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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(value)​

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:147

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:147

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:66

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:157

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:87

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:76

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:37

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:26

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:151

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:155

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:71

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:56