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// -*- mode: rust; -*- // // This file is part of dalek-frost. // Copyright (c) 2020 isis lovecruft // See LICENSE for licensing information. // // Authors: // - isis agora lovecruft <isis@patternsinthevoid.net> //! A variation of Pedersen's distributed key generation (DKG) protocol. //! //! This implementation uses the [typestate] design pattern (also called session //! types) behind the scenes to enforce that more programming errors are discoverable //! at compile-time. Additionally, secrets generated for commitment openings, secret keys, //! nonces in zero-knowledge proofs, etc., are zeroed-out in memory when they are dropped //! out of scope. //! //! # Details //! //! ## Round One //! //! * Step #1: Every participant \\(P\_i\\) samples \\(t\\) random values \\((a\_{i0}, \\dots, a\_{i(t-1)})\\) //! uniformly in \\(\mathbb{Z}\_q\\), and uses these values as coefficients to define a //! polynomial \\(f\_i\(x\) = \sum\_{j=0}^{t-1} a\_{ij} x^{j}\\) of degree \\( t-1 \\) over //! \\(\mathbb{Z}\_q\\). //! //! (Yes, I know the steps are out-of-order. These are the step numbers as given in the paper. I do them //! out-of-order because it saves one scalar multiplication.) //! //! * Step #3: Every participant \\(P\_i\\) computes a public commitment //! \\(C\_i = \[\phi\_{i0}, \\dots, \phi\_{i(t-1)}\]\\), where \\(\phi\_{ij} = g^{a\_{ij}}\\), //! \\(0 \le j \le t-1\\). //! //! * Step #2: Every \\(P\_i\\) computes a proof of knowledge to the corresponding secret key //! \\(a\_{i0}\\) by calculating a pseudo-Schnorr signature \\(\sigma\_i = \(s, r\)\\). (In //! the FROST paper: \\(\sigma\_i = \(\mu\_i, c\_i\)\\), but we stick with Schnorr's //! original notation here.) //! //! * Step #4: Every participant \\(P\_i\\) broadcasts \\(\(C\_i\\), \\(\sigma\_i\)\\) to all other participants. //! //! * Step #5: Upon receiving \\((C\_l, \sigma\_l)\\) from participants \\(1 \le l \le n\\), \\(l \ne i\\), //! participant \\(P\_i\\) verifies \\(\sigma\_l = (s\_l, r\_l)\\), by checking: //! \\(s\_l \stackrel{?}{=} \mathcal{H}(l, \Phi, \phi\_{l0}, g^{r\_l} \cdot \phi\_{l0}^{-s\_i})\\). //! If any participants' proofs cannot be verified, return their participant indices. //! //! ## Round Two //! //! * Step #1: Each \\(P\_i\\) securely sends to each other participant \\(P\_l\\) a secret share //! \\((l, f\_i(l))\\) using their secret polynomial \\(f\_i(l)\\) and keeps \\((i, f\_i(i))\\) //! for themselves. //! //! * Step #2: Each \\(P\_i\\) verifies their shares by calculating: //! \\(g^{f\_l(i)} \stackrel{?}{=} \prod\_{k=0}^{n-1} \\)\\(\phi\_{lk}^{i^{k} \mod q}\\), //! aborting if the check fails. //! //! * Step #3: Each \\(P\_i\\) calculates their secret signing key as the product of all the secret //! polynomial evaluations (including their own): //! \\(a\_i = g^{f\_i(i)} \cdot \prod\_{l=0}^{n-1} g^{f\_l(i)}\\), as well as calculating //! the group public key in similar fashion from the commitments from round one: //! \\(A = C\_i \cdot \prod\_{l=0}^{n-1} C_l\\). //! //! # Examples //! //! ```rust //! use frost_dalek::DistributedKeyGeneration; //! use frost_dalek::Parameters; //! use frost_dalek::Participant; //! //! # fn do_test() -> Result<(), ()> { //! // Set up key shares for a threshold signature scheme which needs at least //! // 2-out-of-3 signers. //! let params = Parameters { t: 2, n: 3 }; //! //! // Alice, Bob, and Carol each generate their secret polynomial coefficients //! // and commitments to them, as well as a zero-knowledge proof of a secret key. //! let (alice, alice_coeffs) = Participant::new(¶ms, 1); //! let (bob, bob_coeffs) = Participant::new(¶ms, 2); //! let (carol, carol_coeffs) = Participant::new(¶ms, 3); //! //! // They send these values to each of the other participants (out of scope //! // for this library), or otherwise publish them somewhere. //! // //! // alice.send_to(bob); //! // alice.send_to(carol); //! // bob.send_to(alice); //! // bob.send_to(carol); //! // carol.send_to(alice); //! // carol.send_to(bob); //! // //! // NOTE: They should only send the `alice`, `bob`, and `carol` structs, *not* //! // the `alice_coefficients`, etc. //! // //! // Bob and Carol verify Alice's zero-knowledge proof by doing: //! //! alice.proof_of_secret_key.verify(&alice.index, &alice.public_key().unwrap())?; //! //! // Similarly, Alice and Carol verify Bob's proof: //! bob.proof_of_secret_key.verify(&bob.index, &bob.public_key().unwrap())?; //! //! // And, again, Alice and Bob verify Carol's proof: //! carol.proof_of_secret_key.verify(&carol.index, &carol.public_key().unwrap())?; //! //! // Alice enters round one of the distributed key generation protocol. //! let mut alice_other_participants: Vec<Participant> = vec!(bob.clone(), carol.clone()); //! let alice_state = DistributedKeyGeneration::<_>::new(¶ms, &alice.index, &alice_coeffs, //! &mut alice_other_participants).or(Err(()))?; //! //! // Alice then collects the secret shares which they send to the other participants: //! let alice_their_secret_shares = alice_state.their_secret_shares()?; //! // send_to_bob(alice_their_secret_shares[0]); //! // send_to_carol(alice_their_secret_shares[1]); //! //! // Bob enters round one of the distributed key generation protocol. //! let mut bob_other_participants: Vec<Participant> = vec!(alice.clone(), carol.clone()); //! let bob_state = DistributedKeyGeneration::<_>::new(¶ms, &bob.index, &bob_coeffs, //! &mut bob_other_participants).or(Err(()))?; //! //! // Bob then collects the secret shares which they send to the other participants: //! let bob_their_secret_shares = bob_state.their_secret_shares()?; //! // send_to_alice(bob_their_secret_shares[0]); //! // send_to_carol(bob_their_secret_shares[1]); //! //! // Carol enters round one of the distributed key generation protocol. //! let mut carol_other_participants: Vec<Participant> = vec!(alice.clone(), bob.clone()); //! let carol_state = DistributedKeyGeneration::<_>::new(¶ms, &carol.index, &carol_coeffs, //! &mut carol_other_participants).or(Err(()))?; //! //! // Carol then collects the secret shares which they send to the other participants: //! let carol_their_secret_shares = carol_state.their_secret_shares()?; //! // send_to_alice(carol_their_secret_shares[0]); //! // send_to_bob(carol_their_secret_shares[1]); //! //! // Each participant now has a vector of secret shares given to them by the other participants: //! let alice_my_secret_shares = vec!(bob_their_secret_shares[0].clone(), //! carol_their_secret_shares[0].clone()); //! let bob_my_secret_shares = vec!(alice_their_secret_shares[0].clone(), //! carol_their_secret_shares[1].clone()); //! let carol_my_secret_shares = vec!(alice_their_secret_shares[1].clone(), //! bob_their_secret_shares[1].clone()); //! //! // The participants then use these secret shares from the other participants to advance to //! // round two of the distributed key generation protocol. //! let alice_state = alice_state.to_round_two(alice_my_secret_shares)?; //! let bob_state = bob_state.to_round_two(bob_my_secret_shares)?; //! let carol_state = carol_state.to_round_two(carol_my_secret_shares)?; //! //! // Each participant can now derive their long-lived secret keys and the group's //! // public key. //! let (alice_group_key, alice_secret_key) = alice_state.finish(alice.public_key().unwrap())?; //! let (bob_group_key, bob_secret_key) = bob_state.finish(bob.public_key().unwrap())?; //! let (carol_group_key, carol_secret_key) = carol_state.finish(carol.public_key().unwrap())?; //! //! // They should all derive the same group public key. //! assert!(alice_group_key == bob_group_key); //! assert!(carol_group_key == bob_group_key); //! //! // Alice, Bob, and Carol can now create partial threshold signatures over an agreed upon //! // message with their respective secret keys, which they can then give to a //! // [`SignatureAggregator`] to create a 2-out-of-3 threshold signature. //! # Ok(())} //! # fn main() { assert!(do_test().is_ok()); } //! ``` //! //! [typestate]: http://cliffle.com/blog/rust-typestate/ #[cfg(feature = "std")] use std::boxed::Box; #[cfg(feature = "std")] use std::vec::Vec; #[cfg(feature = "std")] use std::cmp::Ordering; #[cfg(not(feature = "std"))] use core::cmp::Ordering; #[cfg(feature = "alloc")] use alloc::boxed::Box; #[cfg(feature = "alloc")] use alloc::vec::Vec; use curve25519_dalek::constants::RISTRETTO_BASEPOINT_TABLE; use curve25519_dalek::ristretto::CompressedRistretto; use curve25519_dalek::ristretto::RistrettoPoint; use curve25519_dalek::scalar::Scalar; use curve25519_dalek::traits::Identity; use rand::rngs::OsRng; use zeroize::Zeroize; use crate::nizk::NizkOfSecretKey; use crate::parameters::Parameters; /// A struct for holding a shard of the shared secret, in order to ensure that /// the shard is overwritten with zeroes when it falls out of scope. #[derive(Zeroize)] #[zeroize(drop)] pub struct Coefficients(pub(crate) Vec<Scalar>); /// A commitment to the dealer's secret polynomial coefficients for Feldman's /// verifiable secret sharing scheme. #[derive(Clone, Debug)] pub struct VerifiableSecretSharingCommitment(pub(crate) Vec<RistrettoPoint>); /// A participant created by a trusted dealer. /// /// This can be used to create the participants' keys and secret shares without /// having to do secret sharing or zero-knowledge proofs. It's mostly provided /// for testing and debugging purposes, but there is nothing wrong with using it /// if you have trust in the dealer to not forge rogue signatures. #[derive(Clone, Debug)] pub struct DealtParticipant { pub(crate) secret_share: SecretShare, pub(crate) public_key: IndividualPublicKey, pub(crate) group_key: RistrettoPoint, } /// A participant in a threshold signing. #[derive(Clone, Debug)] pub struct Participant { /// The index of this participant, to keep the participants in order. pub index: u32, /// A vector of Pedersen commitments to the coefficients of this /// participant's private polynomial. pub commitments: Vec<RistrettoPoint>, /// The zero-knowledge proof of knowledge of the secret key (a.k.a. the /// first coefficient in the private polynomial). It is constructed as a /// Schnorr signature using \\( a_{i0} \\) as the signing key. pub proof_of_secret_key: NizkOfSecretKey, } impl Participant { /// Have a trusted dealer generate all participants' key material and /// associated commitments for distribution to the participants. /// /// # Warning /// /// Each participant MUST verify with all other n-1 participants that the /// [`VerifiableSecretSharingCommitment`] given to them by the dealer is /// identical. Otherwise, the participants' secret shares could be formed /// with respect to different polynomials and they will fail to create /// threshold signatures which validate. pub fn dealer(parameters: &Parameters) -> (Vec<DealtParticipant>, VerifiableSecretSharingCommitment) { let mut rng: OsRng = OsRng; let secret = Scalar::random(&mut rng); generate_shares(parameters, secret, rng) } /// Construct a new participant for the distributed key generation protocol. /// /// # Inputs /// /// * The protocol instance [`Parameters`], and /// * This participant's `index`. /// /// # Usage /// /// After a new participant is constructed, the `participant.index`, /// `participant.commitments`, and `participant.proof_of_secret_key` should /// be sent to every other participant in the protocol. /// /// # Returns /// /// A distributed key generation protocol [`Participant`] and that /// participant's secret polynomial `Coefficients` which must be kept /// private. pub fn new(parameters: &Parameters, index: u32) -> (Self, Coefficients) { // Step 1: Every participant P_i samples t random values (a_{i0}, ..., a_{i(t-1)}) // uniformly in ZZ_q, and uses these values as coefficients to define a // polynomial f_i(x) = \sum_{j=0}^{t-1} a_{ij} x^{j} of degree t-1 over // ZZ_q. let t: usize = parameters.t as usize; let mut rng: OsRng = OsRng; let mut coefficients: Vec<Scalar> = Vec::with_capacity(t); let mut commitments: Vec<RistrettoPoint> = Vec::with_capacity(t); for _ in 0..t { coefficients.push(Scalar::random(&mut rng)); } let coefficients = Coefficients(coefficients); // Step 3: Every participant P_i computes a public commitment // C_i = [\phi_{i0}, ..., \phi_{i(t-1)}], where \phi_{ij} = g^{a_{ij}}, // 0 ≤ j ≤ t-1. for j in 0..t { commitments.push(&coefficients.0[j] * &RISTRETTO_BASEPOINT_TABLE); } // Yes, I know the steps are out of order. It saves one scalar multiplication. // Step 2: Every P_i computes a proof of knowledge to the corresponding secret // a_{i0} by calculating a Schnorr signature \alpha_i = (s, R). (In // the FROST paper: \alpha_i = (\mu_i, c_i), but we stick with Schnorr's // original notation here.) let proof: NizkOfSecretKey = NizkOfSecretKey::prove(&index, &coefficients.0[0], &commitments[0], rng); // Step 4: Every participant P_i broadcasts C_i, \alpha_i to all other participants. (Participant { index, commitments, proof_of_secret_key: proof }, coefficients) } /// Retrieve \\( \alpha_{i0} * B \\), where \\( B \\) is the Ristretto basepoint. /// /// This is used to pass into the final call to `DistributedKeyGeneration::<RoundTwo>.finish()`. pub fn public_key(&self) -> Option<&RistrettoPoint> { if !self.commitments.is_empty() { return Some(&self.commitments[0]); } None } } fn generate_shares(parameters: &Parameters, secret: Scalar, mut rng: OsRng) -> (Vec<DealtParticipant>, VerifiableSecretSharingCommitment) { let mut participants: Vec<DealtParticipant> = Vec::with_capacity(parameters.n as usize); // STEP 1: Every participant P_i samples t random values (a_{i0}, ..., a_{i(t-1)}) // uniformly in ZZ_q, and uses these values as coefficients to define a // polynomial f_i(x) = \sum_{j=0}^{t-1} a_{ij} x^{j} of degree t-1 over // ZZ_q. let t: usize = parameters.t as usize; let mut coefficients: Vec<Scalar> = Vec::with_capacity(t as usize); let mut commitment = VerifiableSecretSharingCommitment(Vec::with_capacity(t as usize)); coefficients.push(secret); for _ in 0..t-1 { coefficients.push(Scalar::random(&mut rng)); } let coefficients = Coefficients(coefficients); // Step 3: Every participant P_i computes a public commitment // C_i = [\phi_{i0}, ..., \phi_{i(t-1)}], where \phi_{ij} = g^{a_{ij}}, // 0 ≤ j ≤ t-1. for j in 0..t { commitment.0.push(&coefficients.0[j] * &RISTRETTO_BASEPOINT_TABLE); } // Generate secret shares here let group_key = &RISTRETTO_BASEPOINT_TABLE * &coefficients.0[0]; // Only one polynomial because dealer, then secret shards are dependent upon index. for i in 1..parameters.n + 1 { let secret_share = SecretShare::evaluate_polynomial(&i, &coefficients); let public_key = IndividualPublicKey { index: i, share: &RISTRETTO_BASEPOINT_TABLE * &secret_share.polynomial_evaluation, }; participants.push(DealtParticipant { secret_share, public_key, group_key }); } (participants, commitment) } impl PartialOrd for Participant { fn partial_cmp(&self, other: &Participant) -> Option<Ordering> { match self.index.cmp(&other.index) { Ordering::Less => Some(Ordering::Less), Ordering::Equal => None, // Participants cannot have the same index. Ordering::Greater => Some(Ordering::Greater), } } } impl PartialEq for Participant { fn eq(&self, other: &Participant) -> bool { self.index == other.index } } /// Module to implement trait sealing so that `DkgState` cannot be /// implemented for externally declared types. mod private { pub trait Sealed {} impl Sealed for super::RoundOne {} impl Sealed for super::RoundTwo {} } /// State machine structures for holding intermediate values during a /// distributed key generation protocol run, to prevent misuse. #[derive(Clone, Debug)] pub struct DistributedKeyGeneration<S: DkgState> { state: Box<ActualState>, data: S, } /// Shared state which occurs across all rounds of a threshold signing protocol run. #[derive(Clone, Debug)] struct ActualState { /// The parameters for this instantiation of a threshold signature. parameters: Parameters, /// A vector of tuples containing the index of each participant and that /// respective participant's commitments to their private polynomial /// coefficients. their_commitments: Vec<(u32, VerifiableSecretSharingCommitment)>, /// A secret share for this participant. my_secret_share: SecretShare, /// The secret shares this participant has calculated for all the other participants. their_secret_shares: Option<Vec<SecretShare>>, /// The secret shares this participant has received from all the other participants. my_secret_shares: Option<Vec<SecretShare>>, } /// Marker trait to designate valid rounds in the distributed key generation /// protocol's state machine. It is implemented using the [sealed trait design /// pattern][sealed] pattern to prevent external types from implementing further /// valid states. /// /// [sealed]: https://rust-lang.github.io/api-guidelines/future-proofing.html#sealed-traits-protect-against-downstream-implementations-c-sealed pub trait DkgState: private::Sealed {} impl DkgState for RoundOne {} impl DkgState for RoundTwo {} /// Marker trait to designate valid variants of [`RoundOne`] in the distributed /// key generation protocol's state machine. It is implemented using the /// [sealed trait design pattern][sealed] pattern to prevent external types from /// implementing further valid states. /// /// [sealed]: https://rust-lang.github.io/api-guidelines/future-proofing.html#sealed-traits-protect-against-downstream-implementations-c-sealed pub trait Round1: private::Sealed {} /// Marker trait to designate valid variants of [`RoundTwo`] in the distributed /// key generation protocol's state machine. It is implemented using the /// [sealed trait design pattern][sealed] pattern to prevent external types from /// implementing further valid states. /// /// [sealed]: https://rust-lang.github.io/api-guidelines/future-proofing.html#sealed-traits-protect-against-downstream-implementations-c-sealed pub trait Round2: private::Sealed {} impl Round1 for RoundOne {} impl Round2 for RoundTwo {} /// Every participant in the distributed key generation has sent a vector of /// commitments and a zero-knowledge proof of a secret key to every other /// participant in the protocol. During round one, each participant checks the /// zero-knowledge proofs of secret keys of all other participants. #[derive(Clone, Debug)] pub struct RoundOne {} impl DistributedKeyGeneration<RoundOne> { /// Check the zero-knowledge proofs of knowledge of secret keys of all the /// other participants. /// /// # Note /// /// The `participants` will be sorted by their indices. /// /// # Returns /// /// An updated state machine for the distributed key generation protocol if /// all of the zero-knowledge proofs verified successfully, otherwise a /// vector of participants whose zero-knowledge proofs were incorrect. pub fn new( parameters: &Parameters, my_index: &u32, my_coefficients: &Coefficients, other_participants: &mut Vec<Participant>, ) -> Result<Self, Vec<u32>> { let mut their_commitments: Vec<(u32, VerifiableSecretSharingCommitment)> = Vec::with_capacity(parameters.t as usize); let mut misbehaving_participants: Vec<u32> = Vec::new(); // Bail if we didn't get enough participants. if other_participants.len() != parameters.n as usize - 1 { return Err(misbehaving_participants); } // Step 5: Upon receiving C_l, \sigma_l from participants 1 \le l \le n, l \ne i, // participant P_i verifies \sigma_l = (s_l, r_l), by checking: // // s_l ?= H(l, \Phi, \phi_{l0}, g^{r_l} \mdot \phi_{l0}^{-s_i}) for p in other_participants.iter() { let public_key = match p.commitments.get(0) { Some(key) => key, None => { misbehaving_participants.push(p.index); continue; } }; match p.proof_of_secret_key.verify(&p.index, &public_key) { Ok(_) => their_commitments.push((p.index, VerifiableSecretSharingCommitment(p.commitments.clone()))), Err(_) => misbehaving_participants.push(p.index), } } // [DIFFERENT_TO_PAPER] If any participant was misbehaving, return their indices. if !misbehaving_participants.is_empty() { return Err(misbehaving_participants); } // [DIFFERENT_TO_PAPER] We pre-calculate the secret shares from Round 2 // Step 1 here since it doesn't require additional online activity. // // Round 2 // Step 1: Each P_i securely sends to each other participant P_l a secret share // (l, f_i(l)) and keeps (i, f_i(i)) for themselves. let mut their_secret_shares: Vec<SecretShare> = Vec::with_capacity(parameters.n as usize - 1); // XXX need a way to index their_secret_shares for p in other_participants.iter() { their_secret_shares.push(SecretShare::evaluate_polynomial(&p.index, my_coefficients)); } let my_secret_share = SecretShare::evaluate_polynomial(my_index, my_coefficients); let state = ActualState { parameters: *parameters, their_commitments, my_secret_share, their_secret_shares: Some(their_secret_shares), my_secret_shares: None, }; Ok(DistributedKeyGeneration::<RoundOne> { state: Box::new(state), data: RoundOne {}, }) } /// Retrieve a secret share for each other participant, to be given to them /// at the end of `DistributedKeyGeneration::<RoundOne>`. pub fn their_secret_shares(&self) -> Result<&Vec<SecretShare>, ()> { self.state.their_secret_shares.as_ref().ok_or(()) } /// Progress to round two of the DKG protocol once we have sent each share /// from `DistributedKeyGeneration::<RoundOne>.their_secret_shares()` to its /// respective other participant, and collected our shares from the other /// participants in turn. #[allow(clippy::wrong_self_convention)] pub fn to_round_two( mut self, my_secret_shares: Vec<SecretShare>, ) -> Result<DistributedKeyGeneration<RoundTwo>, ()> { // Zero out the other participants secret shares from memory. if self.state.their_secret_shares.is_some() { self.state.their_secret_shares.unwrap().zeroize(); // XXX Does setting this to None always call drop()? self.state.their_secret_shares = None; } if my_secret_shares.len() != self.state.parameters.n as usize - 1 { return Err(()); } // Step 2: Each P_i verifies their shares by calculating: // g^{f_l(i)} ?= \Prod_{k=0}^{t-1} \phi_{lk}^{i^{k} mod q}, // aborting if the check fails. for share in my_secret_shares.iter() { // XXX TODO implement sorting for SecretShare and also for a new Commitment type for (index, commitment) in self.state.their_commitments.iter() { if index == &share.index { share.verify(commitment)?; } } } self.state.my_secret_shares = Some(my_secret_shares); Ok(DistributedKeyGeneration::<RoundTwo> { state: self.state, data: RoundTwo {}, }) } } /// A secret share calculated by evaluating a polynomial with secret /// coefficients for some indeterminant. #[derive(Clone, Debug, Zeroize)] #[zeroize(drop)] pub struct SecretShare { /// The participant index that this secret share was calculated for. pub index: u32, /// The final evaluation of the polynomial for the participant-respective /// indeterminant. pub(crate) polynomial_evaluation: Scalar, } impl SecretShare { /// Evaluate the polynomial, `f(x)` for the secret coefficients at the value of `x`. // // XXX [PAPER] [CFRG] The participant index CANNOT be 0, or the secret share ends up being Scalar::zero(). pub(crate) fn evaluate_polynomial(index: &u32, coefficients: &Coefficients) -> SecretShare { let term: Scalar = (*index).into(); let mut sum: Scalar = Scalar::zero(); // Evaluate using Horner's method. for (index, coefficient) in coefficients.0.iter().rev().enumerate() { // The secret is the constant term in the polynomial sum += coefficient; if index != (coefficients.0.len() - 1) { sum *= term; } } SecretShare { index: *index, polynomial_evaluation: sum } } /// Verify that this secret share was correctly computed w.r.t. some secret /// polynomial coefficients attested to by some `commitment`. pub(crate) fn verify(&self, commitment: &VerifiableSecretSharingCommitment) -> Result<(), ()> { let lhs = &RISTRETTO_BASEPOINT_TABLE * &self.polynomial_evaluation; let term: Scalar = self.index.into(); let mut rhs: RistrettoPoint = RistrettoPoint::identity(); for (index, com) in commitment.0.iter().rev().enumerate() { rhs += com; if index != (commitment.0.len() - 1) { rhs *= term; } } match lhs.compress() == rhs.compress() { true => Ok(()), false => Err(()), } } } /// During round two each participant verifies their secret shares they received /// from each other participant. #[derive(Clone, Debug)] pub struct RoundTwo {} impl DistributedKeyGeneration<RoundTwo> { /// Calculate this threshold signing protocol participant's long-lived /// secret signing keyshare and the group's public verification key. /// /// # Example /// /// ```ignore /// let (group_key, secret_key) = state.finish(participant.public_key()?)?; /// ``` pub fn finish(mut self, my_commitment: &RistrettoPoint) -> Result<(GroupKey, SecretKey), ()> { let secret_key = self.calculate_signing_key()?; let group_key = self.calculate_group_key(my_commitment)?; self.state.my_secret_share.zeroize(); self.state.my_secret_shares.zeroize(); Ok((group_key, secret_key)) } /// Calculate this threshold signing participant's long-lived secret signing /// key by summing all of the polynomial evaluations from the other /// participants. pub(crate) fn calculate_signing_key(&self) -> Result<SecretKey, ()> { let my_secret_shares = self.state.my_secret_shares.as_ref().ok_or(())?; let mut key = my_secret_shares.iter().map(|x| x.polynomial_evaluation).sum(); key += self.state.my_secret_share.polynomial_evaluation; Ok(SecretKey { index: self.state.my_secret_share.index, key }) } /// Calculate the group public key used for verifying threshold signatures. /// /// # Returns /// /// A [`GroupKey`] for the set of participants. pub(crate) fn calculate_group_key(&self, my_commitment: &RistrettoPoint) -> Result<GroupKey, ()> { let mut keys: Vec<RistrettoPoint> = Vec::with_capacity(self.state.parameters.n as usize); for commitment in self.state.their_commitments.iter() { match commitment.1.0.get(0) { Some(key) => keys.push(*key), None => return Err(()), } } keys.push(*my_commitment); Ok(GroupKey(keys.iter().sum())) } } /// A public verification share for a participant. /// /// Any participant can recalculate the public verification share, which is the /// public half of a [`SecretKey`], of any other participant in the protocol. #[derive(Clone, Debug)] pub struct IndividualPublicKey { /// The participant index to which this key belongs. pub index: u32, /// The public verification share. pub share: RistrettoPoint, } impl IndividualPublicKey { /// Any participant can compute the public verification share of any other participant. /// /// This is done by re-computing each [`IndividualPublicKey`] as \\(Y\_i\\) s.t.: /// /// \\[ /// Y\_i = \prod\_{j=1}^{n} \prod\_{k=0}^{t-1} \phi\_{jk}^{i^{k} \mod q} /// \\] /// /// for each [`Participant`] index \\(i\\). /// /// # Inputs /// /// * The [`Parameters`] of this threshold signing instance, and /// * A vector of `commitments` regarding the secret polynomial /// [`Coefficients`] that this [`IndividualPublicKey`] was generated with. /// /// # Returns /// /// A `Result` with either an empty `Ok` or `Err` value, depending on /// whether or not the verification was successful. #[allow(unused)] pub fn verify( &self, parameters: &Parameters, commitments: &[RistrettoPoint], ) -> Result<(), ()> { let rhs = RistrettoPoint::identity(); for j in 1..parameters.n { for k in 0..parameters.t { // XXX ah shit we need the incoming commitments to be sorted or have indices } } unimplemented!() } } /// A secret key, used by one participant in a threshold signature scheme, to sign a message. #[derive(Debug, Zeroize)] #[zeroize(drop)] pub struct SecretKey { /// The participant index to which this key belongs. pub(crate) index: u32, /// The participant's long-lived secret share of the group signing key. pub(crate) key: Scalar, } impl SecretKey { /// Derive the corresponding public key for this secret key. pub fn to_public(&self) -> IndividualPublicKey { let share = &RISTRETTO_BASEPOINT_TABLE * &self.key; IndividualPublicKey { index: self.index, share, } } } impl From<&SecretKey> for IndividualPublicKey { fn from(source: &SecretKey) -> IndividualPublicKey { source.to_public() } } /// A public key, used to verify a signature made by a threshold of a group of participants. #[derive(Clone, Copy, Debug, Eq)] pub struct GroupKey(pub(crate) RistrettoPoint); impl PartialEq for GroupKey { fn eq(&self, other: &Self) -> bool { self.0.compress() == other.0.compress() } } impl GroupKey { /// Serialise this group public key to an array of bytes. pub fn to_bytes(&self) -> [u8; 32] { self.0.compress().to_bytes() } /// Deserialise this group public key from an array of bytes. pub fn from_bytes(bytes: [u8; 32]) -> Result<GroupKey, ()> { let point = CompressedRistretto(bytes).decompress().ok_or(())?; Ok(GroupKey(point)) } } #[cfg(test)] mod test { use super::*; #[cfg(feature = "std")] use crate::precomputation::generate_commitment_share_lists; #[cfg(feature = "std")] use crate::signature::{calculate_lagrange_coefficients, compute_message_hash}; #[cfg(feature = "std")] use crate::signature::SignatureAggregator; #[cfg(feature = "std")] /// Reconstruct the secret from enough (at least the threshold) already-verified shares. fn reconstruct_secret(participants: &Vec<&DealtParticipant>) -> Result<Scalar, &'static str> { let all_participant_indices: Vec<u32> = participants.iter().map(|p| p.public_key.index).collect(); let mut secret = Scalar::zero(); for this_participant in participants { let my_coeff = calculate_lagrange_coefficients(&this_participant.public_key.index, &all_participant_indices)?; secret += my_coeff * this_participant.secret_share.polynomial_evaluation; } Ok(secret) } #[test] fn nizk_of_secret_key() { let params = Parameters { n: 3, t: 2 }; let (p, _) = Participant::new(¶ms, 0); let result = p.proof_of_secret_key.verify(&p.index, &p.commitments[0]); assert!(result.is_ok()); } #[cfg(feature = "std")] #[test] fn verify_secret_sharing_from_dealer() { let params = Parameters { n: 3, t: 2 }; let mut rng: OsRng = OsRng; let secret = Scalar::random(&mut rng); let (participants, _commitment) = generate_shares(¶ms, secret, rng); let mut subset_participants = Vec::new(); for i in 0..params.t{ subset_participants.push(&participants[i as usize]); } let supposed_secret = reconstruct_secret(&subset_participants); assert!(secret == supposed_secret.unwrap()); } #[test] fn dkg_with_dealer() { let params = Parameters { t: 1, n: 2 }; let (participants, commitment) = Participant::dealer(¶ms); let (_, commitment2) = Participant::dealer(¶ms); // Verify each of the participants' secret shares. for p in participants.iter() { let result = p.secret_share.verify(&commitment); assert!(result.is_ok(), "participant {} failed to receive a valid secret share", p.public_key.index); let result = p.secret_share.verify(&commitment2); assert!(!result.is_ok(), "Should not validate with invalid commitment"); } } #[cfg(feature = "std")] #[test] fn dkg_with_dealer_and_signing() { let params = Parameters { t: 1, n: 2 }; let (participants, commitment) = Participant::dealer(¶ms); // Verify each of the participants' secret shares. for p in participants.iter() { let result = p.secret_share.verify(&commitment); assert!(result.is_ok(), "participant {} failed to receive a valid secret share", p.public_key.index); } let context = b"CONTEXT STRING STOLEN FROM DALEK TEST SUITE"; let message = b"This is a test of the tsunami alert system. This is only a test."; let (p1_public_comshares, mut p1_secret_comshares) = generate_commitment_share_lists(&mut OsRng, 1, 1); let (p2_public_comshares, mut p2_secret_comshares) = generate_commitment_share_lists(&mut OsRng, 2, 1); let p1_sk = SecretKey { index: participants[0].secret_share.index, key: participants[0].secret_share.polynomial_evaluation, }; let p2_sk = SecretKey { index: participants[1].secret_share.index, key: participants[1].secret_share.polynomial_evaluation, }; let group_key = GroupKey(participants[0].group_key); let mut aggregator = SignatureAggregator::new(params, group_key, &context[..], &message[..]); aggregator.include_signer(1, p1_public_comshares.commitments[0], (&p1_sk).into()); aggregator.include_signer(2, p2_public_comshares.commitments[0], (&p2_sk).into()); let signers = aggregator.get_signers(); let message_hash = compute_message_hash(&context[..], &message[..]); let p1_partial = p1_sk.sign(&message_hash, &group_key, &mut p1_secret_comshares, 0, signers).unwrap(); let p2_partial = p2_sk.sign(&message_hash, &group_key, &mut p2_secret_comshares, 0, signers).unwrap(); aggregator.include_partial_signature(p1_partial); aggregator.include_partial_signature(p2_partial); let aggregator = aggregator.finalize().unwrap(); let signing_result = aggregator.aggregate(); assert!(signing_result.is_ok()); let threshold_signature = signing_result.unwrap(); let verification_result = threshold_signature.verify(&group_key, &message_hash); println!("{:?}", verification_result); assert!(verification_result.is_ok()); } #[test] fn secret_share_from_one_coefficients() { let mut coeffs: Vec<Scalar> = Vec::new(); for _ in 0..5 { coeffs.push(Scalar::one()); } let coefficients = Coefficients(coeffs); let share = SecretShare::evaluate_polynomial(&1, &coefficients); assert!(share.polynomial_evaluation == Scalar::from(5u8)); let mut commitments = VerifiableSecretSharingCommitment(Vec::new()); for i in 0..5 { commitments.0.push(&RISTRETTO_BASEPOINT_TABLE * &coefficients.0[i]); } assert!(share.verify(&commitments).is_ok()); } #[test] fn secret_share_participant_index_zero() { let mut coeffs: Vec<Scalar> = Vec::new(); for _ in 0..5 { coeffs.push(Scalar::one()); } let coefficients = Coefficients(coeffs); let share = SecretShare::evaluate_polynomial(&0, &coefficients); assert!(share.polynomial_evaluation == Scalar::one()); let mut commitments = VerifiableSecretSharingCommitment(Vec::new()); for i in 0..5 { commitments.0.push(&RISTRETTO_BASEPOINT_TABLE * &coefficients.0[i]); } assert!(share.verify(&commitments).is_ok()); } #[test] fn single_party_keygen() { let params = Parameters { n: 1, t: 1 }; let (p1, p1coeffs) = Participant::new(¶ms, 1); p1.proof_of_secret_key.verify(&p1.index, &p1.commitments[0]).unwrap(); let mut p1_other_participants: Vec<Participant> = Vec::new(); let p1_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p1.index, &p1coeffs, &mut p1_other_participants).unwrap(); let p1_my_secret_shares = Vec::new(); let p1_state = p1_state.to_round_two(p1_my_secret_shares).unwrap(); let result = p1_state.finish(p1.public_key().unwrap()); assert!(result.is_ok()); let (p1_group_key, p1_secret_key) = result.unwrap(); assert!(p1_group_key.0.compress() == (&p1_secret_key.key * &RISTRETTO_BASEPOINT_TABLE).compress()); } #[test] fn keygen_3_out_of_5() { let params = Parameters { n: 5, t: 3 }; let (p1, p1coeffs) = Participant::new(¶ms, 1); let (p2, p2coeffs) = Participant::new(¶ms, 2); let (p3, p3coeffs) = Participant::new(¶ms, 3); let (p4, p4coeffs) = Participant::new(¶ms, 4); let (p5, p5coeffs) = Participant::new(¶ms, 5); p1.proof_of_secret_key.verify(&p1.index, &p1.public_key().unwrap()).unwrap(); p2.proof_of_secret_key.verify(&p2.index, &p2.public_key().unwrap()).unwrap(); p3.proof_of_secret_key.verify(&p3.index, &p3.public_key().unwrap()).unwrap(); p4.proof_of_secret_key.verify(&p4.index, &p4.public_key().unwrap()).unwrap(); p5.proof_of_secret_key.verify(&p5.index, &p5.public_key().unwrap()).unwrap(); let mut p1_other_participants: Vec<Participant> = vec!(p2.clone(), p3.clone(), p4.clone(), p5.clone()); let p1_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p1.index, &p1coeffs, &mut p1_other_participants).unwrap(); let p1_their_secret_shares = p1_state.their_secret_shares().unwrap(); let mut p2_other_participants: Vec<Participant> = vec!(p1.clone(), p3.clone(), p4.clone(), p5.clone()); let p2_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p2.index, &p2coeffs, &mut p2_other_participants).unwrap(); let p2_their_secret_shares = p2_state.their_secret_shares().unwrap(); let mut p3_other_participants: Vec<Participant> = vec!(p1.clone(), p2.clone(), p4.clone(), p5.clone()); let p3_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p3.index, &p3coeffs, &mut p3_other_participants).unwrap(); let p3_their_secret_shares = p3_state.their_secret_shares().unwrap(); let mut p4_other_participants: Vec<Participant> = vec!(p1.clone(), p2.clone(), p3.clone(), p5.clone()); let p4_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p4.index, &p4coeffs, &mut p4_other_participants).unwrap(); let p4_their_secret_shares = p4_state.their_secret_shares().unwrap(); let mut p5_other_participants: Vec<Participant> = vec!(p1.clone(), p2.clone(), p3.clone(), p4.clone()); let p5_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p5.index, &p5coeffs, &mut p5_other_participants).unwrap(); let p5_their_secret_shares = p5_state.their_secret_shares().unwrap(); let p1_my_secret_shares = vec!(p2_their_secret_shares[0].clone(), // XXX FIXME indexing p3_their_secret_shares[0].clone(), p4_their_secret_shares[0].clone(), p5_their_secret_shares[0].clone()); let p2_my_secret_shares = vec!(p1_their_secret_shares[0].clone(), p3_their_secret_shares[1].clone(), p4_their_secret_shares[1].clone(), p5_their_secret_shares[1].clone()); let p3_my_secret_shares = vec!(p1_their_secret_shares[1].clone(), p2_their_secret_shares[1].clone(), p4_their_secret_shares[2].clone(), p5_their_secret_shares[2].clone()); let p4_my_secret_shares = vec!(p1_their_secret_shares[2].clone(), p2_their_secret_shares[2].clone(), p3_their_secret_shares[2].clone(), p5_their_secret_shares[3].clone()); let p5_my_secret_shares = vec!(p1_their_secret_shares[3].clone(), p2_their_secret_shares[3].clone(), p3_their_secret_shares[3].clone(), p4_their_secret_shares[3].clone()); let p1_state = p1_state.to_round_two(p1_my_secret_shares).unwrap(); let p2_state = p2_state.to_round_two(p2_my_secret_shares).unwrap(); let p3_state = p3_state.to_round_two(p3_my_secret_shares).unwrap(); let p4_state = p4_state.to_round_two(p4_my_secret_shares).unwrap(); let p5_state = p5_state.to_round_two(p5_my_secret_shares).unwrap(); let (p1_group_key, _p1_secret_key) = p1_state.finish(p1.public_key().unwrap()).unwrap(); let (p2_group_key, _p2_secret_key) = p2_state.finish(p2.public_key().unwrap()).unwrap(); let (p3_group_key, _p3_secret_key) = p3_state.finish(p3.public_key().unwrap()).unwrap(); let (p4_group_key, _p4_secret_key) = p4_state.finish(p4.public_key().unwrap()).unwrap(); let (p5_group_key, _p5_secret_key) = p5_state.finish(p5.public_key().unwrap()).unwrap(); assert!(p1_group_key.0.compress() == p2_group_key.0.compress()); assert!(p2_group_key.0.compress() == p3_group_key.0.compress()); assert!(p3_group_key.0.compress() == p4_group_key.0.compress()); assert!(p4_group_key.0.compress() == p5_group_key.0.compress()); assert!(p5_group_key.0.compress() == (p1.public_key().unwrap() + p2.public_key().unwrap() + p3.public_key().unwrap() + p4.public_key().unwrap() + p5.public_key().unwrap()).compress()); } #[test] fn keygen_2_out_of_3() { fn do_test() -> Result<(), ()> { let params = Parameters { n: 3, t: 2 }; let (p1, p1coeffs) = Participant::new(¶ms, 1); let (p2, p2coeffs) = Participant::new(¶ms, 2); let (p3, p3coeffs) = Participant::new(¶ms, 3); p1.proof_of_secret_key.verify(&p1.index, &p1.public_key().unwrap())?; p2.proof_of_secret_key.verify(&p2.index, &p2.public_key().unwrap())?; p3.proof_of_secret_key.verify(&p3.index, &p3.public_key().unwrap())?; let mut p1_other_participants: Vec<Participant> = vec!(p2.clone(), p3.clone()); let p1_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p1.index, &p1coeffs, &mut p1_other_participants).or(Err(()))?; let p1_their_secret_shares = p1_state.their_secret_shares()?; let mut p2_other_participants: Vec<Participant> = vec!(p1.clone(), p3.clone()); let p2_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p2.index, &p2coeffs, &mut p2_other_participants).or(Err(()))?; let p2_their_secret_shares = p2_state.their_secret_shares()?; let mut p3_other_participants: Vec<Participant> = vec!(p1.clone(), p2.clone()); let p3_state = DistributedKeyGeneration::<RoundOne>::new(¶ms, &p3.index, &p3coeffs, &mut p3_other_participants).or(Err(()))?; let p3_their_secret_shares = p3_state.their_secret_shares()?; let p1_my_secret_shares = vec!(p2_their_secret_shares[0].clone(), // XXX FIXME indexing p3_their_secret_shares[0].clone()); let p2_my_secret_shares = vec!(p1_their_secret_shares[0].clone(), p3_their_secret_shares[1].clone()); let p3_my_secret_shares = vec!(p1_their_secret_shares[1].clone(), p2_their_secret_shares[1].clone()); let p1_state = p1_state.to_round_two(p1_my_secret_shares)?; let p2_state = p2_state.to_round_two(p2_my_secret_shares)?; let p3_state = p3_state.to_round_two(p3_my_secret_shares)?; let (p1_group_key, _p1_secret_key) = p1_state.finish(p1.public_key().unwrap())?; let (p2_group_key, _p2_secret_key) = p2_state.finish(p2.public_key().unwrap())?; let (p3_group_key, _p3_secret_key) = p3_state.finish(p3.public_key().unwrap())?; assert!(p1_group_key.0.compress() == p2_group_key.0.compress()); assert!(p2_group_key.0.compress() == p3_group_key.0.compress()); Ok(()) } assert!(do_test().is_ok()); } }