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
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:145
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:145
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:155
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:149
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:153
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
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
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
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
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
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