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: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
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