Nullifier

Defined in: lib/provable/crypto/nullifier.ts:20

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

Defined in: lib/provable/types/struct.ts:133

Parameters

value

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

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

Properties

private

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

Defined in: lib/provable/crypto/nullifier.ts:26

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

---

public

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

Defined in: lib/provable/crypto/nullifier.ts:22

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

---

publicKey

publicKey: Group = Group;

Defined in: lib/provable/crypto/nullifier.ts:21

Inherited from

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

---

_isStruct

static _isStruct: true;

Defined in: lib/provable/types/struct.ts:133

Inherited from

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

---

check()

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

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

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.

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

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

---

empty()

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

Defined in: lib/provable/types/struct.ts:143

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

---

fromFields()

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

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

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

---

fromValue

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

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

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

---

toAuxiliary()

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

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

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.

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

publicKey

Group = Group

Returns

any[]

An array of any type describing how this T element is made up of "auxiliary" (non-provable) data.

Inherited from

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

---

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;
};

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

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

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

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

---

toFields()

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

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

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.

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

publicKey

Group = Group

Returns

Field[]

A Field array describing how this T element is made up of Field elements.

Inherited from

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

---

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][];
};

Defined in: lib/provable/types/struct.ts:137

Parameters

x

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

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

---

toJSON()

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

Defined in: lib/provable/types/struct.ts:141

Parameters

x

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

publicKey

Group = Group

Returns

{
  private: {
     c: string;
     g_r: {
        x: string;
        y: string;
       };
     h_m_pk_r: {
        x: string;
        y: string;
       };
    };
  public: {
     nullifier: {
        x: string;
        y: string;
       };
     s: string;
    };
  publicKey: {
     x: string;
     y: string;
    };
}

private

private: {
  c: string;
  g_r: {
     x: string;
     y: string;
    };
  h_m_pk_r: {
     x: string;
     y: string;
    };
};

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: {
     x: string;
     y: string;
    };
  s: string;
};

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

---

toValue()

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

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

Convert provable type to a normal JS type.

Parameters

x

private

{ c: Field; g_r: Group; h_m_pk_r: Group; } = ...

private.c

Field = Field

private.g_r

Group = Group

private.h_m_pk_r

Group = Group

public

{ nullifier: Group; s: Scalar; } = ...

public.nullifier

Group = Group

public.s

Scalar = Scalar

publicKey

Group = Group

Returns

{
  private: {
     c: bigint;
     g_r: {
        x: bigint;
        y: bigint;
       };
     h_m_pk_r: {
        x: bigint;
        y: bigint;
       };
    };
  public: {
     nullifier: {
        x: bigint;
        y: bigint;
       };
     s: bigint;
    };
  publicKey: {
     x: bigint;
     y: bigint;
    };
}

private

private: {
  c: bigint;
  g_r: {
     x: bigint;
     y: bigint;
    };
  h_m_pk_r: {
     x: bigint;
     y: bigint;
    };
};

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: {
     x: bigint;
     y: bigint;
    };
  s: bigint;
};

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

Methods

assertUnused()

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

Defined in: lib/provable/crypto/nullifier.ts:128

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();

---

getPublicKey()

getPublicKey(): PublicKey

Defined in: lib/provable/crypto/nullifier.ts:157

Returns the PublicKey that is associated with this Nullifier.

Returns

PublicKey

Example

let pk = nullifier.getPublicKey();

---

isUnused()

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

Defined in: lib/provable/crypto/nullifier.ts:108

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();

---

key()

key(): Field

Defined in: lib/provable/crypto/nullifier.ts:95

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();

---

setUsed()

setUsed(witness: MerkleMapWitness): Field

Defined in: lib/provable/crypto/nullifier.ts:143

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);

---

verify()

verify(message: Field[]): void

Defined in: lib/provable/crypto/nullifier.ts:47

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);

---

createTestNullifier()

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

Defined in: lib/provable/crypto/nullifier.ts:170

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

---

fromJSON()

static fromJSON(json: Nullifier): Nullifier

Defined in: lib/provable/crypto/nullifier.ts:32

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

---

sizeInFields()

static sizeInFields(): number

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

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