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@Dusk

While a protocol enabling arbitrary on-chain computation such as Dusk Net- work can act as a host of a virtually unlimited number of unique applications, we designed Dusk Network with a specific set of use cases in mind. More specifi- cally, Dusk Network was primarily conceived with regulatory compliant security tokenization and lifecycle management in mind. The details of the security to- kenization standard are beyond the scope of this paper. We encourage readers to refer to [Mah21] for an in-depth look into this Confidential Security Contract (XSC) Standard. Additionally, a Confidential Token Standard was created to enable seamless interaction between non-regulated and regulated assets within the protocol, without compromising on the privacy of the interacting users. This also enables the Dusk Network protocol to act as a privacy-preserving sidechain for any other existing Layer 1 protocol via trusted or trust-minimized interoperability solutions.
Segregated Byzantine Agreement
SBA is the consensus mechanism utilized to secure the Dusk Network protocol. SBA is a permission-less Proof-of-Stake-based mechanism with statistical final- ity guarantees. The mechanism segregates the consensus participants into two distinct roles:
1. Generator. Generators are responsible for proposing blocks. In other words, Generators perform a similar role to leaders from classic distributed systems literature. Generators are extracted through the privacy-preserving leader extraction procedure called Proof-of-Blind Bid.
2. Provisioner Provisioners are responsible for validating and finalizing the proposed blocks. In other words, Provisioners perform a similar role to replicas from classic distributed systems literature. Provisioners are ex- tracted into the committees through the committee extraction procedure called deterministic sortition.
The mechanism is secure under the honest majority of money assumption, mean- ing that for n DUSK being the cumulative amount staked eligible to participate in the consensus, the ratio of h DUSK under control of honest participants must hold as h > n − f, where f is the ratio of DUSK under the control of Byzan- tine participants and h ≥ 2f. Specifically, we formalize the honest majority of money assumption for the Dusk Network protocol as:

Additionally, we assume that there exists a probabilistic polynomial-time (PPT) Adversary A capable of corrupting a consensus participants with a maximum control of f DUSK. A is assumed to be a mildly adaptive Adversary, meaning that corruption takes place ∆corrupt after A has selected a participant to corrupt. Concretely, ∆corrupt > epoch.
The network conditions are assumed to be synchronous, meaning that there ex- ists a publicly known ∆delay defining the maximum delay by which the message propagation can be delayed to the honest participants of the consensus. In other words, after the initial propagation time of tinitPropagation, the message will be de- livered to every honest consensus participant no later than tinitPropagation +∆delay. We additionally assume that every honest participant will receive the messages in the order that they were propagated.
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The consensus is divided into epochs, rounds and steps. An epoch is defined as a set of rounds, concretely as epoch ≥ c × round, where c is denoted as (f)c ≤ 2−100, for the duration of which the Generators and Provisioner sets re- main unchanged and the epoch seed seedepoch corresponding to the epoch is utilized. A round is defined as a synonym to block height in the context of the consensus, with every round corresponding to a unique block in Chain. A step denotes a consensus step. Specifically, each consensus round is comprised of iterations (i.e. loops) of 4 step.
The consensus mechanism is comprised of three phases:
1. Generation phase, utilizing Proof-of-Blind Bid to extract a leader who is to forge and propagate a candidate block to the consensus participants.
2. Reduction phase, based on [TA84], the two-step phase is responsible for the agreement on a single candidate block to be finalized.
3. Agreement phase, an asynchronous phase running in parallel with the two previous phases and responsible for the finalization of a candidate block. Specifically, an agreement vote is initiated after the successful termination of the Reduction phase.
Definition. A consensus protocol has statistical finality when the probability of a fork during a single execution round is negligible.
Proof. In case of SBA, the fork can be produced by ”double-voting” during the three consequent steps of the execution round, specifically two Reduction steps and an Agreement step). A ”double-vote” occurs when a node votes for two separate candidate blocks in the same voting step. Taking the node as- sumptions defined above into account, a ”double-vote” can only be produced by a Byzantine node, meaning that in order to produce a fork, an Adversary has to receive the control of the supermajority of the cumulative committee stake size in three successive consensus steps. The probability of the aforementioned event happening can be defined below.
Failure Rate
The failure rate is the probability of the safety guarantees of the protocol step (exluding Generation phase) being breached. In particular, the failure rate indicates the probability of an Adversary A obtaining a supermajority in a committee. The probability function is outlined in a formula below, where N ← |committeeround,step| is the committee size, τ ← votethreshold is the threshold of votes in a committee required to proceed to the next step and h is the ratio of the honest participants:

#dusk $DUSK
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