The `range_proof_mpc` module contains the API for performing the aggregated multiparty computation protocol for joint range proof proving.
Only the range proofs are supported, while aggregation of constraint system proofs is under development.
API for the aggregated multiparty computation protocol
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To create the aggregated range proof, \\(m\\) individual parties which each have a secret value exchange messages with one dealer, which does not know their secret values. The protocol to create an aggregated range proof can be run locally or across a network. The protocol should use this API to manage the party states (see [`party`](../range_proof/party/index.html) module), dealer states (see [`dealer`](../range_proof/dealer/index.html) module), and messages (see [`messages`](../range_proof/messages/index.html) module).
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First, \\(m\\) [`Party`](../range_proof/party/struct.Party.html) objects are instantiated with their secret values and the range for the range proof. A [`Dealer`](../range_proof/dealer/struct.Dealer.html) object is instantiated with \\(n\\) and \\(m\\). The dealer assigns a unique index \\(j\\) to each party.
Next, each `Party` commits to their secret value, bits, and blinding factors via \\(V_{(j)}, A_{(j)}, S_{(j)}\\) and sends this data in a [`BitCommitment`](../range_proof/messages/struct.BitCommitment.html) to the dealer. The dealer receives and combines all of the `BitCommitment` messages from all of the parties, generates challenges \\(y, z\\), and sends \\(y, z\\) as [`BitChallenge`](../range_proof/messages/struct.BitChallenge.html) to all of the parties.
Then, each party commits to the resulting polynomials via \\(T_{1, (j)}, T_{2, (j)}\\) and sends this data in a `PolyCommitment` to the dealer. The dealer receives and combines all of the [`PolyCommitment`](../range_proof/messages/struct.PolyCommitment.html) messages from all of the parties, generates challenge \\(x\\), and sends \\(x\\) as [`PolyChallenge`](../range_proof/messages/struct.PolyChallenge.html) to all of the parties.
Finally, each party evaluates their polynomial at \\(x\\) and returns the result as [`ProofShare`](../range_proof/messages/struct.ProofShare.html) to the dealer. The dealer combines all \\(m\\) `ProofShare` messages and returns the aggregated range proof, [`RangeProof`](../struct.RangeProof.html).
Party and Dealer state machines
-------------------------------
We wanted a foolproof model that would prevent users from performing any step other than the correct next step of the protocol. In our implementation, we treated each party and dealer as a state machine, and modeled each party and dealer state as a distinct type. We used move semantics to ensure that a previous state is consumed as it transitions to the next state.
Due to the type system, we have a guarantee that one step of the protocol can't be performed twice, since the first function call for that step would consume the object, and therefore the function would not be able to be called on that object another time. We also have a guarantee that the user can't perform steps out of order or skip steps, since it is impossible to call a function on an object that is not of the correct corresponding type.