DA-04 · LESSON 04

Thresholds and quorum

KEY DEFINITIONS

Terms used in this lesson

FROST: Flexible Round-Optimized Schnorr Threshold signing: a protocol in which a required subset produces one group signature.
Schnorr signature: Bitcoin’s Taproot signature scheme, whose algebra supports compact verification and advanced multi-party signing.
Guardian: A Ducat policy-checking signer that can authorize or reject defined protocol transactions.

A t-of-n topology trades availability against compromise resistance; current tests and planned deployments must not be confused with one permanent quorum.

65 min Difficulty 4/5 Not started

VISUAL MODEL

See the whole mechanism before going step by step

Use the diagrams to orient yourself. Then the guided explanation below teaches every part in depth.

4 explanatory views

CONCEPT-SPECIFIC MAP · ducat vaultA Ducat action moves one Bitcoin-anchored vault state to a successorSelect any state to inspect its exact role.

RELATIONSHIP MAPInputs, rule, and outputs

01
PREDECESSORCurrent vault outpoint
The current Bitcoin output anchors collateral and identifies the state being spent.
02
REQUESTThresholds and quorum
The Thresholds and quorum workflow proposes one exact action and successor state.
03
POLICYProfile, oracle, signatures
Applicable policy, price evidence, authorization, and transaction shape are checked.
04
BITCOIN SPENDScript-valid transaction
Bitcoin miners and nodes can include only a transaction that satisfies Bitcoin rules.
05
SUCCESSORNew outpoint and state
Ducat validators reconstruct debt, collateral, token, and account changes from the confirmed transaction.

Rule shown: Bitcoin checks the spend; Ducat components independently reconstruct and validate the additional protocol state.

STAGE 1 OF 5PREDECESSOR: Current vault outpoint

The current Bitcoin output anchors collateral and identifies the state being spent.

Governing relationship: Bitcoin checks the spend; Ducat components independently reconstruct and validate the additional protocol state. Complete path: 1. PREDECESSOR, Current vault outpoint. The current Bitcoin output anchors collateral and identifies the state being spent. 2. REQUEST, Thresholds and quorum. The Thresholds and quorum workflow proposes one exact action and successor state. 3. POLICY, Profile, oracle, signatures. Applicable policy, price evidence, authorization, and transaction shape are checked. 4. BITCOIN SPEND, Script-valid transaction. Bitcoin miners and nodes can include only a transaction that satisfies Bitcoin rules. 5. SUCCESSOR, New outpoint and state. Ducat validators reconstruct debt, collateral, token, and account changes from the confirmed transaction.

1. State transitionWhat exists, what changes, and what results

BEFORE

These are arithmetic examples, not current operator claims. Required practice compares other topologies.

MECHANISM

An attacker needs enough compromised shares or operators to meet the threshold under the assumed independence model.

AFTER

Service count does not prove independent ownership, custody, software, or governance domains. Required practice uses a separate server-executed vector.

Text equivalent: Starting from These are arithmetic examples, not current operator claims. Required practice compares other topologies. The mechanism begins when An attacker needs enough compromised shares or operators to meet the threshold under the assumed independence model. The resulting lesson is Service count does not prove independent ownership, custody, software, or governance domains. Required practice uses a separate server-executed vector.

2. Mechanism pathSelect a stage to inspect its job

STAGE 1 OF 4

Count safety margin

An attacker needs enough compromised shares or operators to meet the threshold under the assumed independence model.

Complete path: 1. Count safety margin: An attacker needs enough compromised shares or operators to meet the threshold under the assumed independence model. 2. Count liveness margin: The system can tolerate at most n minus t unavailable participants before valid signing stops. 3. Bind one signing set: Each FROST round names the actual participant subset so binding factors and shares cannot be mixed across quorums. 4. Separate topology from labels: A planned public quorum, a test fixture, and a running production set are different dated claims.

3. Rule and failure boundaryWhat accepts the result and where it can stop

ACCEPTED PATH

The worked case executes the named inputs and checks in the displayed order. A planned public quorum, a test fixture, and a running production set are different dated claims.

CHANGED CONDITION

A missing, malformed, stale, unauthorized, or inconsistent required input stops at its first named boundary. Security depends on threshold, operator independence, custody, software diversity, governance, and deployment, not n alone.

Important distinction: A larger Guardian count automatically makes Ducat more decentralized. Security depends on threshold, operator independence, custody, software diversity, governance, and deployment, not n alone.

Text equivalent: The accepted path is enforced by The worked case executes the named inputs and checks in the displayed order. A planned public quorum, a test fixture, and a running production set are different dated claims. If the required condition changes, A missing, malformed, stale, unauthorized, or inconsistent required input stops at its first named boundary. Security depends on threshold, operator independence, custody, software diversity, governance, and deployment, not n alone.

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Learn the idea

A threshold written t-of-n requires any t valid participants from a set of n to sign. FROST is the threshold Schnorr protocol used to combine those participants' shares into one signature. Increasing t makes compromise harder but makes outages more likely to block signing; changing n affects both independence and availability.

GUIDED EXPLANATION1/4 ideas inspected

Count safety margin

An attacker needs enough compromised shares or operators to meet the threshold under the assumed independence model.

The worked example follows the explanation

Inspect every idea above to open it.

Important distinction“A larger Guardian count automatically makes Ducat more decentralized.”

Security depends on threshold, operator independence, custody, software diversity, governance, and deployment, not n alone.

FINISH LEARNING FIRST

The questions unlock after every required learning activity

Inspect every guided idea, open the worked example, rebuild its mechanism, and complete the deterministic lesson tool. Your progress is saved automatically.