Composite proof system

The goal of this crate is to allow creating and combining zero knowledge proofs by executing several protocols as sub-protocols.

The idea is to represent each relation to be proved as a Statement, and any relations between Statements as a MetaStatement. Both of these types contain public (known to both prover and verifier) information and are contained in a ProofSpec whose goal is to unambiguously define what needs to be proven. Some Statements are specific to either the prover or the verifier as those protocols require prover and verifier to use different public parameters. An example is Groth16 based SNARK protocols where the prover needs to have a proving key and the verifier needs to have a verifying key. Both the prover and verifier can know both the proving and verifying key but they don't need to. Thus for such protocols, there are different Statements for prover and verifier, like SaverProver and SaverVerifier are statements for prover and verifier respectively, executing SAVER protocol.

Several Statements might need same public parameters like proving knowledge of several BBS+ from the same signer, or verifiable encryption of several messages for the same decryptor. Its not very efficient to pass the same parameters to each Statement especially when using this code's WASM bindings as the same values will be serialized and deserialized every time. To avoid this, caller can put all such public parameters as SetupParams in an array and then reference those by their index while creating an Statement. This array of SetupParams is then included in the ProofSpec and used by the prover and verifier during proof creation and verification respectively.

A common requirement is to prove equality of certain Witnesss of certain Statements. This is done by using the EqualWitnesses meta-statement. For each set of Witnesss (from the same or different Statements) that need to proven equal, a EqualWitnesses is created which is a set of witness references WitnessRef. Each WitnessRef contains the Statement index and the Witness index in that Statement and thus uniquely identifies any Witness across Statements. The EqualWitnesses meta-statement is also used to prove predicates over signed messages in zero knowledge, when doing a range-proof over a signed message (using BBS+), the EqualWitnesses will refer Witnesss from Statement::PoKBBSSignatureG1 statement and Statement::BoundCheckLegoGroth16 statement. Following are some illustrations of EqualWitnesses

 ┌────────────────────────────┐    ┌──────────────────────────────┐     ┌────────────────────────────┐
 │ PokBBSSignatureG1          │    │ PokBBSSignatureG1            │     │ PokBBSSignatureG1          │
 │ Statement 1                │    │ Statement 2                  │     │ Statement 3                │
 ├────────────────────────────┤    ├──────────────────────────────┤     ├────────────────────────────┤
 │ A1, A2, A3, A4, A5         │    │ B1, B2, B3, B4               │     │ C1, C2, C3, C4, C5, C6     │
 └─────────▲──────────────────┘    └─────▲────────▲───────────────┘     └─▲────────────────▲─────────┘
           │                             │        │                       │                │
           │                             │        │                       │                │
           │                             │        │                       │                │
           │                             │        │                       │                │
           │            ┌-───────────────┴────────┴───┬───────────────────┼──────┬─────────┴──────────────────┐
           └────────────┼(0, 2), (1, 1), (2, 0)       ├───────────────────┘      │ (2, 3), (3, 4)             │
                        ├-────────────────────────────┤                          ├────────────────────────────┤
                        │       EqualWitnesses        │                          │  EqualWitnesses            │
                        │       MetaStatement 1       │                          │  MetaStatement 2           │
                        │ A3, B2 and C1 are equal     │                          │  B4 and C5 are equal       │
                        └─────────────────────────────┘                          └────────────────────────────┘

   For proving certain messages from 3 BBS+ signatures are equal. Here there 2 sets of equalities,
   1. message A3 from 1st signature, B2 from 2nd signature and C1 from 3rd signature
   2. message B4 from 2nd signature and C5 from 3rd signature

   Thus 3 statements, one for each signature, and 2 meta statements, one for each equality

 ┌────────────────────────────┐    ┌──────────────────────────────┐     ┌────────────────────────────┐
 │ PokBBSSignatureG1          │    │ BoundCheckLegoGroth16        │     │ SAVER                      │
 │ Statement 1                │    │ Statement 2                  │     │ Statement 3                │
 ├────────────────────────────┤    ├──────────────────────────────┤     ├────────────────────────────┤
 │ A1, A2, A3, A4, A5         │    │     B1                       │     │             C1             │
 └─────────▲───────▲──────────┘    └─────▲────────-───────────────┘     └───────────────▲────-───────┘
           │       |─────────────────|   │                                              │
           │                         |   │                                              │
           │                         |──-│-────────────────────|                        │
           │                             │                     |                        |───|
           │            ┌-───────────────┴────────-───┬────────|───────────────────────────-|─────────────────┐
           └────────────┼(0, 2),  (1, 0)              |        |─────────────────│── (0, 4), (2, 1)           │
                        ├-────────────────────────────┤                          ├────────────────────────────┤
                        │       EqualWitnesses        │                          │  EqualWitnesses            │
                        │       MetaStatement 1       │                          │  MetaStatement 2           │
                        │ A3 and  B1 are equal        │                          │  A5 and C1 are equal       │
                        └─────────────────────────────┘                          └────────────────────────────┘

   For proving certain messages from a BBS+ signature satisfy 2 predicates,
    1) message A3 satisfies bounds specified in statement 2
    2) message A5 has been verifiably encrypted as per statement 3.

  Thus 3 statements, one for a signature, and one each for a predicate. 2 meta statements, one each
  for proving equality of the message of the signature and the witness of the predicate

After creating the ProofSpec, the prover uses a Witness per Statement and creates a corresponding StatementProof. All StatementProofs are grouped together in a Proof. The verifier also creates its ProofSpec and uses it to verify the given proof. Currently it is assumed that there is one StatementProof per Statement and one Witness per Statement and StatementProofs appear in the same order in Proof as Statements do in ProofSpec.

Statement, Witness and StatementProof are enums whose variants will be entities from different protocols. Each of these protocols are variants of the enum SubProtocol. SubProtocols can internally call other SubProtocols, eg SaverProtocol invokes several SchnorrProtocols

Currently supports

• proof of knowledge of a BBS or BBS+ signature and signed messages
• proof of knowledge of multiple BBS or BBS+ signature and equality of certain messages
• proof of knowledge of accumulator membership and non-membership
• proof of knowledge of Pedersen commitment opening.
• proof of knowledge of BBS or BBS+ signature(s) and that certain message(s) satisfy given bounds (range proof)
• verifiable encryption of messages in a BBS or BBS+ signature
• proof of knowledge of BBS or BBS+ signature(s) and that certain message(s) satisfy given R1CS. The R1CS is generated from Circom and the proof system used is LegoGroth16. LegoGroth16 is similar to Groth16 but in addition to the zero knowledge proof, it provides a Pedersen commitment to the witness (signed messages in our case). This commitment allows us to prove that the witness in the proof protocol are the same as the signed messages using the Schnorr proof of knowledge protocol.

See following tests for examples:

• test pok_of_3_bbs_plus_sig_and_message_equality proves knowledge of 3 BBS+ signatures and also that certain messages are equal among them without revealing them.
• test pok_of_bbs_plus_sig_and_accumulator proves knowledge of a BBS+ signature and also that certain messages are present and absent in the 2 accumulators respectively.
• test pok_of_knowledge_in_pedersen_commitment_and_bbs_plus_sig proves knowledge of a BBS+ signature and opening of a Pedersen commitment.
• test requesting_partially_blind_bbs_plus_sig shows how to request a blind BBS+ signature by proving opening of a Pedersen commitment.
• test verifier_local_linkability shows how a verifier can link separate proofs from a prover (with prover's permission) and assign a unique identifier to the prover without learning any message from the BBS+ signature. Also this identifier cannot be linked across different verifiers (intentional by the prover).
• test pok_of_bbs_plus_sig_and_bounded_message shows proving knowledge of a BBS+ signature and that a specific message satisfies some upper and lower bounds i.e. min <= signed message <= max. This is a range proof.
• test pok_of_bbs_plus_sig_and_verifiable_encryption shows how to verifiably encrypt a message signed with BBS+ such that the verifier cannot decrypt it but still ensure that it is encrypted correctly for the specified decryptor.
• test pok_of_bbs_plus_sig_with_reusing_setup_params shows proving knowledge of several BBS+ signatures using SetupParamss. Here the same signers are used in multiple signatures thus their public params can be put as a variant of enum SetupParams. Similarly test pok_of_knowledge_in_pedersen_commitment_and_equality_with_commitment_key_reuse shows use of SetupParams when the same commitment key is reused in several commitments and test pok_of_bbs_plus_sig_and_verifiable_encryption_of_many_messages shows use of SetupParams when several messages are used in verifiable encryption for the same decryptor.
• For R1CS/Circom, see various tests like using less than, not-equals comparison operators on messages signed with BBS+, proving that the preimage of an MiMC hash is the message signed with BBS+, sum of certain signed messages (from same or different signatures) is bounded by a given value, etc here. The Circom compiler output and circuits are here. The circuits were compiled and tested for BLS12-381 curve.

Note: This design is largely inspired from my work at Hyperledger Ursa.

Note: The design is tentative and will likely change as more protocols are integrated.