the T type in terms of Field type, as Field is the primitive type.

Returns​

number

A number representing the size of the T type in terms of Field type.

Inherited from​

Struct({ publicKey: Group, public: { nullifier: Group, s: Scalar, }, private: { c: Field, g_r: Group, h_m_pk_r: Group, }, }).sizeInFields

Source​

lib/provable/types/provable-intf.ts:66