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<li><a href="#initial-opinion">Initial opinion</a></li>
<li><a href="#setup-parameters">Setup Parameters</a></li>
<li><a href="#phase-one-query">Phase One: Query</a></li>
<li><a href="#phase-two-computation">Phase Two: Computation</a></li>
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<h1 id="38consensus-claro">
38/CONSENSUS-CLARO
<a class="anchor" href="#38consensus-claro">#</a>
</h1>
<h1 id="claro-consensus-protocol">
Claro Consensus Protocol
<a class="anchor" href="#claro-consensus-protocol">#</a>
</h1>
<img src="https://img.shields.io/badge/status-raw-lightgrey?style=flat-square" />
<ul>
<li>Status: raw</li>
<li>Editor: Corey Petty <a href="mailto:corey@status.im">corey@status.im</a></li>
<li>Contributors:
Álvaro Castro-Castilla
,
Mark Evenson
</li>
</ul><h1 id="abstract">
Abstract
<a class="anchor" href="#abstract">#</a>
</h1>
<p>This document specifies Claro: a Byzantine, fault-tolerant, binary decision
agreement algorithm that utilizes bounded memory for its execution.
Claro is a novel variant of the Snow family providing a probabilistic
leaderless BFT consensus algorithm that achieves metastablity via
network sub-sampling. We present an application context of the use of
Claro in an efficient, leaderless, probabilistic permission-less
consensus mechanism. We outline a simple taxonomy of Byzantine
adversaries, leaving explicit explorations of to subsequent
publication.</p>
<p>NOTE: We have renamed this variant to <code>Claro</code> from <code>Glacier</code> in order to disambiguate from a previously released research endeavor by <a href="https://arxiv.org/pdf/2210.03423.pdf">Amores-Sesar, Cachin, and Tedeschi</a>. Their naming was coincidentally named the same as our work but is sufficiently differentiated from how ours works.</p>
<h1 id="motivation">
Motivation
<a class="anchor" href="#motivation">#</a>
</h1>
<p>This work is a part of a larger research endeavor to explore highly scalable Byzantine Fault Tolerant (BFT) consensus protocols. Consensus lies at the heart of many decentralized protocols, and thus its characteristics and properties are inherited by applications built on top. Thus, we seek to improve upon the current state of the art in two main directions: base-layer scalability and censorship resistance.</p>
<p>Avalanche has shown to exibit the former in a production environment in a way that is differentiated from Nakamoto consensus and other Proof of Stake (PoS) protocols based in practical Byzantine Fault Tolerant (pBFT) methodologies. We aim to understand its limitations and improve upon them.</p>
<h2 id="background">
Background
<a class="anchor" href="#background">#</a>
</h2>
<p>Our starting point is Avalanche’s Binary Byzantine Agreement algorithm, called Snowball. As long as modifications allow a DAG to be constructed later on, this simplifies the design significantly. The DAG stays the same in principle: it supports confidence, but the core algorithm can be modeled without.</p>
<p>The concept of the Snowball algorithm is relatively simple. Following is a simplified description (lacking some details, but giving an overview). For further details, please refer to the <a href="https://assets.website-files.com/5d80307810123f5ffbb34d6e/6009805681b416f34dcae012_Avalanche%20Consensus%20Whitepaper.pdf">Avalanche paper</a>.</p>
<ol>
<li>The objective is to vote yes/no on a decision (this decision could be a single bit, or, in our DAG use case, whether a vertex should be included or not).</li>
<li>Every node has an eventually-consistent complete view of the network. It will select at random k nodes, and will ask their opinion on the decision (yes/no).</li>
<li>After this sampling is finished, if there is a vote that has more than an <code>alpha</code> threshold, it accumulates one count for this opinion, as well as changes its opinion to this one. But, if a different opinion is received, the counter is reset to 1. If no threshold <code>alpha</code> is reached, the counter is reset to 0 instead.</li>
<li>After several iterations of this algorithm, we will reach a threshold <code>beta</code>, and decide on that as final.</li>
</ol>
<p>Next, we will proceed to describe our new algorithm, based on Snowball.</p>
<p>We have identified a shortcoming of the Snowball algorithm that was a perfect starting point for devising improvements. The scenario is as follows:</p>
<ul>
<li>There is a powerful adversary in the network, that controls a large percentage of the node population: 10% to ~50%.</li>
<li>This adversary follows a strategy that allows them to rapidly change the decision bit (possibly even in a coordinated way) so as to maximally confuse the honest nodes.</li>
<li>Under normal conditions, honest nodes will accumulate supermajorities soon enough, and reach the <code>beta</code> threshold. However, when an honest node performs a query and does not reach the threshold <code>alpha</code> of responses, the counter will be set to 0.</li>
<li>The highest threat to Snowball is an adversary that keeps it from reaching the <code>beta</code> threshold, managing to continuously reset the counter, and steering Snowball away from making a decision.</li>
</ul>
<p>This document only outlines the specification to Claro. Subsequent analysis work on Claro (both on its performance and how it differentiates with Snowball) will be published shortly and this document will be updated.</p>
<h1 id="claro-algorithm-specification">
Claro Algorithm Specification
<a class="anchor" href="#claro-algorithm-specification">#</a>
</h1>
<p>The Claro consensus algorithm computes a boolean decision on a
proposition via a set of distributed computational nodes. Claro is
a leaderless, probabilistic, binary consensus algorithm with fast
finality that provides good reliability for network and Byzantine
fault tolerance.</p>
<h2 id="algorithmic-concept">
Algorithmic concept
<a class="anchor" href="#algorithmic-concept">#</a>
</h2>
<p>Claro is an evolution of the Snowball Byzantine Binary Agreement (BBA) algorithm, in which we tackle specifically the perceived weakness described above. The main focus is going to be the counter and the triggering of the reset. Following, we elaborate the different modifications and features that have been added to the reference algorithm:</p>
<ol>
<li>Instead of allowing the latest evidence to change the opinion completely, we take into account all accumulated evidence, to reduce the impact of high variability when there is already a large amount of evidence collected.</li>
<li>Eliminate the counter and threshold scheme, and introduce instead two regimes of operation:
<ul>
<li>One focused on grabbing opinions and reacting as soon as possible. This part is somewhat closer conceptually to the reference algorithm.</li>
<li>Another one focused on interpreting the accumulated data instead of reacting to the latest information gathered.</li>
</ul>
</li>
<li>Finally, combine those two phases via a transition function. This avoids the creation of a step function, or a sudden change in behavior that could complicate analysis and understanding of the dynamics. Instead, we can have a single algorithm that transfers weight from one operation to the other as more evidence is gathered.</li>
<li>Additionally, we introduce a function for weighted sampling. This will allow the combination of different forms of weighting:
<ul>
<li>Staking</li>
<li>Heuristic reputation</li>
<li>Manual reputation.</li>
</ul>
</li>
</ol>
<p>It’s worth delving a bit into the way the data is interpreted in order to reach a decision. Our approach is based conceptually on the paper <a href="https://cis.temple.edu/~pwang/Publication/confidence.pdf">Confidence as Higher-Order Uncertainty</a>, which describes a frequentist approach to decision certainty. The first-order certainty, measured by frequency, is caused by known positive evidence, and the higher-order certainty is caused by potential positive evidence. Because confidence is a relative measurement defined on evidence, it naturally follows comparing the amount of evidence the system knows with the amount that it will know in the near future (defining “near” as a constant).</p>
<p>Intuitively, we are looking for a function of evidence, <strong><code>w</code></strong>, call it <strong><code>c</code></strong> for confidence, that satisfies the following conditions:</p>
<ol>
<li>Confidence <code>c</code> is a continuous and monotonically increasing function of <code>w</code>. (More evidence, higher confidence.)</li>
<li>When <code>w = 0</code>, <code>c = 0</code>. (Without any evidence, confidence is minimum.)</li>
<li>When <code>w</code> goes to infinity, <code>c</code> converges to 1. (With infinite evidence, confidence is maximum.)</li>
</ol>
<p>The paper describes also a set of operations for the evidence/confidence pairs, so that different sources of knowledge could be combined. However, we leave here the suggestion of a possible research line in the future combining an algebra of evidence/confidence pairs with swarm-propagation algorithm like the one described in <a href="http://replicated.cc/files/schmebulock.pdf">this paper</a>.</p>
<h3 id="initial-opinion">
Initial opinion
<a class="anchor" href="#initial-opinion">#</a>
</h3>
<p>A proposal is formulated to which consensus of truth or falsity is
desired. Each node that participates starts the protocol with an
opinion on the proposal, represented in the sequel as <code>NO</code>, <code>NONE</code>,
and <code>YES</code>.</p>
<p>A new proposition is discovered either by local creation or in
response to a query, a node checks its local opinion. If the node can
compute a justification of the proposal, it sets its opinion to one of
<code>YES</code> or <code>NO</code>. If it cannot form an opinion, it leaves its opinion as
<code>NONE</code>.</p>
<p>For now, we will ignore the proposal dissemination process and assume all nodes participating have an initial opinion to respond to within a given request. Further research will relax this assumption and analyze timing attacks on proposal propagation through the network.</p>
<p>The node then participates in a number of query rounds in which it
solicits other node&rsquo;s opinion in query rounds. Given a set of <code>N</code>
leaderless computational nodes, a gossip-based protocol is presumed to
exist which allows members to discover, join, and leave a weakly
transitory maximally connected graph. Joining this graph allows each
node to view a possibly incomplete node membership list of all other
nodes. This view may change as the protocol advances, as nodes join
and leave. Under generalized Internet conditions, the membership of
the graph would experience a churn rate varying across different
time-scales, as the protocol rounds progress. As such, a given node
may not have a view on the complete members participating in the
consensus on a proposal in a given round.</p>
<p>The algorithm is divided into 4 phases:</p>
<ol>
<li>Querying</li>
<li>Computing <code>confidence</code>, <code>evidence</code>, and <code>accumulated evidence</code></li>
<li>Transition function</li>
<li>Opinion and Decision</li>
</ol>
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<h3 id="setup-parameters">
Setup Parameters
<a class="anchor" href="#setup-parameters">#</a>
</h3>
<p>The node initializes the following integer ratios as constants:</p>
<pre tabindex="0"><code># The following values are constants chosen with justification from experiments
# performed with the adversarial models
#
confidence_threshold
&lt;-- 1
# constant look ahead for number of rounds we expect to finalize a
# decision. Could be set dependent on number of nodes
# visible in the current gossip graph.
look_ahead
&lt;-- 19
# the confidence weighting parameter (aka alpha_1)
certainty
&lt;-- 4 / 5
doubt ;; the lack of confidence weighting parameter (aka alpha_2)
&lt;-- 2 / 5
k_multiplier ;; neighbor threshold multiplier
&lt;-- 2
;;; maximal threshold multiplier, i.e. we will never exceed
;;; questioning k_initial * k_multiplier ^ max_k_multiplier_power peers
max_k_multiplier_power
&lt;-- 4
;;; Initial number of nodes queried in a round
k_initial
&lt;-- 7
;;; maximum query rounds before termination
max_rounds ;; placeholder for simulation work, no justification yet
&lt;-- 100
</code></pre><p>The following variables are needed to keep the state of Claro:</p>
<pre tabindex="0"><code>;; current number of nodes to attempt to query in a round
k
&lt;-- k_original
;; total number of votes examined over all rounds
total_votes
&lt;-- 0
;; total number of YES (i.e. positive) votes for the truth of the proposal
total_positive
&lt;-- 0
;; the current query round, an integer starting from zero
round
&lt;-- 0
</code></pre><h3 id="phase-one-query">
Phase One: Query
<a class="anchor" href="#phase-one-query">#</a>
</h3>
<p>A node selects <code>k</code> nodes randomly from the complete pool of peers in the
network. This query is can optionally be weighted, so the probability
of selecting nodes is proportional to their</p>
<p>Node Weighting
$$
P(i) = \frac{w_i}{\sum_{j=0}^{j=N} w_j}
$$</p>
<p>where <code>w</code> is evidence. The list of nodes is maintained by a separate protocol (the network
layer), and eventual consistency of this knowledge in the network
suffices. Even if there are slight divergences in the network view
from different nodes, the algorithm is resilient to those.</p>
<p>A query is sent to each neighbor with the node&rsquo;s current <code>opinion</code> of
the proposal.</p>
<p>Each node replies with their current opinion on the proposal.</p>
<p>See <a href="#wire-protocol">the wire protocol Interoperability section</a> for
details on the semantics and syntax of the &ldquo;on the wire&rdquo;
representation of this query.</p>
<p><strong>Adaptive querying</strong>. An additional optimization in the query
consists of adaptively growing the <em><code>k</code></em> constant in the event of
<strong>high confusion</strong>. We define high confusion as the situation in
which neither opinion is strongly held in a query (<em>i.e.</em> a
threshold is not reached for either yes or no). For this, we will
use the <em><code>alpha</code></em> threshold defined below. This adaptive growth of
the query size is done as follows:</p>
<p>Every time the threshold is not reached, we multiply <em><code>k</code></em> by a
constant. In our experiments, we found that a constant of 2 works
well, but what really matters is that it stays within that order of
magnitude.</p>
<p>The growth is capped at 4 times the initial <em><code>k</code></em> value. Again, this
is an experimental value, and could potentially be increased. This
depends mainly on complex factors such as the size of the query
messages, which could saturate the node bandwidth if the number of
nodes queried is too high.</p>
<p>When the query finishes, the node now initializes the following two
values:</p>
<pre><code>new_votes
&lt;-- |total vote replies received in this round to the current query|
positive_votes
&lt;-- |YES votes received from the query|
</code></pre>
<h3 id="phase-two-computation">
Phase Two: Computation
<a class="anchor" href="#phase-two-computation">#</a>
</h3>
<p>When the query returns, three ratios are used later on to compute the
transition function and the opinion forming. Confidence encapsulates
the notion of how much we know (as a node) in relation to how much we
will know in the near future (this being encoded in the look-ahead
parameter <em><code>l</code></em>.) Evidence accumulated keeps the ratio of total positive
votes vs the total votes received (positive and negative), whereas the
evidence per round stores the ratio of the current round only.</p>
<p>Parameters
$$
\begin{array}{lc}
\text{Look-ahead parameter} &amp; l = 20 \newline
\text{First evidence parameter} &amp; \alpha_1 = 0.8 \newline
\text{Second evidence parameter} &amp; \alpha_2 = 0.5 \newline
\end{array}
$$</p>
<p>Computation
$$
\begin{array}{lc}
\text{Confidence} &amp; c_{accum} \impliedby \frac{total\ votes}{total\ votes + l} \newline
\text{Total accumulated evidence}&amp; e_{accum} \impliedby \frac{total\ positive\ votes}{total\ votes} \newline
\text{Evidence per round} &amp; e_{round} \impliedby \frac{round\ positive\ votes}{round\ votes} \newline
\end{array}
$$</p>
<p>The node runs the <code>new_votes</code> and <code>positive_votes</code> parameters received
in the query round through the following algorithm:</p>
<pre><code>total_votes
+== new_votes
total_positive
+== positive_votes
confidence
&lt;-- total_votes / (total_votes + look_ahead)
total_evidence
&lt;-- total_positive / total_votes
new_evidence
&lt;-- positive_votes / new_votes
evidence
&lt;-- new_evidence * ( 1 - confidence ) + total_evidence * confidence
alpha
&lt;-- doubt * ( 1 - confidence ) + certainty * confidence
</code></pre>
<h3 id="phase-three-computation">
Phase Three: Computation
<a class="anchor" href="#phase-three-computation">#</a>
</h3>
<p>In order to eliminate the need for a step function (a conditional in
the code), we introduce a transition function from one regime to the
other. Our interest in removing the step function is twofold:</p>
<ol>
<li>
<p>Simplify the algorithm. With this change the number of branches is
reduced, and everything is expressed as a set of equations.</p>
</li>
<li>
<p>The transition function makes the regime switch smooth,
making it harder to potentially exploit the sudden regime change in
some unforeseen manner. Such a swift change in operation mode could
potentially result in a more complex behavior than initially
understood, opening the door to elaborated attacks. The transition
function proposed is linear with respect to the confidence.</p>
</li>
</ol>
<p>Transition Function
$$
\begin{array}{cl}
evidence &amp; \impliedby e_{round} (1 - c_{accum}) + e_{accum} c_{accum} \newline
\alpha &amp; \impliedby \alpha_1 (1 - c_{accum}) + \alpha_2 c_{accum} \newline
\end{array}
$$</p>
<p>Since the confidence is modeled as a ratio that depends on the
constant <em><code>l</code></em>, we can visualize the transition function at
different values of <em><code>l</code></em>. Recall that this constant encapsulates
the idea of “near future” in the frequentist certainty model: the
higher it is, the more distant in time we consider the next
valuable input of evidence to happen.</p>
<p>We have observed via experiment that for a transition function to be
useful, we need establish two requirements:</p>
<ol>
<li>
<p>The change has to be balanced and smooth, giving an
opportunity to the first regime to operate and not jump directly
to the second regime.</p>
</li>
<li>
<p>The convergence to 1.0 (fully operating in the second regime)
should happen within a reasonable time-frame. We’ve set this
time-frame experimentally at 1000 votes, which is in the order of
~100 queries given a <em><code>k</code></em> of 9.</p>
</li>
</ol>
<p>[[ Note: Avalanche uses k = 20, as an experimental result from their
deployment. Due to the fundamental similarities between the
algorithms, it’s a good start for us. ]]</p>
<p>The node updates its local opinion on the consensus proposal by
examining the relationship between the evidence accumulated for a
proposal with the confidence encoded in the <code>alpha</code> parameter:</p>
<pre><code>IF
evidence &gt; alpha
THEN
opinion &lt;-- YES
ELSE IF
evidence &lt; 1 - alpha
THEN
opinion &lt;-- NO
</code></pre>
<p>If the opinion of the node is <code>NONE</code> after evaluating the relation
between <code>evidence</code> and <code>alpha</code>, adjust the number of uniform randomly
queried nodes by multiplying the neighbors <code>k</code> by the <code>k_multiplier</code>
up to the limit of <code>k_max_multiplier_power</code> query size increases.</p>
<pre><code>;; possibly increase number nodes to uniformly randomly query in next round
WHEN
opinion is NONE
AND
k &lt; k_original * k_multiplier ^ max_k_multiplier_power
THEN
k &lt;-- k * k_multiplier
</code></pre>
<h3 id="decision">
Decision
<a class="anchor" href="#decision">#</a>
</h3>
<p>The next step is a simple one: change our opinion if the threshold
<em><code>alpha</code></em> is reached. This needs to be done separately for the <code>YES/NO</code>
decision, checking both boundaries. The last step is then to <em><code>decide</code></em>
on the current opinion. For that, a confidence threshold is
employed. This threshold is derived from the network size, and is
directly related to the number of total votes received.</p>
<p>Decision
$$
\begin{array}{cl}
evidence &gt; \alpha &amp; \implies \text{opinion YES} \newline
evidence &lt; 1 - \alpha &amp; \implies \text{opinion NO} \newline
if\ \text{confidence} &gt; c_{target} &amp; THEN \ \text{finalize decision} \newline
\end{array}
$$</p>
<p>After the <code>OPINION</code> phase is executed, the current value of <code>confidence</code>
is considered: if <code>confidence</code> exceeds a threshold derived from the
network size and directly related to the total votes received, an
honest node marks the decision as final, and always returns this
opinion is response to further queries from other nodes on the
network.</p>
<pre><code>IF
confidence &gt; confidence_threshold
OR
round &gt; max_rounds
THEN
finalized &lt;-- T
QUERY LOOP TERMINATES
ELSE
round +== 1
QUERY LOOP CONTINUES
</code></pre>
<p>Thus, after the decision phase, either a decision has been finalized
and the local node becomes quiescent never initiating a new query, or
it initiates a <a href="#query">new query</a>.</p>
<h3 id="termination">
Termination
<a class="anchor" href="#termination">#</a>
</h3>
<p>A local round of Claro terminates in one of the following
execution model considerations:</p>
<ol>
<li>
<p>No queries are received for any newly initiated round for temporal
periods observed via a locally computed passage of time. See <a href="#clock">the
following point on local time</a>.</p>
</li>
<li>
<p>The <code>confidence</code> on the proposal exceeds our threshold for
finalization.</p>
</li>
<li>
<p>The number of <code>rounds</code> executed would be greater than
<code>max_rounds</code>.</p>
</li>
</ol>
<h4 id="quiescence">
Quiescence
<a class="anchor" href="#quiescence">#</a>
</h4>
<p>After a local node has finalized an <code>opinion</code> into a <code>decision</code>, it enters a quiescent
state whereby it never solicits new votes on the proposal. The local
node MUST reply with the currently finalized <code>decision</code>.</p>
<h4 id="clock">
Clock
<a class="anchor" href="#clock">#</a>
</h4>
<p>The algorithm only requires that nodes have computed the drift of
observation of the passage of local time, not that that they have
coordinated an absolute time with their peers. For an implementation
of a phase locked-loop feedback to measure local clock drift see
<a href="https://www.rfc-editor.org/rfc/rfc5905.html">NTP</a>.</p>
<h2 id="further-points">
Further points
<a class="anchor" href="#further-points">#</a>
</h2>
<h3 id="node-receives-information-during-round">
Node receives information during round
<a class="anchor" href="#node-receives-information-during-round">#</a>
</h3>
<p>In the query step, the node is envisioned as packing information into
the query to cut down on the communication overhead a query to each of
this <code>k</code> nodes containing the node&rsquo;s own current opinion on the
proposal (<code>YES</code>, <code>NO</code>, or <code>NONE</code>). The algorithm does not currently
specify how a given node utilizes this incoming information. A
possible use may be to count unsolicited votes towards a currently
active round, and discard the information if the node is in a
quiescent state.</p>
<h4 id="problems-with-weighting-node-value-of-opinions">
Problems with Weighting Node Value of Opinions
<a class="anchor" href="#problems-with-weighting-node-value-of-opinions">#</a>
</h4>
<p>If the view of other nodes is incomplete, then the sum of the optional
weighting will not be a probability distribution normalized to 1.</p>
<p>The current algorithm doesn&rsquo;t describe how the initial opinions are formed.</p>
<h1 id="implementation-status">
Implementation status
<a class="anchor" href="#implementation-status">#</a>
</h1>
<p>The following implementations have been created for various testing and simulation purposes:</p>
<ul>
<li><a href="https://github.com/logos-co/consensus-research">Rust</a></li>
<li><a href="">Python</a> - FILL THIS IN WITH NEWLY CREATED REPO</li>
<li><a href="">Common Lisp</a> - FILL THIS IN WITH NEWLY CREATED REPO</li>
</ul>
<h1 id="wire-protocol">
Wire Protocol
<a class="anchor" href="#wire-protocol">#</a>
</h1>
<p>For interoperability we present a wire protocol semantics by requiring
the validity of the following statements expressed in Notation3 (aka
<code>n3</code>) about any query performed by a query node:</p>
<pre tabindex="0"><code class="language-n3" data-lang="n3">@prefix rdf: &lt;http://www.w3.org/1999/02/22-rdf-syntax-ns#&gt; .
@prefix rdfs: &lt;http://www.w3.org/2000/01/rdf-schema#&gt; .
@prefix xsd: &lt;http://www.w3.org/2001/XMLSchema#&gt; .
@prefix Claro &lt;https://rdf.logos.co/protocol/Claro#&gt; .
Claro:query
:holds (
:_0 [ rdfs:label &#34;round&#34;;
a xsd:postitiveInteger; ],
rdfs:comment &#34;&#34;&#34;
The current round of this query
A value of zero corresponds to the initial round.
&#34;&#34;&#34; ;
:_1 [ rdfs:label &#34;uri&#34;;
rdfs:comment &#34;&#34;&#34;
A unique URI for the proposal.
It MAY be possible to examine the proposal by resolving this resource,
and its associated URIs.
&#34;&#34;&#34; ;
a xsd:anyURI ],
:_2 [ rdfs:label &#34;opinion&#34;;
rdfs:comment &#34;&#34;&#34;
The opinion on the proposal
One of the strings &#34;YES&#34; &#34;NO&#34; or &#34;NONE&#34;.
&#34;&#34;&#34; ;
# TODO constrain as an enumeration on three values efficiently
a xsd:string ]
) .
</code></pre><p>Nodes are advised to use Waku messages to include their own
metadata in serializations as needed.</p>
<h2 id="syntax">
Syntax
<a class="anchor" href="#syntax">#</a>
</h2>
<p>The semantic description presented above can be reliably round-tripped
through a suitable serialization mechanism. JSON-LD provides a
canonical mapping to UTF-8 JSON.</p>
<p>At their core, the query messages are a simple enumeration of the
three possible values of the opinion:</p>
<pre><code>{ NO, NONE, YES }
</code></pre>
<p>When represented via integers, such as choosing</p>
<pre><code> { -1, 0, +1 }
</code></pre>
<p>the parity summations across network invariants often become easier to
manipulate.</p>
<h1 id="security-considerations">
Security Considerations
<a class="anchor" href="#security-considerations">#</a>
</h1>
<h2 id="privacy">
Privacy
<a class="anchor" href="#privacy">#</a>
</h2>
<p>In practice, each honest node gossips its current opinion which
reduces the number of messages that need to be gossiped for a given
proposal. The resulting impact on the privacy of the node&rsquo;s opinion
is not currently analyzed.</p>
<h2 id="security-with-respect-to-various-adversarial-models">
Security with respect to various Adversarial Models
<a class="anchor" href="#security-with-respect-to-various-adversarial-models">#</a>
</h2>
<p>Adversarial models have been tested for which the values for current
parameters of Claro have been tuned. Exposition of the
justification of this tuning need to be completed.</p>
<h3 id="local-strategies">
Local Strategies
<a class="anchor" href="#local-strategies">#</a>
</h3>
<h4 id="random-adversaries">
Random Adversaries
<a class="anchor" href="#random-adversaries">#</a>
</h4>
<p>A random adversary optionally chooses to respond to all queries with a
random decision. Note that this adversary may be in some sense
Byzantine but not malicious. The random adversary also models some
software defects involved in not &ldquo;understanding&rdquo; how to derive a truth
value for a given proposition.</p>
<h4 id="infantile-adversary">
Infantile Adversary
<a class="anchor" href="#infantile-adversary">#</a>
</h4>
<p>Like a petulant child, an infantile adversary responds with the
opposite vote of the honest majority on an opinion.</p>
<h3 id="omniscient-adversaries">
Omniscient Adversaries
<a class="anchor" href="#omniscient-adversaries">#</a>
</h3>
<p>Omniscient adversaries have somehow gained an &ldquo;unfair&rdquo; participation in
consensus by being able to control <code>f</code> of <code>N</code> nodes with a out-of-band
&ldquo;supra-liminal&rdquo; coordination mechanism. Such adversaries use this
coordinated behavior to delay or sway honest majority consensus.</p>
<h4 id="passive-gossip-adversary">
Passive Gossip Adversary
<a class="anchor" href="#passive-gossip-adversary">#</a>
</h4>
<p>The passive network omniscient adversary is fully aware at all times
of the network state. Such an adversary can always chose to vote in
the most efficient way to block the distributed consensus from
finalizing.</p>
<h4 id="active-gossip-adversary">
Active Gossip Adversary
<a class="anchor" href="#active-gossip-adversary">#</a>
</h4>
<p>An omniscient gossip adversary somehow not only controls <code>f</code> of <code>N</code>
nodes, but has also has corrupted communications between nodes such
that she may inspect, delay, and drop arbitrary messages. Such an
adversary uses capability to corrupt consensus away from honest
decisions to ones favorable to itself. This adversary will, of
course, choose to participate in an honest manner until defecting is
most advantageous.</p>
<h1 id="future-directions">
Future Directions
<a class="anchor" href="#future-directions">#</a>
</h1>
<p>Although we have proposed a normative description of the
implementation of the underlying binary consensus algorithm (Claro),
we believe we have prepared for analysis its adversarial performance
in a manner that is amenable to replacement by another member of the
<a href="#snow*">snow*</a> family.</p>
<p>We have presumed the existence of a general family of algorithms that
can be counted on to vote on nodes in the DAG in a fair manner.
Avalanche provides an example of the construction of votes on UTXO
transactions. One can express all state machine, i.e. account-based
models as checkpoints anchored in UTXO trust, so we believe that this
presupposition has some justification. We can envision a need for
tooling abstraction that allow one to just program the DAG itself, as
they should be of stable interest no matter if Claro isn&rsquo;t.</p>
<h1 id="informative-references">
Informative References
<a class="anchor" href="#informative-references">#</a>
</h1>
<ol start="0">
<li>
<p><a href="https://logos.co/">Logos</a></p>
</li>
<li>
<p><a href="https://dahliamalkhi.github.io/posts/2022/06/dag-bft/">On BFT Consensus Evolution: From Monolithic to
DAG</a></p>
</li>
<li>
<p><a href="https://ipfs.io/ipfs/QmUy4jh5mGNZvLkjies1RWM4YuvJh5o2FYopNPVYwrRVGV">snow-ipfs</a></p>
</li>
<li>
<p><a href="https://www.avalabs.org/whitepapers">snow*</a> The Snow family of
algorithms</p>
</li>
<li>
<p><a href="https://cloud.google.com/composer/docs/how-to/using/writing-dags">Move</a>
Move: a Language for Writing DAG Abstractions</p>
</li>
<li>
<p><a href="http://www.w3.org/1999/02/22-rdf-syntax-ns#">rdf</a></p>
</li>
<li>
<p><a href="http://www.w3.org/2000/01/rdf-schema#">rdfs</a></p>
</li>
<li>
<p><a href="http://www.w3.org/2001/XMLSchema#">xsd</a></p>
</li>
<li>
<p><a href="https://www.w3.org/TeamSubmission/n3/">n3-w3c-notes</a></p>
</li>
<li>
<p><a href="https://www.ntp.org/downloads.html">ntp</a></p>
</li>
</ol>
<h2 id="normative-references">
Normative References
<a class="anchor" href="#normative-references">#</a>
</h2>
<ol start="0">
<li>
<p><a href="https://rdf.logos.co/protocol/Claro/1/0/0/raw">Claro</a></p>
</li>
<li>
<p><a href="https://www.w3.org/DesignIssues/Notation3.html">n3</a></p>
</li>
<li>
<p><a href="https://json-ld.org/">json-ld</a></p>
</li>
</ol>
<h2 id="copyright">
Copyright
<a class="anchor" href="#copyright">#</a>
</h2>
<p>Copyright and related rights waived via
<a href="https://creativecommons.org/publicdomain/zero/1.0/">CC0</a>.</p>
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<div class="book-toc-content">
<nav id="TableOfContents">
<ul>
<li><a href="#background">Background</a></li>
</ul>
<ul>
<li><a href="#algorithmic-concept">Algorithmic concept</a>
<ul>
<li><a href="#initial-opinion">Initial opinion</a></li>
<li><a href="#setup-parameters">Setup Parameters</a></li>
<li><a href="#phase-one-query">Phase One: Query</a></li>
<li><a href="#phase-two-computation">Phase Two: Computation</a></li>
<li><a href="#phase-three-computation">Phase Three: Computation</a></li>
<li><a href="#decision">Decision</a></li>
<li><a href="#termination">Termination</a></li>
</ul>
</li>
<li><a href="#further-points">Further points</a>
<ul>
<li><a href="#node-receives-information-during-round">Node receives information during round</a></li>
</ul>
</li>
</ul>
<ul>
<li><a href="#syntax">Syntax</a></li>
</ul>
<ul>
<li><a href="#privacy">Privacy</a></li>
<li><a href="#security-with-respect-to-various-adversarial-models">Security with respect to various Adversarial Models</a>
<ul>
<li><a href="#local-strategies">Local Strategies</a></li>
<li><a href="#omniscient-adversaries">Omniscient Adversaries</a></li>
</ul>
</li>
</ul>
<ul>
<li><a href="#normative-references">Normative References</a></li>
<li><a href="#copyright">Copyright</a></li>
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