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Prad Nukala
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//
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// Copyright Coinbase, Inc. All Rights Reserved.
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//
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// SPDX-License-Identifier: Apache-2.0
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//
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// Package dkg implements the Distributed Key Generation (DKG) protocol of [DKLs18](https://eprint.iacr.org/2018/499.pdf).
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// The DKG protocol is defined in "Protocol 2" page 7, of the paper. The Zero Knowledge Proof ideal functionalities are
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// realized using schnorr proofs. Moreover, the seed OT is realized using the Verified Simplest OT protocol.
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package dkg
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import (
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"crypto/rand"
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"github.com/gtank/merlin"
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"github.com/pkg/errors"
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"github.com/sonr-io/sonr/crypto/core/curves"
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"github.com/sonr-io/sonr/crypto/ot/base/simplest"
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"github.com/sonr-io/sonr/crypto/ot/extension/kos"
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"github.com/sonr-io/sonr/crypto/zkp/schnorr"
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)
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// AliceOutput is the result of running DKG for Alice. It contains both the public and secret values that are needed
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// for signing.
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type AliceOutput struct {
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// PublicKey is the joint public key of Alice and Bob.
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// This value is public.
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PublicKey curves.Point
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// SecretKeyShare is Alice's secret key for the joint public key.
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// This output must be kept secret. If it is lost, the users will lose access and cannot create signatures.
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SecretKeyShare curves.Scalar
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// SeedOtResult are the outputs that the receiver will obtain as a result of running the "random" OT protocol.
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// This output must be kept secret. Although, if it is lost the users can run another OT protocol and obtain
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// new values to replace it.
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SeedOtResult *simplest.ReceiverOutput
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}
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// BobOutput is the result of running DKG for Bob. It contains both the public and secret values that are needed
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// for signing.
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type BobOutput struct {
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// PublicKey is the joint public key of Alice and Bob.
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// This value is public.
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PublicKey curves.Point
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// SecretKeyShare is Bob's secret key for the joint public key.
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// This output must be kept secret. If it is lost, the users will lose access and cannot create signatures.
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SecretKeyShare curves.Scalar
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// SeedOtResult are the outputs that the sender will obtain as a result of running the "random" OT protocol.
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// This output must be kept secret. Although, if it is lost the users can run another OT protocol and obtain
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// new values to replace it.
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SeedOtResult *simplest.SenderOutput
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}
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// Alice struct encoding Alice's state during one execution of the overall signing algorithm.
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// At the end of the joint computation, Alice will NOT obtain the signature.
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type Alice struct {
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// prover is a schnorr prover for Alice's portion of public key.
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prover *schnorr.Prover
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// proof is alice's proof to her portion of the public key. It is stored as an intermediate value, during commitment phase.
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proof *schnorr.Proof
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// receiver is the base OT receiver.
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receiver *simplest.Receiver
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// secretKeyShare is Alice's secret key for the joint public key.
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secretKeyShare curves.Scalar
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// publicKey is the joint public key of Alice and Bob.
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publicKey curves.Point
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curve *curves.Curve
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transcript *merlin.Transcript
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}
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// Bob struct encoding Bob's state during one execution of the overall signing algorithm.
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// At the end of the joint computation, Bob will obtain the signature.
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type Bob struct {
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// prover is a schnorr prover for Bob's portion of public key.
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prover *schnorr.Prover // this is a "schnorr statement" for pkB.
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// sender is the base OT sender.
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sender *simplest.Sender
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// secretKeyShare is Bob's secret key for the joint public key.
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secretKeyShare curves.Scalar
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// publicKey is the joint public key of Alice and Bob.
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publicKey curves.Point
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// schnorr proof commitment to Alice's schnorr proof.
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aliceCommitment schnorr.Commitment
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// 32-byte transcript salt which will be used for Alice's schnorr proof
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aliceSalt [simplest.DigestSize]byte
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curve *curves.Curve
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transcript *merlin.Transcript
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}
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// Round2Output contains the output of the 2nd round of DKG.
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type Round2Output struct {
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// Seed is the random value used to derive the joint unique session id.
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Seed [simplest.DigestSize]byte
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// Commitment is the commitment to the ZKP to Alice's secret key share.
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Commitment schnorr.Commitment
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}
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// NewAlice creates a party that can participate in 2-of-2 DKG and threshold signature.
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func NewAlice(curve *curves.Curve) *Alice {
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return &Alice{
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curve: curve,
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transcript: merlin.NewTranscript("Coinbase_DKLs_DKG"),
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}
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}
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// NewBob creates a party that can participate in 2-of-2 DKG and threshold signature. This party
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// is the receiver of the signature at the end.
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func NewBob(curve *curves.Curve) *Bob {
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return &Bob{
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curve: curve,
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transcript: merlin.NewTranscript("Coinbase_DKLs_DKG"),
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}
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}
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// Round1GenerateRandomSeed Bob flips random coins, and sends these to Alice
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// in this round, Bob flips 32 random bytes and sends them to Alice.
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// note that this is not _explicitly_ given as part of the protocol in https://eprint.iacr.org/2018/499.pdf, Protocol 1).
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// rather, it is part of our generation of a unique session identifier, for use in subsequent schnorr proofs / seed OT / etc.
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// we do it by having each party sample 32 bytes, then by appending _both_ as salts. secure if either party is honest
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func (bob *Bob) Round1GenerateRandomSeed() ([simplest.DigestSize]byte, error) {
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bobSeed := [simplest.DigestSize]byte{}
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if _, err := rand.Read(bobSeed[:]); err != nil {
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return [simplest.DigestSize]byte{}, errors.Wrap(
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err,
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"generating random bytes in bob DKG round 1 generate",
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)
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}
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bob.transcript.AppendMessage(
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[]byte("session_id_bob"),
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bobSeed[:],
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) // note: bob appends first here
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return bobSeed, nil
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}
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// Round2CommitToProof steps 1) and 2) of protocol 2 on page 7.
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func (alice *Alice) Round2CommitToProof(bobSeed [simplest.DigestSize]byte) (*Round2Output, error) {
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aliceSeed := [simplest.DigestSize]byte{}
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if _, err := rand.Read(aliceSeed[:]); err != nil {
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return nil, errors.Wrap(err, "generating random bytes in bob DKG round 1 generate")
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}
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alice.transcript.AppendMessage([]byte("session_id_bob"), bobSeed[:])
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alice.transcript.AppendMessage([]byte("session_id_alice"), aliceSeed[:])
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var err error
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uniqueSessionId := [simplest.DigestSize]byte{} // note: will use and re-use this below for sub-session IDs.
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copy(
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uniqueSessionId[:],
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alice.transcript.ExtractBytes([]byte("salt for simplest OT"), simplest.DigestSize),
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)
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alice.receiver, err = simplest.NewReceiver(alice.curve, kos.Kappa, uniqueSessionId)
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if err != nil {
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return nil, errors.Wrap(err, "alice constructing new seed OT receiver in Alice DKG round 1")
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}
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alice.secretKeyShare = alice.curve.Scalar.Random(rand.Reader)
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copy(
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uniqueSessionId[:],
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alice.transcript.ExtractBytes([]byte("salt for alice schnorr"), simplest.DigestSize),
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)
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alice.prover = schnorr.NewProver(alice.curve, nil, uniqueSessionId[:])
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var commitment schnorr.Commitment
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alice.proof, commitment, err = alice.prover.ProveCommit(
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alice.secretKeyShare,
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) // will mutate `pkA`
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if err != nil {
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return nil, errors.Wrap(err, "prove + commit in alice DKG Commit round 1")
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}
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return &Round2Output{
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Commitment: commitment,
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Seed: aliceSeed,
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}, nil
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}
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// Round3SchnorrProve receives Bob's Commitment and returns schnorr statment + proof.
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// Steps 1 and 3 of protocol 2 on page 7.
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func (bob *Bob) Round3SchnorrProve(round2Output *Round2Output) (*schnorr.Proof, error) {
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bob.transcript.AppendMessage([]byte("session_id_alice"), round2Output.Seed[:])
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bob.aliceCommitment = round2Output.Commitment // store it, so that we can check when alice decommits
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var err error
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uniqueSessionId := [simplest.DigestSize]byte{} // note: will use and re-use this below for sub-session IDs.
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copy(
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uniqueSessionId[:],
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bob.transcript.ExtractBytes([]byte("salt for simplest OT"), simplest.DigestSize),
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)
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bob.sender, err = simplest.NewSender(bob.curve, kos.Kappa, uniqueSessionId)
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if err != nil {
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return nil, errors.Wrap(err, "bob constructing new OT sender in DKG round 2")
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}
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// extract alice's salt in the right order; we won't use this until she reveals her proof and we verify it below
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copy(
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bob.aliceSalt[:],
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bob.transcript.ExtractBytes([]byte("salt for alice schnorr"), simplest.DigestSize),
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)
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bob.secretKeyShare = bob.curve.Scalar.Random(rand.Reader)
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copy(
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uniqueSessionId[:],
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bob.transcript.ExtractBytes([]byte("salt for bob schnorr"), simplest.DigestSize),
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)
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bob.prover = schnorr.NewProver(bob.curve, nil, uniqueSessionId[:])
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proof, err := bob.prover.Prove(bob.secretKeyShare)
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if err != nil {
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return nil, errors.Wrap(err, "bob schnorr proving in DKG round 2")
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}
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return proof, err
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}
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// Round4VerifyAndReveal step 4 of protocol 2 on page 7.
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func (alice *Alice) Round4VerifyAndReveal(proof *schnorr.Proof) (*schnorr.Proof, error) {
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var err error
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uniqueSessionId := [simplest.DigestSize]byte{}
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copy(
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uniqueSessionId[:],
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alice.transcript.ExtractBytes([]byte("salt for bob schnorr"), simplest.DigestSize),
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)
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if err = schnorr.Verify(proof, alice.curve, nil, uniqueSessionId[:]); err != nil {
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return nil, errors.Wrap(
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err,
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"alice's verification of Bob's schnorr proof failed in DKG round 3",
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)
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}
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alice.publicKey = proof.Statement.Mul(alice.secretKeyShare)
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return alice.proof, nil
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}
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// Round5DecommitmentAndStartOt step 5 of protocol 2 on page 7.
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func (bob *Bob) Round5DecommitmentAndStartOt(proof *schnorr.Proof) (*schnorr.Proof, error) {
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var err error
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if err = schnorr.DecommitVerify(proof, bob.aliceCommitment, bob.curve, nil, bob.aliceSalt[:]); err != nil {
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return nil, errors.Wrap(err, "decommit + verify failed in bob's DKG round 4")
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}
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bob.publicKey = proof.Statement.Mul(bob.secretKeyShare)
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seedOTRound1Output, err := bob.sender.Round1ComputeAndZkpToPublicKey()
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if err != nil {
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return nil, errors.Wrap(err, "bob computing round 1 of seed OT within DKG round 4")
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}
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return seedOTRound1Output, nil
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}
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// Round6DkgRound2Ot is a thin wrapper around the 2nd round of seed OT protocol.
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func (alice *Alice) Round6DkgRound2Ot(
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proof *schnorr.Proof,
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) ([]simplest.ReceiversMaskedChoices, error) {
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return alice.receiver.Round2VerifySchnorrAndPadTransfer(proof)
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}
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// Round7DkgRound3Ot is a thin wrapper around the 3rd round of seed OT protocol.
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func (bob *Bob) Round7DkgRound3Ot(
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compressedReceiversMaskedChoice []simplest.ReceiversMaskedChoices,
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) ([]simplest.OtChallenge, error) {
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return bob.sender.Round3PadTransfer(compressedReceiversMaskedChoice)
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}
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// Round8DkgRound4Ot is a thin wrapper around the 4th round of seed OT protocol.
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func (alice *Alice) Round8DkgRound4Ot(
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challenge []simplest.OtChallenge,
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) ([]simplest.OtChallengeResponse, error) {
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return alice.receiver.Round4RespondToChallenge(challenge)
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}
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// Round9DkgRound5Ot is a thin wrapper around the 5th round of seed OT protocol.
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func (bob *Bob) Round9DkgRound5Ot(
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challengeResponses []simplest.OtChallengeResponse,
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) ([]simplest.ChallengeOpening, error) {
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return bob.sender.Round5Verify(challengeResponses)
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}
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// Round10DkgRound6Ot is a thin wrapper around the 6th round of seed OT protocol.
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func (alice *Alice) Round10DkgRound6Ot(challengeOpenings []simplest.ChallengeOpening) error {
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return alice.receiver.Round6Verify(challengeOpenings)
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}
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// Output returns the output of the DKG operation. Must be called after step 9. Calling it before that step
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// has undefined behaviour.
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func (alice *Alice) Output() *AliceOutput {
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return &AliceOutput{
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PublicKey: alice.publicKey,
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SecretKeyShare: alice.secretKeyShare,
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SeedOtResult: alice.receiver.Output,
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}
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}
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// Output returns the output of the DKG operation. Must be called after step 9. Calling it before that step
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// has undefined behaviour.
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func (bob *Bob) Output() *BobOutput {
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return &BobOutput{
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PublicKey: bob.publicKey,
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SecretKeyShare: bob.secretKeyShare,
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SeedOtResult: bob.sender.Output,
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}
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}
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