Module simplex 

Simple and fast BFT agreement inspired by Simplex Consensus.

Inspired by Simplex Consensus, simplex provides simple and fast BFT agreement with network-speed view (i.e. block time) latency and optimal finalization latency in a partially synchronous setting.

Features

• Wicked Fast Block Times (2 Network Hops)
• Optimal Finalization Latency (3 Network Hops)
• Externalized Uptime and Fault Proofs
• Require Certification Before Finalization
• Decoupled Block Broadcast and Sync
• Lazy Message Verification
• Application-Defined Block Format
• Pluggable Hashing and Cryptography
• Embedded VRF (via scheme::bls12381_threshold::vrf)

Design

Protocol Description

Genesis

Genesis (view 0) is implicitly finalized. There is no finalization certificate for genesis; Config::floor supplies the initial finalized state. Voting begins at view 1, with the first proposal referencing genesis as its parent.

Specification for View v

Upon entering view v:

• Determine leader l for view v
• Set timer for leader proposal t_l = 2Δ and advance t_a = 3Δ
  • If leader l has not been active for the configured skip timeout while a quorum of participants has been, set both t_l and t_a to 0.
• If leader l, broadcast notarize(c,v)
  • If can’t propose container in view v because missing notarization/nullification for a previous view v_m, request v_m

Upon receiving first notarize(c,v) from l:

• Cancel t_l
• If the container’s parent c_parent is finalized (or both notarized and certified) at v_parent and we have required nullifications covering the skipped views between v_parent and v (a nullification covers the rest of its term; when v is not a term start, v_parent must be exactly v-1), verify c and broadcast notarize(c,v)
  • If verification of c fails, immediately broadcast nullify(v)

Upon receiving 2f+1 notarize(c,v):

• Mark c as notarized
• Broadcast notarization(c,v) (even if we have not verified c)
• Attempt to certify c (see Certification), leaving t_a armed so a stalled certification still times out the view
  • On success: enter v+1 and broadcast finalize(c,v) (skipped if we have broadcast nullify(v) or observed l equivocate in v)
  • On failure: treat as immediate timeout expiry and broadcast nullify(v)

Upon receiving 2f+1 nullify(v):

• Broadcast nullification(v)
• Enter next_term_start(v) (equivalent to v+1 when term_length = 1)

Upon receiving 2f+1 finalize(c,v):

• Mark c as finalized (and recursively finalize its parents)
• Broadcast finalization(c,v) (even if we have not verified c)

Upon t_l or t_a firing:

• Broadcast nullify(v)
• Every retry interval t_r after nullify(v) broadcast that we are still in view v:
  • Rebroadcast nullify(v) alongside the best certificate for entering view v we hold at that time: the finalization of v-1 if we have one, otherwise the highest nullification we hold for the previous term (checked only when v starts a term, as every view does when term_length is 1), otherwise the notarization of v-1. If we hold none (as in view 1), rebroadcast nullify(v) alone.

When 2f+1 votes of a given type (notarize(c,v), nullify(v), or finalize(c,v)) have been collected from unique participants, a certificate (notarization(c,v), nullification(v), or finalization(c,v)) can be assembled. These certificates serve as a standalone proof of consensus progress that downstream systems can ingest without executing the protocol.

Joining Consensus

As soon as 2f+1 nullifies or finalizes are observed for some view v, the Voter will enter the corresponding successor view (next_term_start(v) for nullification, v+1 for finalization). Notarizations advance the view if-and-only-if the application certifies them. This means that a new participant joining consensus will immediately jump ahead on the previous view’s nullification or finalization and begin participating in consensus at the current view.

Certification

After a payload is notarized, the application can optionally delay or prevent finalization via the CertifiableAutomaton::certify method. By default, certify returns true for all payloads, meaning finalization proceeds immediately after notarization.

Customizing certify is useful for systems that employ erasure coding, where participants may want to wait until they have received enough shards to reconstruct and validate the full block before voting to finalize.

If certify returns true, the participant broadcasts a finalize vote for the payload (unless it has broadcast nullify or observed the leader equivocate) and enters the next view. If certify returns false, the participant broadcasts nullify for the view instead (treating it as an immediate timeout), and will refuse to build upon the proposal or notarize proposals that build upon it. Thus, a payload can only be finalized if a quorum of participants certify it.

Certification of some notarization should only be abandoned once a finalization at the same or higher view is observed. Until then (say a nullification certificate for a view arrives before certification completes), the application should continue attempting to complete certification. This increases the likelihood that we can vote on the next honest proposer’s block (which may build on our in-flight certification or the nullification). If we did not do this, it is possible that different parts of the network (neither with quorum) would refuse to vote on each other’s blocks (halting consensus).

The decision returned by certify must be deterministic and consistent across all honest participants to ensure liveness.

Deviations from Simplex Consensus

• Fetch missing notarizations/nullifications as needed rather than assuming each proposal contains a set of all notarizations/nullifications for all historical blocks.
• Introduce distinct messages for notarize and nullify rather than referring to both as a vote for either a “block” or a “dummy block”, respectively.
• Introduce a “leader timeout” to trigger early view transitions for unresponsive leaders.
• Skip “leader timeout” and “certification timeout” if a designated leader has not participated for the configured skip timeout while a quorum of participants has (again to trigger early view transition for an unresponsive leader).
• Introduce message rebroadcast to continue making progress if messages from a given view are dropped (only way to ensure messages are reliably delivered is with a heavyweight reliable broadcast protocol).
• Treat local proposal failure as immediate timeout expiry and broadcast nullify(v).
• Treat local verification failure as immediate timeout expiry and broadcast nullify(v).
• Consider the current leader’s nullify(v) as immediate timeout expiry and broadcast nullify(v).
• Upon seeing notarization(c,v), instead of moving to the view v+1 immediately, request certification from the application (see Certification). Only move to view v+1 and broadcast finalize(c,v) if certification succeeds, otherwise broadcast nullify(v) and refuse to build upon c.
• With stable leaders (term_length > 1), a prior same-term nullify vote blocks later finalize votes until a covering finalization is observed; notarize votes are never withheld (see Same-Term Vote Safety).
• With stable leaders, optionally verify proposals and broadcast notarize votes up to optimistic_views views ahead of certified ancestry within a term (configured alongside the term length, see elector::Terms::stable); certification and finalize votes always wait for explicit parent certification (see Optimistic Validation).
• If an entered view remains unfinalized for the stall timeout (configured alongside the term length, see elector::Terms) and we are still in the same term, we locally time out the current view and vote nullify. In practice, this tracks the oldest unfinalized view we have entered in the current term.
• Votes are tracked down to view_retention views below the highest finalized view: late votes in that window are still reported, even though they are no longer verified or used for certificate construction. By default, certification releases full vote evidence, making later conflict reporting and peer blocking best effort. Config::track_historical_votes instead retains each recorded vote until its round is pruned. Votes below the window are ignored on arrival, so downstream systems consuming per-vote activity (rewards, slashing) never observe them.

Protocol Properties

Forced Inclusion (Tail-Forking Resistance)

A notarized payload in view v must appear in the canonical chain if no nullification certificate covers v. With stable leaders, a nullification covers the view it was created for and the rest of that term. This follows directly from the protocol rules:

1. To propose in view v+k, the leader must reference a certified parent in some view v_p and possess required nullifications covering the skipped views from v_p to v+k.
2. A nullification certificate requires 2f+1 nullify votes for the covered view or an earlier view in the same term.
3. An honest participant only broadcasts nullify on a nullify trigger: an expired timeout (t_l, t_a, or the stall timeout) or an event treated as immediate timeout expiry (proposal build failure, verification failure, certification failure, the leader’s own nullify, or leader inactivity, as listed in Deviations).

Therefore, a nullification covering v can only form if at least f+1 honest participants broadcast nullify at a single view u in [term_start(v), v]. If every view in that term prefix completes without any nullify trigger (just view v itself when term_length is 1), no honest participant has broadcast a covering nullify: at most f covering votes exist at any single view, which is insufficient to form a nullification certificate. Without that certificate, no future leader can skip view v, and the notarized payload must be included as an ancestor in all subsequent proposals. Note that a clean view v alone is not enough when term_length > 1: an honest nullify broadcast at an earlier view of the term (say, after a transient timeout at a view that later notarized) covers v even though no trigger fired at v itself.

Same-Term Vote Safety

With stable leaders, a nullification covers the view it was created for and the rest of that term: a later proposal may use it to skip all of those views at once. This is only safe if no covered view is finalized, so the protocol must maintain the invariant that a finalization at view v rules out a nullification at any view u <= v in the same term (otherwise a proposal could fork around a finalized view).

The finalize gate maintains this invariant: a participant that voted nullify(u) withholds finalize votes for later views in that term until it observes a same-term finalization at or above its highest nullify vote. To see why the invariant holds, suppose both a nullification at u and a finalization at v >= u form in the same term. Their quorums intersect in at least one honest participant that voted both nullify(u) and finalize(c,v). If u = v, this is impossible outright: no honest participant votes both nullify and finalize in a single view. If u < v, the gate means that participant first observed a same-term finalization at some v* with u <= v* < v: at or above u because the gate requires covering its highest nullify vote, and below v because participants only vote finalize for views above their highest observed finalization. Applying this same argument to the finalization at v* shows, by induction, that no nullification can form at or below v*, contradicting the nullification at u <= v*.

The gate also recovers from a nullify vote that never became a nullification (e.g., a transient timeout on an otherwise healthy network): by the invariant, an observed same-term finalization at or above the vote proves the nullification can never form, so the vote is inert and the gate reopens (“heals”). This prevents one transient timeout from degrading the rest of the term. In a healthy network this takes one view: peers broadcast finalize(v) when they certify v, so the finalization for v typically arrives shortly after entering v+1.

Healing does not proactively revisit earlier views: a finalize vote for a view certified while the gate was blocked is only emitted if a later message (such as a redelivered notarization) touches that view again. If more than f participants were blocked, that view may never gather its own finalization certificate, and neither may any later view in the term (healing itself requires a same-term finalization, which cannot assemble while more than f participants withhold finalize). Such a view is either finalized transitively by the finalization of a descendant in a later term or skipped entirely by a covering nullification: the timeouts that blocked the gate also mean forced inclusion does not apply to it.

Optimistic Validation

With stable leaders, a leader can propose for view v+1 as soon as its proposal for view v is notarized, but participants that wait for v’s certification before verifying the new proposal add a round of certification latency to every view. When a nonzero optimistic_views lookahead is configured (see elector::Terms::stable), a participant instead verifies a proposal and broadcasts its notarize vote before the parent is certified, if all of the following hold:

• The proposal’s view is in the same term as its parent (optimism never crosses a term boundary; a term start always requires explicitly certified ancestry).
• At most optimistic_views views lie between the proposal’s view and the last directly notarized view (a view with an observed notarization or finalization certificate; a view is indirectly notarized when only a descendant’s certificate implies it), bounding how far local votes run ahead of certified ancestry. This is the issuance window.
• There is local evidence for the immediate parent: our own broadcast notarize vote, an observed notarization certificate (unless our own certification rejected it), or (once the proposal’s view is current) the parent’s explicit certification.

Certification requests and finalize votes never run ahead: both require the parent’s explicit certification first. If an optimistic ancestor fails to notarize or certify, the usual timeout and nullification path skips it, and any optimistic votes above it are inert.

Peers admit and buffer votes up to optimistic_views views beyond their own current view (the admission window), so optimistic votes are not dropped by participants that have not yet observed the sender’s ancestry. The setting is local: mismatched values across participants only degrade the optimization (votes beyond a peer’s window are dropped until it catches up), never safety.

Optimistic Finality

The forced inclusion property provides a weaker but faster form of finality: a payload notarized at view v can be treated as speculatively final, because no future sequence of proposals can exclude it from the canonical chain if every view in [term_start(v), v] completes without any nullify trigger (just view v itself when term_length is 1).

This “speculative finality” is available after just 2 network hops (proposal + notarization), compared to the 3 hops required for full finalization (proposal + notarization + finalization). Observing the notarization does not by itself rule out exclusion: honest participants may still be inside a view of the term prefix, where a trigger can still fire (say, a certification that outlives t_a). Exclusion requires f+1 or more honest participants to broadcast nullify at a single view of that prefix. Because certification is deterministic, it either fails for all honest participants or none, so a certification failure always produces a nullification. In the common case (no faults, no timeouts), exclusion cannot happen.

A Byzantine leader, however, can exclude even its own valid, certifiable, and timely proposal: honest participants treat the leader’s nullify(v) as an immediate timeout, so a leader can single-handedly revoke its own notarized proposal. This is no new power. A leader can achieve the same exclusion by delivering its proposal so late that honest participants notarize it but time out before certifying. Speculative finality therefore assumes the term’s leader wants its proposal to survive.

Unchained Finalization

Finalization does not require consecutive honest views. When a participant certifies notarization(c,v), it broadcasts finalize(c,v) and immediately enters v+1, regardless of what happens in subsequent views. These finalize(c,v) votes accumulate independently of the current view: even if views v+1 through v+k all time out (producing nullifications), the finalize(c,v) votes still count toward the 2f+1 threshold needed to form finalization(c,v).

This means a payload notarized in view v can be finalized while the network is in view v+k for any k >= 1. There is no requirement that a particular view after v succeeds or that any subsequent leader cooperates. As long as 2f+1 participants eventually certify and broadcast finalize(c,v), the finalization certificate will form.

Architecture

All logic is split into four components: the Batcher, the Voter, the Resolver, and the Application (provided by the user). The Batcher is responsible for collecting messages from peers and lazily verifying them when a quorum is met. The Voter is responsible for directing participation in the current view. The Resolver is responsible for fetching artifacts from previous views required to verify proposed blocks in the latest view. Lastly, the Application is responsible for proposing new blocks and indicating whether some block is valid.

To drive great performance, all interactions between Batcher, Voter, Resolver, and Application are non-blocking. This means that, for example, the Voter can continue processing messages while the Application verifies a proposed block or the Resolver fetches a notarization.

                           +------------+          +++++++++++++++
                           |            +--------->+             +
                           |  Batcher   |          +    Peers    +
                           |            |<---------+             +
                           +-------+----+          +++++++++++++++
                               |   ^
                               |   |
                               |   |
                               |   |
                               v   |
+---------------+           +---------+            +++++++++++++++
|               |<----------+         +----------->+             +
|  Application  |           |  Voter  |            +    Peers    +
|               +---------->|         |<-----------+             +
+---------------+           +--+------+            +++++++++++++++
                               |   ^
                               |   |
                               |   |
                               |   |
                               v   |
                           +-------+----+          +++++++++++++++
                           |            +--------->+             +
                           |  Resolver  |          +    Peers    +
                           |            |<---------+             +
                           +------------+          +++++++++++++++

Batched Verification

Unlike other consensus constructions that verify all incoming messages received from peers, for schemes where Verifier::is_batchable() returns true (such as scheme::ed25519, scheme::bls12381_multisig and scheme::bls12381_threshold), simplex lazily verifies messages (only when a quorum is met), enabling efficient batch verification. For schemes where is_batchable() returns false (such as scheme::secp256r1), signatures are verified eagerly as they arrive since there is no batching benefit.

If an invalid signature is detected, the Batcher will perform repeated bisections over collected messages to find the offending message (and block the peer(s) that sent it via commonware_p2p::Blocker).

If using a p2p implementation that is not authenticated, it is not safe to employ this optimization as any attacking peer could simply reconnect from a different address. We recommend commonware_p2p::authenticated.

Fetching Missing Certificates

Background repair fetches nullifications above the local certified or finalized floor. If honest participants complete a view with different certificate types, both sides can still consider it complete while rejecting the other’s proposal ancestry.

Proposal verification repairs this split by requesting the first missing nullification or named parent from the proposal’s elected leader, even below the certified floor. The voter rechecks the full ancestry after each delivery and votes only once it is valid. The voter does not request an uncertified parent inside the optimistic issuance window: its certificate is still forming from live votes (see Optimistic Validation).

The same split can block certification. A notarized view certifies only after its parent certifies, and certifying the parent requires its exact-view notarization. When the voter holds a view’s notarization but not its parent’s, the parent’s votes have stopped circulating, and peers broadcast a certificate only once. A leader that withheld the certificate may never answer a fetch, so the voter requests the parent’s notarization from any peer.

A resolver key identifies a view, not a certificate. A notarization and a covering nullification for one view answer opposite questions, so a peer can return valid evidence that does not settle the request. The requester records that evidence and retries without faulting the peer. A delivered notarization completes its fetch on arrival, because certification judges evidence already in hand. Matching evidence or finalization retires pending work.

Pluggable Hashing and Cryptography

Hashing is abstracted via the commonware_cryptography::Hasher trait and cryptography is abstracted via the commonware_cryptography::certificate::Scheme trait, allowing deployments to employ approaches that best match their requirements (or to provide their own without modifying any consensus logic). The following schemes are supported out-of-the-box:

scheme::ed25519

commonware_cryptography::ed25519 signatures are “High-speed high-security signatures” with 32 byte public keys and 64 byte signatures. While they are well-supported by commercial HSMs and offer efficient batch verification, the signatures are not aggregatable (and certificates grow linearly with the quorum size).

scheme::bls12381_multisig

commonware_cryptography::bls12381 is a “digital signature scheme with aggregation properties”. Unlike commonware_cryptography::ed25519, signatures from multiple participants (say the signers in a certificate) can be aggregated into a single signature (reducing bandwidth usage per broadcast). That being said, commonware_cryptography::bls12381 is much slower to verify than commonware_cryptography::ed25519 and isn’t supported by most HSMs (a standardization effort expired in 2022).

scheme::secp256r1

commonware_cryptography::secp256r1 signatures use the NIST P-256 elliptic curve (also known as prime256v1), which is widely supported by commercial HSMs and hardware security modules. Unlike commonware_cryptography::ed25519, Secp256r1 does not benefit from batch verification, so signatures are verified individually. Certificates grow linearly with quorum size (similar to ed25519).

scheme::bls12381_threshold

scheme::bls12381_threshold employs threshold cryptography (BLS12-381 threshold signatures with a 2f+1 of 3f+1 quorum) to generate succinct consensus certificates (verifiable with just the static public key). This scheme requires instantiating the shared secret via commonware_cryptography::bls12381::dkg and resharing whenever participants change.

Two (non-attributable) variants are provided:

• scheme::bls12381_threshold::standard: Certificates contain only a vote signature.

• scheme::bls12381_threshold::vrf: Certificates contain a vote signature and a view signature (i.e. a seed that can be used as a VRF). This variant can be configured for random leader election (via elector::Random) and/or incorporate this randomness into execution.

Embedded VRF (scheme::bls12381_threshold::vrf)

Every notarize(c,v), nullify(v), or finalize(c,v) message includes an attestation(v) (a partial signature over the view v). After 2f+1 attestations are collected from unique participants, seed(v) can be recovered. Because attestation(v) is only over the view v, the seed derived for a given view v is the same regardless of which block (if any) is notarized in view v. The 2f+1 attestations can come from mutually incompatible messages (notarize for different blocks, nullify, finalize), so seed(v) is recoverable even when no certificate forms for view v.

The value of seed(v) cannot be known prior to message broadcast by any participant (including the leader) in view v and cannot be manipulated by any participant (deterministic for any 2f+1 signers at a given view v), so it is a sound beacon for leader election (where seed(v) determines the leader for v+1). It is not safe as a source of randomness for execution within view v itself: a coalition of f Byzantine participants recovers seed(v) after only f+1 honest attestations, before the round resolves, letting a malicious leader front-run the outcome. Consume seed(v) only in a later view or epoch (see scheme::bls12381_threshold::vrf for extended discussion of the attack and the commit-then-reveal mitigation).

Succinct Certificates

All broadcast consensus messages (notarize(c,v), nullify(v), finalize(c,v)) contain attestations (partial signatures) for a static public key (derived from a group polynomial that can be recomputed during reconfiguration using dkg). As soon as 2f+1 messages are collected, a threshold signature over notarization(c,v), nullification(v), and finalization(c,v) can be recovered, respectively. Because the public key is static, any of these certificates can be verified by an external process without following the consensus instance and/or tracking the current set of participants (as is typically required to operate a lite client).

These threshold signatures over notarization(c,v), nullification(v), and finalization(c,v) (i.e. the consensus certificates) can be used to secure interoperability between different consensus instances and user interactions with an infrastructure provider (where any data served can be proven to derive from some finalized block of some consensus instance with a known static public key).

Persistence

The Voter caches all data required to participate in consensus to avoid any disk reads on on the critical path. To enable recovery, the Voter writes valid messages it receives from consensus and messages it generates to a write-ahead log (WAL) implemented by commonware_storage::journal::segmented::variable::Journal. Before sending a message, any pending Journal appends are synced to prevent inadvertent Byzantine behavior on restart (especially in the case of unclean shutdown). All appends made in the same event loop iteration are coalesced into a single sync that runs after messages are constructed and before any are broadcast (even if there is nothing to broadcast). The proposal payload relay is not a consensus message and is not gated on this sync: to lower view latency, it is requested as soon as the automaton returns a payload, which is safe because extra payload bytes (unlike votes) cannot form a conflicting certificate (see Plan::Propose).

Automaton Failure Semantics

If a validator is the leader for a view but cannot build a valid payload yet (for example because it is still syncing), it should decline the Automaton::propose request by dropping the response channel. Simplex treats this as a missing proposal, broadcasts nullify(v), and other validators can use the leader-nullify fast path to skip the view.

Once propose returns a payload, the local proposer is committed to that payload for verification and certification. Automaton::verify and CertifiableAutomaton::certify are stable verdict APIs, not backpressure or syncing signals. While missing data may still arrive (and/or a validator cannot immediately determine if a payload is valid), implementations should keep these requests pending rather than returning false or closing the channel.

Returning false from verify means the proposal is permanently invalid and causes a local nullify. Returning false from certify means the notarized payload is permanently uncertifiable for that round and also causes a local nullify. Closing certify does not cause nullify(v) to be broadcast before the normal round deadline and can halt progress because certification requests are not retried during the same run. The safe way to stop working on certification is to keep the request pending until Simplex drops it after finalizing the block or a descendant.

Re-exports

pub use config::Config;

pub use config::Floor;

pub use config::ForwardPolicy;

pub use config::SkipBudget;

pub use config::SkipPolicy;

Modules

config

elector

Leader election strategies for simplex consensus.

scheme

Signing scheme implementations for simplex.

types

Types used in crate::simplex.

Structs

Engine

Instance of simplex consensus engine.

Enums

Plan

Describes how a payload should be broadcast to the network.