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Blockchain (BC) systems mainly depend on the consistent state of the Distributed Ledger (DL) at different logical and physical places of the network. The majority of network nodes need to be enforced to use one or both of the following approaches to remain consistent: i) to wait for certain delays (i.e. by requesting a hard puzzle solution as in PoW and PoUW, or to wait for random delays as in PoET, etc.) ii) to propagate shared data through shortest possible paths within the network. The first approach may cause higher energy consumption and/or lower throughput rates if not optimized, and in many cases these features are conventionally fixed. Therefore, it is preferred to enhance the second approach with some optimization. Previous works for this approach have the following drawbacks: they may violate the identity privacy of miners, only locally optimize the Neighbor Selection method (NS), do not consider the dynamicity of the network, or require the nodes to know the precise size of the network at all times. In this paper, we address these issues by proposing a Dynamic and Optimized NS protocol called DONS, using a novel privacy-aware leader election within the public BC called AnoLE, where the leader anonymously solves the The Minimum Spanning Tree problem (MST) of the network in polynomial time. Consequently, miners are informed about the optimum NS according to the current state of network topology. We analytically evaluate the complexity, the security and the privacy of the proposed protocols against state-of-the-art MST solutions for DLs and well known attacks. Additionally, we experimentally show that the proposed protocols outperform state-of-the-art NS solutions for public BCs. Our evaluation shows that the proposed DONS and AnoLE protocols are secure, private, and acutely outperform all current NS solutions in terms of block finality and fidelity.
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Future Generation Computer Systems 130 (2022) 75–90
Contents lists available at ScienceDirect
Future Generation Computer Systems
journal homepage: www.elsevier.com/locate/fgcs
DONS: Dynamic Optimized Neighbor Selection for smart blockchain
networks
Hamza Baniata a,,Ahmad Anaqreh b,Attila Kertesz a
aDepartment of Software Engineering, University of Szeged, Szeged 6720, Hungary
bDepartment of Computational Optimization, University of Szeged, Szeged 6720, Hungary
article info
Article history:
Received 19 April 2021
Received in revised form 27 August 2021
Accepted 15 December 2021
Available online 22 December 2021
Keywords:
Smart networking
Blockchain
Optimized neighbor selection
Minimum Spanning Tree
Anonymized Leader Election
abstract
Blockchain (BC) systems mainly depend on the consistent state of the Distributed Ledger (DL) at
different logical and physical places of the network. The majority of network nodes need to be enforced
to use one or both of the following approaches to remain consistent: (i) to wait for certain delays (i.e.
by requesting a hard puzzle solution as in PoW and PoUW, or to wait for random delays as in PoET, etc.)
(ii) to propagate shared data through shortest possible paths within the network. The first approach
may cause higher energy consumption and/or lower throughput rates if not optimized, and in many
cases these features are conventionally fixed. Therefore, it is preferred to enhance the second approach
with some optimization. Previous works for this approach have the following drawbacks: they may
violate the identity privacy of miners, only locally optimize the Neighbor Selection method (NS), do
not consider the dynamicity of the network, or require the nodes to know the precise size of the
network at all times. In this paper, we address these issues by proposing a Dynamic and Optimized
NS protocol called DONS, using a novel privacy-aware leader election within the public BC called
AnoLE, where the leader anonymously solves the The Minimum Spanning Tree problem (MST) of the
network in polynomial time. Consequently, miners are informed about the optimum NS according
to the current state of network topology. We analytically evaluate the complexity, the security and
the privacy of the proposed protocols against state-of-the-art MST solutions for DLs and well known
attacks. Additionally, we experimentally show that the proposed protocols outperform state-of-the-art
NS solutions for public BCs. Our evaluation shows that the proposed DONS and AnoLE protocols are
secure, private, and they acutely outperform all current NS solutions in terms of block finality and
fidelity.
©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc- nd/4.0/).
1. Introduction
Blockchain (BC) [1] is the backbone of the famous, robust and
reliable P2P Bitcoin network, which proposes many simple so-
lutions for different problems that faced a successful distributed
digital currency system for years. One of those problems was the
consistency of the Distributed Ledger (DL) at any given time [2].
A system is consistent, when it ensures that every reading is
the same on any node, i.e., the nodes have a global view of the
system state [3,4]. Different criteria imposes different readings,
This research work was supported by the Hungarian Scientific Research
Fund, under the grant number OTKA FK 131793, and by the TruBlo project
of the European Union’s Horizon 2020 research and innovation program under
grant agreement No. 957228, and by the National Research, Development and
Innovation Office within the framework of the Artificial Intelligence National
Laboratory Programme, and by the University of Szeged Open Access Fund under
the grant number 5544.
Corresponding author.
E-mail address: baniatah@inf.u-szeged.hu (H. Baniata).
e.g. the fluctuating transmission delay between nodes and the
continuous alteration of data [5]. Although BC did not directly
solve this open problem, it founded an approach assuring data
saved on the DL would be synchronized soon enough, so that the
DL is consistent [6]. Previous studies show that in a BC-based DL,
more neighbors per miner and higher delivery time rates between
neighbors, both lead to lower levels of DL consistency [7,8]. These
results served as a motivation to our research for designing an
optimized BC networking and gossiping protocol. Such a protocol
shall require minimum number of neighbors per miner, directing
the miners to communicate with globally-optimized selection of
neighbors.
A scalable system is one that maintains constant, or slowly
degrading, overheads and performance as its size increases [9].
The dynamicity in P2P networks, which are the physical infras-
tructure of BCs, imposes even more complicated problems than
the DL inconsistency [10] as it directly affects its scalability.
That is, the constantly changing topology of the network leads
to non-consistent propagation delays between its entities. BC
https://doi.org/10.1016/j.future.2021.12.010
0167-739X/©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
peers are connected to several neighboring peers, and they usu-
ally adopt a Random Neighbor Selection (RNS) with which they
share data [11]. Generally, shared data between peers include
new blocks or information regarding the state of the sender’s
ledger (i.e. gossiping). Gossiping also includes sharing the best
DL version between peers, which is defined according to certain
criteria (e.g. longest chain). The RNS method implies randomized
paths, walked by shared data [12], leading to an inefficient data
propagation scheme. This is due to several redundant exchanged
messages caused by the probability of cycle appearance on the
randomly selected path of data, leading to higher average finality
time and lower consistency levels.
Although it is not an optimized method, RNS is currently
adopted by most BC systems. Those BCs compensate the high
finality time by enforcing miners to spend more time solving
the puzzle. This compensation technique does indeed achieve its
goal, yet it leads to both lower overall system throughput (due to
delayed new block generation), and higher energy consumption
(in case the puzzle solution consumes energy. e.g. the PoW and
the PoUW consensus models). Few other methods were proposed
to locally optimize Neighbor Selection (NS), and indeed addressed
the dynamicity issue (e.g. [13]). However, none of these solutions
proposed optimum NS.
We envision a better solution to allow peers to communicate
with selected neighbors according to globally optimized criterion.
This criterion has to fulfill mainly three conditions:
1. It decreases the number of cycles within a path, that shared
data walks, from any peer to any other peer (i.e. no cycles,
hence a Spanning Tree is an optimal solution [14]).
2. It decreases the maximum time spent from generating
data, by any peer, till it reaches all the peers of the network.
3. It addresses the scalability issues of the network, leading to
adaptive optimization of NS in spite of continuous change
in network topology.
The optimum selection of paths within a connected network,
such as the discussed P2P BC network, is in fact finding the
Minimum Spanning Tree (MST) of the network. Utilizing the MST
of a given BC network shall lead to increased number of peers
receiving a shared piece of data in minimum time, which results
in both enhanced data finality and enhanced DL consistency.
In this paper, we propose a Dynamic and Optimized Neigh-
bor Selection protocol called DONS that computes the MST of
a public BC network, while preserving the privacy of the par-
ticipating peers. DONS is also able to dynamically update the
MST as peers join and leave the network. This protocol includes
a privacy-preserving leader election method, allowing one of
the peers within the BC network to compute the MST without
previous knowledge of network peers identities (e.g. IP address).
The leader nominates itself and becomes active once the majority
of voters accepted it as a leader within a predefined round-time.
Once active, the leader builds a global demonstration of the BC
network topology. The local views sent by voters contain no pri-
vate data of the senders and, thus, these views can only be used
to determine an anonymized topology of the network. Using one
of the famous MST algorithms (e.g. Prim’s or Kruskal’s), the leader
computes the MST and broadcasts it to the network. Every recip-
ient of the MST then can read only its identity and its neighbors’
identities, leading to each peer of the network communicating
with the optimized selection of neighbors. As a result, our current
research work addresses the Neighbor Selection Problem (NSP) of
public BCs.
Although the recipient peers can then know the anonymized
MST, they cannot, by any means, know the identities of peers
other than themselves and their neighbors. We evaluate the pro-
posed DONS protocol against other approaches, utilizing two ran-
domized network models, namely Erdős–Rényi (ER) model [15]
and Barabási–Albert (BA) model [16]. The DONS protocol is an-
alytically evaluated in terms of security and privacy [17], and
is experimentally evaluated in terms of propagation time and
message overhead against the currently used RNS and local RTT-
based NS methods. The leader election method is theoretically
and experimentally evaluated, in terms of time and message
complexity [18], against a recent solution proposed in [19]. The
results of our evaluation shows that our proposed protocols are
secure, private, efficient and significantly outperform the current
related methods.
As will be discussed in later sections, we found no previous
work that specifically proposed a privacy-aware leader election
method, within the frame of public permissionless BCs, and de-
ployed it to dynamically solve the NSP by finding the network
MST. To the best of our knowledge, this is the first research paper
that proposes such a protocol.
The remainder of this paper is organized as follows: Sec-
tion 2discusses the state-of-the-art regarding the NSP of public
BC networks, MSTP, and the leader election problem. Section 3
defines the basic preliminaries and notations on which we build
our methods. Section 4presents the proposed DONS and AnoLE
protocols. Section 5presents our evaluation of the proposed pro-
tocols in terms of privacy, security, time and message complexity,
finality and fidelity. Section 6discusses the proposed protocol
in terms of future potential and open issues. Finally, Section 7
concludes our work.
2. Related work
Finding the MST of general distributed systems by different
means, for example by building a binary tree in distributed fash-
ion within the network and select the root node to search for
shortest paths, have already been proposed in the literature [20,
21]. Additionally, many leader election algorithms have been
proposed within other contexts, e.g. general distributed systems,
or even BC networks, that do not consider the identity privacy
as a constraint [22], or ad-hoc wireless sensor networks that
have gateway controllers [23,24]. In those methods, the leader
is utilized to administrate the network, mine new blocks, select
next miners, or perform specific computations for specific slave
nodes [9,25].
2.1. NSP in public BC networks
It has been shown in several previous works how optimizing
the NS decreases the probability of DL forking [26]. In this sub-
section, we investigate approaches other than RNS [27], as it is
the most used in BC networks while it is the least optimized.
Examples of such networks include Bitcoin [1] and Hyberledger
Fabric [28].
Bi et al. [13] proposed a latency-based NS protocol where
miners measure the Round Trip Time (RTT) to their neighbors.
Accordingly, miners favor neighbors with lowest RTT, when they
need to perform NS. Similarly, a bandwidth informed NS pro-
tocol was proposed by Wang and Kim [29], where BC miners
favor communications with neighbors that offer higher band-
width transmission. Accordingly, more data may flow through the
network as links with relatively limited bandwidth are ignored,
leading to decreased congestion and enhanced overall through-
put. Aoki and Shudo [30] proposed a score-based NS protocol
where each miner scores its neighbors according to difference
between block generation time (which is typically consisted as
a timestamp within a shared block), and block receiving time at
the receiver side. That is, a neighbor that usually delivers new
blocks faster than other neighbors shall have better communica-
tions with the network, thus is given higher score. Consequently,
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
miners favor neighbors with higher scores when they need to
perform NS. Notably, this method suggests that miners select
neighbors to communicate with depending on the history of the
neighbors, which implies that it may take much time to arrive to
optimal NS in dense and dynamic networks.
Jin et al. [31] proposed clustering the Bitcoin network and
sharing the Transaction (TX) IDs instead of the TXs themselves.
That is, TXs to be shared with neighboring clusters are only
shared with them if they have not been yet received. Exchanged
messages are, then, shared with targeted destinations rather
than in a randomized fashion. The proposal was found efficient
in terms of network traffic, yet it deviates the network model
from distributed towards centralized, as each cluster has its own
leader. Additionally, security and privacy analysis were not con-
ducted, although the leader election protocol, performed within
each cluster, required private information to be shared among the
cluster (e.g. number of Bitcoins obtained by each miner, length of
online time, miners’ IDs, etc.).
Yu et al. [32] proposed that a shared block within a BC network
shall include the IDs of miners who have already received it.
Each recipient adds its ID to each received block, and forwards
it to all neighbors who have not yet received it. Apparently,
such approach requires a tree topology of the network, which
is not guaranteed in public BCs, and implies that shared blocks
are constantly modified. To solve the first issue, a method to
divide the network into subareas was proposed. The second issue,
however, may raise concerns regarding the credibility of shared
data as some nodes may behave dishonestly. Similar approaches
were proposed in Li [33] and He et al. [34], where multi-link con-
current communication schemes were utilized. The adoption of
tree structures was recommended so that a failure node shall only
isolate a sub-tree compared to a whole component in case the
network topology was mesh. Obviously, such proposal includes
several conditions that do not necessarily apply in current public
BCs. On the other hand, He et al. [34] proposed that each miner
maintains a locally saved historical log of peers’ IDs. Referring to
this log, miners may select peers to gossip with if they are not in
the historical log.
To summarize our survey, all of the presented approaches
indeed perform better than the currently adopted RNS approach.
However, all of these approaches address the NSP depending
on local views of the network, leading to local NS optimization.
Additionally, a group of those approaches requires modifying the
underlying network topology and/or violates the identity privacy
constraints usually present in public BCs.
We argue that a protocol that solves the NSP can be assumed
comprehensive if it fulfills three main criteria: (1) It optimizes
the NS depending on a global view of the network topology in a
timely manner (2) It requires no modification of the underlying
network topology and (3) It preserves the Identity privacy of all
peers within the network. As none of the current protocols has
fulfilled these requirements, one can state that the NSP has not
yet been solved for public BCs.
2.2. Semi-Distributed Minimum Spanning Tree (Semi-DMST)
To fulfill the first criterion of a comprehensive protocol that
addresses the NSP, one needs to utilize the global view of the
BC network using Graph Theory. Using this representation, one
can notice that solving its NSP is a central optimization problem,
namely the Minimum Spanning Tree Problem (MSTP) [14]. That
is, finding the MST of the graph that represents the BC network is,
in fact, finding the global solution of the NSP. This approach also
fulfills the second criterion above, as no new edges are enforced
into the graph.
It is trivial to find the MST of a given network in polynomial
time, if its topology is known, using famous algorithms such
as Prim’s [35] or Kruskal’s [36]. Accordingly, BC networks that
consist of a Trusted Third Party (TTP, which tracks system entities
and is trusted to build a global view relation graphs demon-
strating the network) can calculate the MST using one of the
well known algorithms. However, public and permissionless BCs
do not usually consist of a TTP, which implies that no entity
within the network can build a graph that demonstrates the
network. Accordingly, Prim’s, Kruskal’s, or any other algorithm
that requires a global view of the network, cannot be used in fully
distributed BCs.
Since fully-distributed BC networks are actually distributed
systems, the NSP in those BC networks can be formalized using
the Distributed Minimum Spanning Tree (DMST) problem [37].
This problem aims at computing the MST of a distributed system
without prior knowledge of network topology. This problem has
a long line of research dating back to 1926 [38], until 2018 when
the problem could finally enjoy a singular optimality state with
the protocol proposed by Pandurangan et al. [19]. That is, the pro-
posed algorithm solved the DMST problem with, simultaneously,
optimal time and optimal message complexity.
Although DMST problem has been solved in [19], and can
theoretically be deployed in public BCs, it actually cannot be
adopted by current public BCs. That is, the algorithm requires its
participants to share their identities, along with other (perhaps
considered private) data. Such requirement imposes a privacy
issue that will mostly forbid public BCs from utilizing the solution
of [19].
According to this brief description of MST and DMST problems
and their solutions, the former can be easily utilized in any BC
that consists a TTP, a network administrator who has a global
view of the network, or a gateway through which new miners
shall be confirmed. Specifically, the TTP periodically finds the MST
of the network using one of the previously mentioned methods.
Accordingly, the TTP suggests to miners the Optimum Neighbor
Selection (ONS) to enhance overall system efficiency. As the con-
dition of a TTP does not apply to public permissionless BCs, such
approach does not fulfill the first criterion of a comprehensive NS
solution.
The DMST problem, and its solution, can be used to optimize
NS in public-permissionless BCs as long as peers trust all other
peers with their private identities. That is, each node can deduce
the ONS according to data aggregated to it from all nodes of
the network, and it can communicate with all nodes in return.
However, such approach does not fulfill the third criterion of a
comprehensive NS solution.
Following these analysis, this paper attempts to solve Semi-
Distributed MST problem, which formalizes the NSP in public-
permissionless BCs. In such problem model, peers do not trust
each other with their private IDs (except for their neighboring
peers), while the network is dynamic and does not have a TTP.
The solution we propose for this problem is detailed in Section 4.
2.3. Leader election problem
A leader node in a distributed system might be needed to
perform one or more centralized tasks. In static networks, a
leader node might be statically configured, or periodically re-
selected according to a predefined criteria. Leaders are, then,
similar in their properties to all other nodes. Selecting a leader
node in dynamic networks, however, is a well known prob-
lem for distributed, P2P systems, namely the Leader Election
Problem [39]. Depending on the various aspects of the studied
distributed system, such as network topology, type of nodes,
system architecture, communication channels etc., many leader
election algorithms have been proposed. Examples of such solu-
tions include Abraham et al. [40], Al Refai [41,42] and Biswas et al.
[43].
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Mapping the Leader Election Problem to a public and permis-
sionless BC, the number of nodes and the upper limit of nodes
cannot be specified. Such problem projection requires a solution
with more restrictions and higher levels of uncertainty. Never-
theless, previously proposed solutions addressed such challeng-
ing settings even with mobile distributed systems and wireless
communications (which is not the case in the vast majority of
BC-based networks, yet even if it was, it is solved). Examples
for single leader election algorithms that can be deployed in
a public permissionless BC include the TORA algorithm [44],
Malpani algorithm [45] and SEFA algorithm [46]. Examples for
multi-leader election algorithms proper for such BC model set-
tings include Kelea [47,48]. Nonetheless, those algorithms are
of general usability and were not specifically proposed for BC
systems. The most famous leader election method, specifically
implemented for different BC network models is the RAFT elec-
tion [49]. RAFT is, basically, one step among many in the RAFT
consensus protocol. This step can be utilized within different sce-
narios. The RAFT leader election process fulfills the three main re-
quirements of a successful leader election, namely safety, liveness
and fairness [50].
Overall, most of these leader election algorithms are imple-
mentable in public BCs, if sharing the IDs and domains (e.g. IP-
addresses) of network peers have no privacy implications. That
is, if peers of the network trust all other peers with their identity
information. However, this is generally not the case in public BCs,
where each peer is only aware of its neighbors’ identities.
For such requirements, a deterministic and privacy-aware
leader election protocol, namely the Right-of-Stake (RoS), was
recently proposed by Tan et al. [51]. The RoS protocol suggests
that a peer elects itself according to local information, namely
its stake and its counter. Accordingly, if the peer fulfilled a given
condition, it starts behaving as a leader. Consequently, other peers
receiving data from the elected peer confirm it is sent by a leader
once the leader reveals its ID. Thus, only when the leader is
elected, it will give up its private ID and stake value to other
peers. Although this is indeed a privacy aware leader election
suitable for public BCs, the authors assumed that the BC network
is distributed among pools for necessity. Additionally, the RoS
protocol is suitable for synchronous BC networks. Those two con-
ditions limit the utilization of this leader election protocol in case
of asynchronous networks or non-pooled BCs. Note that nodes
of the network shall be eventually aware of the real identity of
the leader, which violates the third criterion of a comprehensive
protocol that solves the NSP in public-permissionless BCs. This
issue was addressed in [52], yet the proposed algorithms assumed
that network nodes are initially aware of the network size. Such
information is not necessarily available for miner nodes of public-
permessionless BCs, thus, the proposed algorithms are irrelevant
for our application.
According to the presented literature review of leader election
protocols, we found no previous work that is applicable to the
problem of our current research. Thus, we propose a novel pro-
tocol, namely AnoLE to address the leader election requirements
we seek. We formally define our research problem in Section 3
and detail the proposed solutions in Section 4.
3. Preliminaries and problem statement
Referring to [53], we define a public-permissionless BC net-
work as a connected, undirected, and weighted graph G=
(V,E, w), where Vis the set of nodes in Grepresenting miner
nodes, Eis the set of edges in G, representing the communication
lines between the miners, where each ei,jE, connecting exactly
two nodes i,jV, can be traveled in both directions. The nodes
of Gcommunicate by message passing via (strictly) the edges of
G. Each eEis associated with a distinct non-negative value,
namely weight (wi,jor we), which represents the transmission
time needed to deliver 1 bit of data from node ito node jor vice
versa, computed in µs.
The weight of any given graph is the sum of the weights of
all its edges. We define the set of neighbors of a node iV
as mi=(mi,1, ..mi,j). We assume that every node iGis
initially aware of its mi, and is aware of the weight associated
with each edge ei,jconnecting it with any of its neighbors. To
mathematically represent a graph, we use the adjacency matrix,
which is a matrix of size |V ×V|. The elements of the matrix are
the weights wi,jif there is ei,jand the maximum size of an integer
provided by the interpreter otherwise.
A sub-graph of Gis any graph G(V,E, w), such that VV
and EE.Gis also undirected, and weighted as it inherits the
properties of the original graph. A Spanning Tree (ST) of Gis a
connected acyclic sub-graph of Gwhere V=Vand E=V1.
A Minimum Spanning Tree (MST) of G(with distinct weeE)
is a unique ST where the weight of MST is minimum compared
to all STs of G.
A hashing function, or a one-way encryption function, h(.)
is a mathematical function that takes a variable-length input
string and converts it into a fixed-length binary sequence that
is computationally difficult to invert [54]. A hashing function
enables the determination of a message’s integrity: any change to
the message will, with a very high probability, result in a different
message digest [55].
Our research problem is to find the subset ki=(k1, ..kn)mi,
iV, such that ei,kMSTGkki. We call the solution
of our problem the Optimum Neighbor Selection of node iV
(ONSi) of a public-permissionless BC network. We aim at solving
this problem using a protocol that fulfills the following privacy
condition:
iVσ
i=σi+ONSi(1)
where σiis the total knowledge of miner ibefore starting the pro-
tocol and σ
iis the total knowledge of miner iafter the protocol
is terminated.
4. The proposed DONS protocol
In this section, we describe the phases of the proposed DONS
protocol and the proposed algorithms and methods for each
phase. The generalized framework addresses a public permission-
less BC with no TTP, and initially assumes all network entities are
honest. However, we discuss counter assumptions where applica-
ble. The phases and steps of the DONS protocol are demonstrated
in Fig. 1.
4.1. Phase-1: Leader election
First of all, the DONS protocol requires a global view of the
underlying BC network, so that the MST can be computed. Ad-
ditionally, miners joining and leaving the network implies that
this global view, and accordingly the computed MST, shall be
regularly updated. In a public and permissionless BC model, all
BC miners have the same access permissions and the same level
of abstraction. However, one (or a committee) of these miners
may perform the MST computations for all other miners. This
way, the network decides best practices regarding networking
and gossiping without administrative interference, which leads
to Smart Networking [56].
In this section, we propose the Anonymous Leader Election
(AnoLE) protocol which shall not violate any of the comprehen-
sive NS solution criteria discussed in Section 2.1. The elected
leader (single leader in our current work) shall collect non-private
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Fig. 1. Phases and steps of the proposed DONS protocol. Each step is performed by one (or more) system entity(s). A step may depend on the result of a preceding
step of the current round, or on the result of a subsequent step of the previous round.
local views from all peers, construct a network demonstration,
solve the MST problem of the network graph, and finally broad-
cast the anonymized MST throughout the network. The recipient
nodes shall only be able to read their own, and their neighbors’
IDs. Thus, neither the leader nor any other network entity can
deduce miners’ private data throughout the run of the protocol.
Note that this condition implies that a miner does not know
the identity of the leader, unless the miner itself (or one of its
neighbors) was the leader.
The challenge of this phase is to dynamically select the
leader(s). Specifically, selected leader(s) has similar properties to
all other nodes, such as failure/unavailability probability (with
different failure rates), and nodes being aware of minimum prop-
agation delays only with their adjacent neighbors. The gener-
alized workflow of the proposed AnoLE protocol is depicted in
Fig. 2. Different system entities utilize the AnoLE protocol as
follows:
Step-0 (Initialization): All nodes know their neighbors iden-
tities and the corresponding Round-Trip-Time (RTT) ex-
pected when communicating with each of them. All nodes
use this protocol honestly, with default status ’Normal_Peer’,
Default Required Confirmations (DRCs) equals the aver-
age number of neighbors per peer, ’Current_Leader’ = null,
default round time T, and MST set to empty array.
Step-1 (LE trigger): Once a node ifails/joins the network,
its neighbors, denoted mi= {mi,1, ..mi,j}, are triggered to
start the AnoLE protocol. Each neighbor mi,kk1, ..jsets
its status to ’Probable_Leader’, sleeps for an arbitrary time
(default setting: waiting time is randomly selected between
0 and T/2), and sends ’AnoLE-1’ message to all neighbors.
The ’AnoLE-1’ message contains h(i) and h(mi,k), along with
timestamp t. votes = Dict{} and LVs =list[] are initiated to
later save the responses of the AnoLE-1 message.
Step-2 (Failure check): all nodes that receive ‘AnoLE’ mes-
sages, run Algorithm 1. Accordingly, Normal_Peers (NPs) run
Algorithms 2,3and 4, sequentially, in order to obtain the
Required Confirmations (RCs), a list of hashes of nodes in the
set mi, and the Local View (LV), respectively. These recipient
nodes wait until they receive a number of distinct AnoLE
messages equal to RCs (if Ttime units passed with no suffi-
cient AnoLE messages, the node does not vote). The recipient
checks three conditions to consider the node failure/joining
reports correct: (1) Every distinct AnoLE message shall con-
tain similar h(i) and different h(mi,k). These messages repre-
sent failure/joining proofs (2) Each h(mi,k) should belong to
the list of Neighbors returned by Algorithm 3, which assures
that reports are only sent by genuine neighbors and (3) All
neighbors in this list shall send an AnoLE-1 message. This
represents a consensus among neighbors on the honesty of
the AnoLE protocol trigger (i.e. those neighbors do not know
or trust each other by assumption).
In the special case of an empty MST (which happens only
at the first time the protocol is run), recipients ignore con-
ditions 2 and 3. When iis joining the network, the DRCs is
used instead of the RCs.
Step-3 (Voting): Once a recipient node receives a suffi-
cient number of ‘AnoLE’ messages that fulfill the condi-
tions in Step-2, the recipient can be sure that ihas indeed
failed/joined as all its neighbors witnessed. The NP then
selects one of the received h(mi,k)s according to a predefined
criteria (e.g. randomized, first sender, highest hash value,
etc.) and modifies its ’Current_Leader’ to the selected h(mi,k).
After that, NPs broadcast ’AnoLE-2’ messages to all its neigh-
bors, which contain their hashed IDs along with the contents
of ’AnoLE-1’. AnoLE-2 messages, then, declare that NPs who
generated them vote for, specifically, the candidate leader
whose hash is included in their AnoLE-2 message. In the
context of the DONS protocol, NPs also deposit their current
LVs of the network into their generated AnoLE-2 messages.
LV is obtained by running Algorithm 4. NPs who have a
previous version of the MST (i.e. obtained from previous
AnoLE protocol run), may utilize it to share their AnoLE
messages with their ONSs. A condition to be fulfilled in order
to utilize the previous ONS, however, is that non of the ONS
members has an ID whose hash is equal to h(i).
Step-4 (Leader Declaration): Whenever a message of type
’AnoLE-2’ is received by a ’Probable_Leader’, it runs Algo-
rithm 5, which saves new votes and LVs. Once a ’Proba-
ble_Leader’ finds that: current_time - t T, it runs Algo-
rithm 6, which counts the votes received so far and converts
the node’s status into either ‘Leader’ or ’Normal_Peer’.
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Algorithm 1: Message handler
1Input AnoLE_msg;
2Function Share_msg_with_neighbors(msg)
3if ONS and AnoLE_msg[h(i)] not in ONS then
4neighbors = ONS
5else
6neighbors = self.neighbors
7end
8for neighbor in neighbors do
9send(msg, neighbor)
10 end
11 end
12 if AnoLE_msg[’type’] == ’AnoLE-3’ and current_leader ==
AnoLE_msg[’leader’] then
13 run Algorithm 8
14 else
15 if self.status == ’Normal_Peer’ then
16 if current_time - AnoLE_msg[t] < T then
17 run Algorithm 2;
18 Share_msg_with_neighbors(AnoLE_msg)
19 end
20 end
21 if self.status == ’Probable_Leader’ then
22 if current_time - AnoLE_msg[t] Tthen
23 Share_msg_with_neighbors(AnoLE_msg)
24 if AnoLE_msg.type == 2 then
25 run Algorithm 5
26 end
27 else
28 run Algorithm 6
29 end
30 end
31 end
The identification criteria of nodes can be selected upon sys-
tem design. That is, in a public permissionless BC, such as Bitcoin,
pseudonyms are used to preserve the privacy of end-users [1].
However, true identities in a private or permissioned BC may be
used. We believe the distinction between identity management
schemes, and thus the adoption of one over the other, is be-
yond the scope of our work. That is, the selection of an identity
management scheme is dependent on/related to the application
definition and the required trust model. Our proposal, on the
other hand, is specifically concerned with the optimization of
neighbor selection, which shall be related to both the Consen-
sus and the Network layers of any given BC. Consequently, no
matter what identity scheme is applied, our proposed AnoLE
protocol satisfies the condition described in relation (1). Detailed
information regarding different BC layers can be found in [57].
Note that a generated/received AnoLE message might be sent
to all neighbors, which implies that all probable leaders shall
eventually know the winner leader if Twas sufficient. However,
a subset of the network might not have enough time to vote for
a leader and receive its MST. This seems OK as nodes use their
ONS if available, and broadcast otherwise. With several runs of
the AnoLE protocol, and dynamic modification technique of T,T
would become more precisely adequate/sufficient. A simple mod-
ification technique of Tcan be defined according to application
requirements. For example, nodes may assume that not receiving
the MST from the leader they voted for indicates insufficient T.
Thus, those nodes may double Tfor next rounds. On the other
hand, receiving the MST sooner than the end of Tindicates that
Algorithm 2: Check local records
1Input AnoLE_msg;
2if AnoLE_msg[h(i)] in self.AnoLE_records then
3if AnoLE_msg[h(mi,k)] NOT in
self.AnoLE_records[h(i)][’Ks’] then
4self.AnoLE_records[h(i)][’Ks’].append(h(mi,k))
5end
6else
7self.AnoLE_records[h(i)] = Dict{}
8self.AnoLE_records[h(i)][’Ks’] = h(mi,k)
9self.AnoLE_records[h(i)][’voted’] = False
10 end
11 M_K, RC = RFC(AnoLE_msg) (Algorithm 3)
12 if M_K is NOT empty then
13 C_1 = AnoLE_msg[h(mi,k)] in M_K
14 C_2 = M_K self.AnoLE_records[h(i)][’Ks’]
15 else
16 C_1 = C_2 = True
17 end
18 C_3 = len(self.AnoLE_records[h(i)][’Ks’]) RC
19 C_4 = NOT self.AnoLE_records[h(i)][’voted’]
20 if C_1 AND C_2 AND C_3 AND C_4 then
21 self.Current_Leader = self.AnoLE_records[h(i)][’Ks’][0]
22 my_LV = LV_Computation() (Algorithm 4)
23 my_AnoLE-2 = [AnoLE_msg[t], h(self.ID),
AnoLE_msg[h(i)], self.Current_Leader, my_LV]
24 self.AnoLE_records[h(i)][’voted’] = True
25 Share_msg_with_neighbors(my_AnoLE-2)
26 end
Algorithm 3: RFC
1Input AnoLE[h(i), h(mi,k), t];
2Function FIND_neighbors(entity)
3Neighbors = List[]
4for row, column in MST do
5if row[0] == entity and MST[row][column] < infinity
then
6Neighbors.append(MST[0][column])
7end
8end
9return Neighbors
10 end
11 list_of_m = List[];
12 if MST is NOT empty then
13 list_of_m = FIND_neighbors(h(i))
14 end
15 RC = len(list_of_m);
16 if RC == 0 then
17 RC = DRC
18 end
19 return list_of_m, RC
Tis bigger than needed. Thus, nodes may compute the average
of Tand the time elapsed from voting till receiving the MST.
The AnoLE protocol utilizes the Epoch time which implies that
the location of miners, and distinct transmission delays would
not impose a synchronization problem. All nodes thus use the
same reference time and all nodes will track Taccurately. Hence,
all nodes will initiate/terminate the protocol according to unified
timestamps.
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Algorithm 4: Local View (LVi) Computation
1Anonymized_LV = List[];
2Hashed_IDs = List[];
3Weights = List[];
4for k in mido
5Hashed_IDs.append(h(k));
6Weights.append(RTT(k)/2)
7end
8Anonymized_LV.append(Hashed_IDs);
9Anonymized_LV.append(Weights);
10 return Anonymized_LV
Algorithm 5: Voting
1Input AnoLE-2[t,h(voter), h(i), h(mi,k), LV];
2if NOT votes[h(i)]then
3votes[h(i)] = Dict{timestamp,
4info:{’voters’: [h(voter)],
5’votes’: 1}}
6self.LVs.append([h(i), h(voter), AnoLE-2[LV]])
7end
8if NOT votes[h(i)][h(mi,k)]then
9votes[h(i)][’info’][h(mi,k)] = Dict{’voters’:
[h(voter)];’votes’: 1}
10 self.LVs.append([h(i), voter, AnoLE-2[LV]])
11 end
12 if NOT h(voter) in votes[h(i)][’info’][h(mi,k)][’voters’] then
13 votes[h(i)][’info’][h(mi,k)][’voters’].append(h(voter))
14 votes[h(i)][’info’][h(mi,k)][’votes’] += 1
15 self.LVs.append([h(i), h(voter), AnoLE-2[LV]])
16 end
Algorithm 6: Leader Recognition
1Input AnoLE[t,h(i)];
2global_max_votes = 0;
3Leader = null;
4for PL in votes[h(i)]do
5PL_votes = PL[’votes’]
6if PL_votes > max_votes then
7max_votes = PL_votes
8Leader = PL
9end
10 end
11 self.current_leader = PL
12 if Leader == h(self.ID) then
13 self.status = ’Leader’
14 else
15 self.status = ’Normal_Peer’
16 end
4.2. Phase-2: Computing and broadcasting MST
Assuming that Twas sufficient for all NPs to vote and for all
PLs to receive those votes, we anticipate that by the end of Phase-
1, the Leader (L) is recognized by all PLs and by the majority
of network miners. Each PL returns to the state ‘NP’ except for
L. Consequently, Phase-2 is triggered and is performed by Las
follows:
Step-1 (Construct NT): Luses its locally saved LVs to con-
struct the anonymized global network topology (NT), repre-
sented by an adjacency matrix NT. Algorithm 7details how
Lcomputes NT.
Step-2 (Compute MST): Lutilizes Prim’s approach [35] to
find MSTNT . Note that any other (perhaps better) approach
can be utilized here, e.g. [58,59].
Step-3 (Broadcast MST): Lastly, the Leader derives its own
ONS from the MST it built, as described in Step-2 of Phase-
3, and uses it to send the MST to its neighbors in its ONS.
The MST is encapsulated in an AnoLE-3 message, which also
contains h(L) and the time of MST generation.
Algorithm 7: Construct Network Topology
1Input h(i);
2Network_topology = array[[0]];
3Function ADD_node(node)
4if NOT node in Network_topology[0] then
5Network_topology[0].append(node)
6Network_topology.append([node])
7end
8end
9for LV in self.LVs do
10 if LV[0] == h(i)then
11 ADD_node(LV[1])
12 for neighbor in LV[2][0] do
13 ADD_node(neighbor)
14 node_index_NT =
Network_topology[0][LV[1]].index
15 neighbor_index_NT =
Network_topology[0][neighbor].index
16 neighbor_index_LV = LV[2][0][neighbor].index
17 weight = LV[2][1][neighbor_index_LV]
18 Network_topology[neighbor][node_index_NT] =
weight
19 Network_topology[LV[1]][neighbor_index_NT] =
weight
20 end
21 self.LVs.delete(LV )
22 end
23 end
24 if Network_topology is connected then
25 return Network_topology
26 else
27 return None
28 end
Algorithm 8: Derive ONS from MST
1Input AnoLE-3;
2for key in MST do
3if key == h(self .id)then
4return MST[key]
5end
6end
4.3. Phase-3: Processing received MST to get ONS
Step-1 (Verify L): Once a NP receives an AnoLE-3 message,
it checks whether this message was generated by the leader
it previously voted for. The assumption of an adversary
node impersonating the real leader is valid. However, such
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
impersonation probability may be solved using asymmetric
encryption techniques, where the leader couples a public
key with its AnoLE-1 message. Later, the leader can sign the
AnoLE-3 message using its private key. This step also implies
that the recipient NP is expecting to be present within the
proposed MST. Otherwise, this NP will not accept the MST
despite it was sent by the leader the NP elected.
Step-2 (Derive ONSi): Every miner (including current Land
previous PLs) that receives a verified MST (within an AnoLE-
3 message) derives its own ONS by running Algorithm 8. The
derived ONS is utilized then to optimally select and share
data.
Step-3 (Award Land utilize ONSi): In case the leader shall be
incentivized for its work, the leader may include its wallet
id within its AnoLE-1 message. The leader then includes this
piece of information within its signature, which adds an-
other layer of verification. Miners which receive the AnoLE-3
message award the leader by adding a predefined amount of
digital assets into the leader’s wallet. Note that in this case,
the AnoLE-3 message also represents a TX that needs not to
contain the leader’s wallet ID nor its public key because they
have already been shared within the AnoLE-1 message.
5. Evaluation
In this section we perform a detailed evaluation of our pro-
posed DONS protocol in terms of security, privacy, time and mes-
sage complexities, Finality and Fidelity. We compare the AnoLE
and the DONS protocols with current methods, and we indicate
the strengths, the weaknesses, and open issues of our proposed
methods.
Our experiments were carried out on a DELL PC with an
Intel i5-8265U CPU (8-Cores, 3.8 GHz) with 12 GB DDR4-SDRAM,
500 GB of SSD and Windows-10 OS.
5.1. Security analysis
Referring to Cachin et al. [60], the following security properties
must be guaranteed by a successful distributed protocol:
1. Strong validity: If all honest nodes propose the same value
v, then no honest node decides a value different from v.
This property is indeed guaranteed by the AnoLE and DONS
protocols. That is, if all NPs voted for a probable leader k,
all probable leaders will announce kas leader. Later, all
nodes who voted for kwill accept its proposed MST. The
processes that guarantee this property is detailed in Algo-
rithm 1(lines: 12–14) and Algorithm 6. Further, NPs only
vote for a PL who they heard from, which is guaranteed by
Algorithm 5.
2. Agreement: No two honest nodes decide differently. This
property is implicitly guaranteed by the AnoLE and DONS
protocols. That is, if Twas not sufficient, different PLs
may announce different leaders, and different NPs may
vote for different PLs. However, only one leader can obtain
a majority of votes, leading later to the ineffectiveness
of other PLs announcements. The MST computed by PL
whom was voted for by the majority of NPs, will be the
only MST adopted by this majority. If incentivization was
included, the PL who was voted for by the majority will
be incentivized by the majority as well. Accordingly, the
decisions of the minority of NPs who voted for, adopted
the MST of, and incentivized other PLs, will not be adopted
by the network as the majority rule applies in BC systems.
Nevertheless, this property can be surely guaranteed if T
was sufficient, resulting in all votes arriving to all PLs and,
thus, all honest PLs announcing the same leader. The pro-
cesses that guarantee this property is detailed in Algorithm
1(lines:12–14) and Algorithm 6.
Fig. 2. Workflow of the proposed Anonymous Leader Election (AnoLE) protocol.
3. Termination: Every honest node eventually decides some
value. This property is guaranteed in the AnoLE protocol
as each PL changes its status to either L or NP once T
has passed. Consequently, any following AnoLE messages
received by the node after changing its status shall be
ignored. The leader also changes its status to NP once it
calculated the MST and shared it with its neighbors. The
termination point of the protocol is detailed in Algorithm
1(lines: 16 and 22). Additionally, all NPs decide which LP
they want to vote for, as declared in Algorithm 2(line:
21). All PLs decide what their next status is, who is the
winning PL, and who is their current leader, as declared in
Algorithm 6.
4. Integrity: No honest node decides twice. This property is
guaranteed in the AnoLE protocol for both PLs and NPs,
while leaders do not make any decisions. The integrity of
decisions made by PLs and NPs are guaranteed using the
processes detailed in Algorithm 6(lines: 11 to 16) and
Algorithm 2(line: 19). Later, every NP shall decide whether
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
to accept or reject a received MST for the current round,
depending on the generator. If the leader who generated
the MST was voted for by this NP, the MST is adopted and
the leader may then be awarded. This process in declared
in Algorithm 1(lines: 12–13).
A successful distributed ledger shall provide three properties,
namely the Consistency, the Availability, and the Partition Tol-
erance[61]. Mapping these properties onto our DONS security
discussion, we state that these issues are not of a concern with
the DONS protocol. That is, non consistent MST distribution leads
to some NPs performing NS according to randomized selection
rather than ONS, which is declared in Algorithm 1(lines: 2–
11). This may negatively affect the overall finality time, yet it
has nothing to do with the consistency of the distributed ledger.
Furthermore, in the case where leaders are to be incentivized, the
original majority rule applies, which implies that if the original BC
was consistent before adopting DONS, it will remain consistent
after. Similar argument can be stated regarding the Availability
issues.
Regarding the Partition tolerance issues, the BC network could
be partitioned into two networks if a failing node was a bridge
node, which should be solved by the original network architec-
ture, e.g., by requiring a minimum number of neighbor connec-
tions upon joining the network. However, it is not harmful to
adopt different MSTs by different parts of the network, as this
would lead to higher finality time but not a disconnected network
(i.e. compared to finality time with unified MST. However, even in
such case, DONS shall perform better than RNS and RTT-NS). Note
that a disconnected network topology constructed by the leader
would not trigger the leader to compute and share the MST, as
declared in Algorithm 7(lines: 24–28). Eventually, NPs who do
not receive the MST by the end of T, shall terminate the round and
continue using their original NS method (e.g. RNS or RTT-NS). If a
minority of NPs receives an MST from another leader, they may
use it and incentivize their leader, yet the incentive would not
be confirmed by the majority of miners, leading to correct and
consistent ledger even with partitioned network.
From another point of view, it could be argued that the uti-
lization of our proposed protocols and the resulting provision of
network topology may encourage an eclipse attack [62] leading
to DoS [63] or Double Spending [64] attacks. However, Wüst
and Gervais [65] described several countermeasures that can be
adopted to prevent eclipsing. To address this issue in DONS, we
emphasize that each peer in the network maintains its own set
of connections, out of which a subset is used to communicate.
This is, a peer is not practically isolated from the network and
can simply adopt a checker mechanism to secure itself against
a logical isolation. Note also that the subset derived from the
MST (i.e. ONS) could include more than one, randomly selected
neighbor according to the structure of the MST.
A checker mechanism aims at regularly validating the peer’s
local BC version against neighbors’ versions. This way, peers can
be sure that they have not been eclipsed by an adversary leader
or neighbor. ONS can be simply withdrawn by a peer that has
been eclipsed, and it can get back to using its original NS method
until a new AnoLE round is triggered. Furthermore, a reputation
mechanism, similar to the one adopted by the Proof-of-Stake
protocol [66], can be developed.
Next, we discuss the security issues provided by DONS and
AnoLE protocols in probable situations that may appear in real-
life scenarios:
1. Problem: Leader provides an MST that provides the ONS of
only a minority (or none) of the network.
Solution: The puzzle that the leader needs to solve is to
find the networks’ MST that includes as many network
nodes as possible. Accordingly, the proposed MST would be
accepted by the majority upon verification. As the puzzle
solution is hard to find, the solution is easy to be verified on
the NP side by checking if it was included in the proposed
MST. Every NP checks whether the MST is proposed by the
leader the NP voted for, and whether it is included in the
MST. Thus, the MST can be rejected even if it was generated
by the leader the NP voted for. Consequently, the more
nodes included in the MST, the higher the probability for
the MST to be accepted by the majority. This is declared in
Algorithm 8(line: 3).
2. Problem: No Leader was announced, which means each PL
announced other PL due to inconsistency in voting distri-
bution.
Solution: Network nodes would keep running using their
previous ONS or, in case they had no ONS, a random-
ized/RTT -based NS. This is declared in Algorithm 1(lines:
2–11).
3. Problem: Multiple Leaders were announced.
Solution: Only one MST will be adopted by the majority
of network nodes, as each node only adopts the MST pro-
posed by the Leader it already voted for. If incentives to
be granted upon proposing a new MST, the Leader with
actual majority number of voters will be incentivized by
the majority. Thus, only one Leader will be eventually
incentivized by the network. This is declared in Algorithm
1(lines: 12–14) and Algorithm 2(line: 21). As PLs know
this, no PL node shall dishonestly claim to be a leader node
as the work spent to find the MST would not be recognized
by the majority. This is declared in Algorithm 1.
4. Problem: Round-time Tis not sufficient to deliver all votes
to leaders.
Solution: Round-time Tshall be dynamically modified as
would be discussed in Section 6. Furthermore, this would
lead to MST proposal that is not inclusive. Accordingly, the
leader would not be incentivized. when a node receives an
MST that does not include its ONS, it shall automatically
increase its default Round-Time Tas it would assume that
its LV did not have sufficient time to arrive to the leader.
Nevertheless, this should not imply a problem as discussed
regarding the partition tolerance above.
5. Problem: A dishonest PL claimed there was a failing/joining
node in order to get incentivized, but the truth is there was
no failing/joining node.
Solution: NPs require a minimum number of RCs, as de-
clared in Algorithm 3. These could only be generated ran-
domly and it is unlikely that all neighbors are adversaries
and that they collaborate with each other. In any public-
permissionless BC, a node is connected, upon joining, to
a group of randomly selected neighbors. Accordingly, it
is nearly impossible to get all neighbors to agree on the
failure of a node that did not fail. However, a dishonest PL
may generate several fake AnoLE-1 messages claiming that
a node has just joined the network. In this case, NPs assume
that the RCs they receive are from nodes that are already
existent in the network and they are not just joining. Ac-
cordingly, a NP checks the validity of each received RC, by
looking for the RC’s generator in its previous MST (i.e. the
NP’s MST). Consequently, RCs are only accepted by nodes
who are already proven as nodes of the network. This is
declared in Algorithm 3(lines: 2–10).
6. Problem: A dishonest NP provided a faulty LV.
Solution: if hashes of neighbors of this NP are faulty, this
NP will not be connected to the network in the proposed
MST and will not be able to obtain its ONS. As described
in Algorithm 7: lines 12–20. Nevertheless, neighbors of the
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Table 1
Time complexity of each algorithm utilized during the first two phases of the
DONS protocol (the AnoLE protocol).
Algorithms Time complexity
worst-case(dense graph) best-case (sparse graph)
Algorithm-1O(|V|2)(1)
Algorithm-2O(|V|2)(1)
Algorithm-3O(|V|2)(1)
Algorithm-4O(|V|)(1)
Algorithm-5O(1) (1)
Algorithm-6O(|V|)(1)
Algorithm-7O(|V|3)(V)
DONS time complexity O(|V|3)(V)
DMST O(D+|V|) -
faulty NP will provide correct LVs as it is unlikely that
neighbors collaborate. Accordingly, the ONS the faulty NP
would eventually get would be correct. As the fake neigh-
bors claimed by the faulty NP have only been claimed to be
connected to by this NP, then these fake neighbors would
be leafs in the produced MST and would not affect ONSs of
other honest NPs. If hashes were correct but the weights
are non-correct, non of the neighbors of this NP will pro-
vide similar faulty information, unless the neighbors are
collaborating in this. Such collaboration is not possible as
described above. The purpose of Algorithm 7is to solve
such problem on the leader side, and for this reason it has
the highest time complexity, as will be detailed later.
7. Problem: PL cheated and did not wait for randomly se-
lected time after AnoLE trigger.
Solution: This might lead to one or more of the previ-
ously discussed problems (specifically 1–4). Accordingly,
a cheating PL would not benefit from such behavior as
discussed earlier. However, to guarantee that PLs accu-
rately wait for the selected random waiting time, Trusted
Execution Environments (TEE) [67] can be used. Note that
this is not mandatory for security reasons but for efficiency
guarantees reasons.
5.2. Privacy analysis
Next, we discuss the identity privacy preservation [68] pro-
vided by our proposed AnoLE and DONS protocols. As detailed
in Sections 2.1 and 2.3, our proposed methods must guarantee
the privacy condition (1) proposed in Section 3. Following the
description of the proposed protocols in the previous sections,
one can notice that data shared between network nodes are
exchanged in the form of AnoLE messages. For any given node
a, it can receive the three types of AnoLE messages generated by
all, or a subset of, network nodes.
The AnoLE-1 message includes the hash of the node iid that
left/joined the network, the hash of its neighbor jid, and the
timestamp of the message. According to the definition of a hash
function provided in Section 3, node acannot obtain any private
information about ior jfrom AnoLE-1 messages.
The AnoLE-2 message is similar to the AnoLE-1 message, with
the addition of the hash of a’s id, the hash of the elected leader
id, and the Local View of a(LVa). LVaconsists of the hashes of
ids belonging to the neighbors of a, in addition to the RTT ahas
measured between itself and its neighbors. Thus, any other node
bcan see that a node with id hash h(a) is connected to a number
of neighbors with id hashes h(1), ..h(n) with links of some given
weights. However, bcannot determine the true identities of anor
its neighbors, which makes the knowledge of weights on the links
useless. In the case where a, or any of its neighbors, is a neighbor
to b,bcan only determine the true identity of its neighbors.
The last type of exchanged messages is the AnoLE-3 message,
which includes the hash of the leader id h(L) and the MST. Note
that the MST is a collection of reduced LVs and, thus, what applies
to the LV knowledge deduction applies to the MST. Note also,
that network nodes accept the anonymized MST and deduce their
ONSs by comparison and not by decryption. That is, each node
constructs a list of hashes of its neighbors and compares these
hashes with hashes in the MST. Additionally, nodes compare the
hash of the leader they voted for, with the hash of the AnoLE-3
message generator. If the two were compatible, the MST within
the AnoLE-3 message is accepted.
As can be noted from this description, by the end of the
protocol run, network nodes can only read the true identities of
their neighbors. Additionally, even the leader cannot read any
true identity in the MST it builds unless it was for itself or for
one of its neighbors. Network nodes further vote for leaders, and
accept leaders’ MSTs without any knowledge of true identities of
leaders.
5.3. Time and message complexity for generating the MST
Next, we evaluate the time and message complexity of the
DONS protocol, from the moment when the AnoLE protocol is
triggered, until all network nodes are aware of the network’s
MST (i.e. until the end of Phase-2). Table 1 presents the time
complexity of each algorithm utilized in Phase-1 and Phase-2.
Table 2 presents the message complexity of each step of the
two phases. We compare the final complexities of the first two
phases of DONS with the complexities of the method proposed
in [19] (notated as DMST). This is because the first two phases
of the DONS protocol, which consists of the AnoLE algorithms,
aim at providing each node in the network with knowledge
about the MST. This objective is similar to the objective of the
method proposed in [19]. Following this notation, both the AnoLE
protocol and the DMST protocol can be effectively deployed into
the DONS protocol. The distinction between the outperformance
of the AnoLE protocol compared with the DMST protocol in
terms of privacy is discussed in the previous subsection. Higher
AnoLE complexities, however, are the cost of a privacy preserving
protocol to obtain MST in a our semi-distributed model.
We have implemented the AnoLE protocol using Python 3.8
with utilization of popular packages such as multiprocessing,
threading, networkx, hashlib, among others. Our implemented
code is publicly available at GitHub.1To validate our implemen-
tation, we performed several experiments utilizing two random
network models, namely Erdős–Rényi (ER) model and Barabási–
Albert (BA) model. We oscillated the number of nodes to cap-
ture the protocol behavior within different network sizes. The
configuration we used for running our experiments, along with
the simulation results, are presented in Table 3 and depicted in
Figs. 3,4,5and 6.
5.4. Comparison with current methods
In this subsection, we experimentally evaluate the perfor-
mance of DONS-based BC networks, in terms of block finality
time [5] and Fidelity [69]. We compare our results to two NS ap-
proaches, discussed previously in Section 2.1, namely randomized
NS (RNS) and RTT-based NS (RTT-NS). We utilize two random
network models to perform our experiments, namely Erdős–
Rényi (ER) model [15] and Barabási–Albert (BA) model [16]. For
both models, we oscillate the configuration of network size and
1https://github.com/HamzaBaniata/AnoLE_Protocol.
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Table 2
Message complexity of each step during the first two phases of the DONS protocol (the AnoLE
protocol).
Phases Steps Message complexity
worst-case(dense graph) best-case (sparse graph)
Phase-1
Step-1 O(|V|3)(|V|)
Step-2 –
Step-3 O(|V|3)(|V|)
Step-4 –
Phase-2
Step-1 –
Step-2 –
Step-3 O(|V|)(|V|)
DONS message complexity O(|V|3)(|V|)
DMST O(|V|2)(|V|)
Table 3
Results of the AnoLE protocol simulation experiments on two random network models with different sizes.
Network model
BA ER
Number of nodes 100 200 300 500 100 200 300 500
Avg.no.neighbors 2 2 2 5 – – –
Connection probability – – – 0.05 0.02 0.015 0.01
Default round-time 30 40 60 60 30 40 50 60
DRC 2 2 1 2 2 2 2 2
Time(s) 15.9 25.84 33.6 55.44 16.05 23.18 29.6 56.38
No.of exchanged messages 676,071 3,237,133 5,871,463 16,380,174 788,139 3,321,310 7,054,606 13,617,211
Fig. 3. Required time (seconds) for running the AnoLE protocol until delivering
a connected MST to nodes of a Barabási–Albert random network with different
sizes.
average number of neighbors per miner, to demonstrate the
consistency of our previous analysis with real-life scenarios.
Specifically, we developed a (Python v:3.8) network simulator,
where a random BC network is built and a randomly selected
miner represents the source node of a block of data. The gen-
erated block is then shared by the source node with a group of
neighbors, each of the neighbors shares the block similarly with
a group of its neighbors, etc. The simulation terminates once the
block reaches all nodes of the network, mimicking the push-based
gossiping approach generally adopted by all BC applications. The
compared three NS methods are utilized consequently using the
same network for the same block being generated by the same
source node. At the termination of each simulated scenario, total
finality time and number of redundant messages are calculated.
As miners in public-permissionless BC networks are randomly
connected, analyzing the results obtained from running our de-
veloped simulator indicates the best NS approach in terms of
fidelity and finality. Consequently, we could experimentally prove
that the adoption of such NS approach leads to enhanced DL
consistency. Our implementation workflow is demonstrated in
Fig. 7.
Fig. 4. Required time (seconds) for running the AnoLE protocol until delivering
a connected MST to nodes of an Erdős–Rényi random network with different
sizes.
Fig. 5. Total number of exchanged messages for running the AnoLE protocol
until delivering a connected MST to nodes of a Barabási–Albert random network
with different sizes.
Finality is the assurance or guarantee that data cannot be
altered, reversed, or canceled after they are completed [70]. To
achieve optimal finality in a given BC, shared data needs to be
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Fig. 6. Total number of exchanged messages for running the AnoLE protocol
until delivering a connected MST to nodes of a Erdős–Rényi random network
with different sizes.
Fig. 7. Simulation workflow for push-based gossiping in BCs utilizing DONS, RNS
and RTT-NS protocols.
spread as soon as possible through the BC network, so that miners
can adopt this data before a new piece of data is generated. The
latency level of a BC shall, then, ultimately affect its finality rate.
Fidelity, on the other hand, is the degree to which a technique
can provide consistency guarantees [69]. To evaluate DONS in
terms of fidelity, we count the number of cycles a generated
data walks, in a BC network, when utilizing DONS, RNS and
RTT-NS. That is, more cycles indicate the overhead on network
connection links, overhead in computation at the node level and,
accordingly, higher overall finality time. To count the number of
cycles a shared data walks, nodes are instructed to count the
number of replicated messages they receive. Simultaneously with
running the simulation scenarios, a finality-checker process is
implemented that regularly checks whether all nodes have yet
received the shared data. Once returned a True value, all nodes
are shut down and the main Analysis function is triggered.
We made our simulator code publicly available at a GitHub
repository.2We run several simulation scenarios, as described in
Table 4. The results of our experiments are presented in Table 4
and Figs. 8–11.
2https://github.com/HamzaBaniata/DONS_simulator.
Fig. 8. Total Finality time of a randomly generated block by a randomly selected
miner, in a Erdős–Rényi (ER) network model (with connection probability =0.1).
Fig. 9. Total number of exchanged messages until a randomly generated block,
by a randomly selected miner, is delivered to all network nodes, in a Erdős–Rényi
(ER) network model (with connection probability =0.1).
Fig. 10. Total Finality time of a randomly generated block by a randomly
selected miner, in a Barabási–Albert (BA) network model (with avg. no. of
neighbors per miner =5, 5, 7, 10, respectively).
6. Discussion
In the previous sections, we presented our proposed algo-
rithms and techniques in detail for both DONS and AnoLE proto-
cols, and shared their open-source implementations. We further
discussed how our proposed protocols address different misbe-
havior situations of system entities in Section 5.1, in order to
validate the security of our proposal. In Section 5.3 we compared
the AnoLE protocol with a recently proposed method for solving
the distributed MSTP, in terms of time and message complex-
ities. Furthermore, we compared the performance of different
network models in terms of Finality and Fidelity in Section 5.4,
by validating our proposed protocols against earlier methods.
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H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
Table 4
Performance of the DONS protocol against RTT-NS and RNS protocols, on two random network models with different sizes.
Model Number of nodes Network parameter Finality time (µs) Number of exchanged messages
Avg.no.neighbors/node DONS RTT-NS RNS DONS RTT-NS RNS
BA
50 5 204 2,343 8,463 50 74 253
100 5 367 5,139 24,667 100 142 751
150 7 310 5,008 40,870 150 182 1,514
200 10 176 6,927 61,429 200 251 2,241
Connection probability
ER
50 0.1 629 4,176 14,510 50 79 371
100 0.1 450 3,558 14,533 100 123 496
150 0.1 257 5,795 26,932 150 199 851
200 0.1 260 4,363 45,656 200 236 1,676
Fig. 11. Total number of exchanged messages until a randomly generated block,
by a randomly selected miner, is delivered to all network nodes, in a Barabási–
Albert (BA) network model (with avg. no. of neighbors per miner =5, 5, 7, 10,
respectively).
Based on the results we can state that our proposed protocols
significantly enhance the levels of Finality and Fidelity in the
studied networks, due to the provision of globally optimal NS
techniques.
Although the time and message complexities for the first
two phases of the DONS protocol are higher than those of the
recently proposed DMST method, we argue that this shall not be
problematic in real-life scenarios. That is, the first two phases of
the DONS protocol (represented by the AnoLE protocol) are only
triggered, when a node joins or leaves the network. With average
miner active time extending to weeks, and even months for
many cases, average complexities of the DONS protocol, through
long periods of time, shall be decreased. That is, the significant
enhancement in terms of Finality and Fidelity once the network
nodes utilize the MST, shall positively compensate for the rarely
performed high complexities of the AnoLE protocol. Note that in
public-permissionless BCs, a new block is generated every few
seconds (e.g. Ethereum) or minutes (e.g. Bitcoin), while a node is
probably staying online for weeks or months [71]. Furthermore,
many miners cooperate in mining pools and warehouses that
never leave the network [72].
The adoption of the proposed protocols, then, shall consider
the average active time of nodes in the network. That is, rel-
atively rare node failure (e.g. an average active time of nodes
equals to a month) implies that the AnoLE protocol is rarely
triggered. Accordingly, triggering this protocol may indeed cost
much exchanged messages, yet the MST proposed afterwards
would definitely enhance data propagation through the network
for a long period of time, until a new trigger appears. As a result,
adopting our proposed protocols enhances the overall propaga-
tion time although it occasionally costs much to find the MST of
the new network topology.
Taking as an example, a BA network with size 200 nodes,
where the average active time of nodes equals to one week
(i.e. 168 h), and a new block is generated every minute (i.e. 1440
block per 24 h), we can clarify our last argument. It can be seen
in Table 3 that triggering the AnoLE protocol in such network
would cost nearly 3.2×106exchanged messages. Once the MST is
available to network nodes, they will be able to share their data
with a total number of exchanged messages equals to 200 per
block of data (Table 4). As a result, the network would exchange
a total of 200×1440×72×106messages per week. Adding this
to the 3.2×106exchanged messages to obtain the MST gives a
total of almost 5.2×106messages per week. If this network uses
the RNS method to share data, the total number of exchanged
messages per week would be 1440 ×2,241 ×722.6×106
messages per week. Apparently, even with the high rates of
exchanged messages by the AnoLE protocol, utilizing it would still
be more efficient compared to the currently used methods. The
following additional arguments can further be highlighted:
The AnoLE protocol is one component within the DONS
protocol and can be optimized as well as replaced with a
better protocol whenever available, leading to even better
results.
As indicated previously, the DMST method can be adopted
in BC networks where sharing real identities of nodes is
not considered an issue. Such deployment would produce
an enhanced DONS protocol in terms of time and message
complexities, in addition to being optimized in terms of
finality and fidelity.
The experimental results presented in Section 5.3 repre-
sent the complexities of the AnoLE protocol utilized for the
first time. This means that nodes broadcast the messages
they receive from their neighbors. However, with multiple
leader election rounds run consequently, resulting in larger
number of nodes finding their ONSs, total round-time and
number of exchanged messages will be significantly de-
creased as discussed in Section 5.4. Simply put, the results
presented in Section 5.3 are the upper bound complexities
of the AnoLE protocol.
The potential behind our proposed protocols is apparent for
possible extension of current Proof-of-Work (PoW) algorithms
into Proof-of-Useful-Work (PoUW) [73]. That is, redefining the
puzzle to require finding the MST of the network, instead of solv-
ing a mathematical puzzle with no beneficial utility. Such redefi-
nition would maintain the puzzle to be random, fair, verifiable,
with an unpredictable solution. Meanwhile, it would definitely
enhance the overall throughput and energy consumption of the
system. However, more investigations must be carried out for
such utilization.
The initial configuration of Round-Time Tis highly critical.
Very high Tvalue may result in longer times to obtain the
needed votes, leading to higher overall time. On the other hand,
very low Tvalue may result in limited arrival of LVs leading to
exclusive MST, or worse non-connected NT. In such cases, our
87
H. Baniata, A. Anaqreh and A. Kertesz Future Generation Computer Systems 130 (2022) 75–90
implementation directs the leader to just not construct the MST.
Accordingly, NPs keep using their original NS method (i.e. either a
previous ONS or randomized NS). A method to modify the default
round time, at the node level, upon the receipt of an MST might be
practical. For example, NPs who voted for a leader and have not
received the expected MST after Tpassed, may assume that their
current Twas not sufficient to perform all steps of the protocol.
Accordingly, they double their Tvalue and use the updated value
in the next time the AnoLE protocol is triggered. Similarly, NPs
that received the expected MST before Tpasses, may compute the
average of: Tand time elapsed from the trigger appeared until the
MST was received. This way, Tis constantly updated according to
the size of the network, without NPs being actually aware of the
network size. The most recent value of Tis used afterwards when
the NP is triggered to be a PL (i.e. by a joining or leaving event of
one of its neighbors).
The DRC value is only effective while the node has no previous
ONS. Once the node obtained its ONS, it can deduce the exact RC
value from its previously received MST. We also noted, during the
experiments we performed, that higher average number of neigh-
bors initial configuration results in increased latency of AnoLE
messages. This is in fact a trivial observation, as broadcasting
in random networks leads to more cycles a shared data walks
through the network until it is delivered to all nodes. After several
rounds of AnoLE and DONS, the number of walked cycles is re-
duced until it reaches 0 cycles, leading to 0 redundant exchanged
messages and 0% fidelity.
We have not provided the detailed algorithm to find the MST
as many such algorithms had been proposed in the literature. The
algorithm we deployed, i.e. Prim’s, has a complexity of O(V2).
This is consistent with the AnoLE protocol complexities as pre-
sented in Table 1. Using a more efficient algorithm to find MST,
then, does not enhance the overall time efficiency of the AnoLE
protocol. However, it shall decrease the energy consumption on
the leader side and, consequently, produce the MST faster which
affects T.
Although not mentioned in Algorithm 1for short, we par-
tially adopted a message passing approach inspired by the one
proposed by He et al. [34]. A message is not passed to system
entities if it has been historically passed to them according to a
local log. We use this approach within DONS if the set of selected
neighbors was built according to the ONS of the sender. We found
this approach not practical when the set of selected neighbors is
built according to RNS or RTT-NS methods. For identity privacy
reasons, miners in DONS only save messages passed to/from their
neighbors, rather than from any other miner in the network as
suggested in [34].
7. Conclusion and future work
In this paper, we addressed the Neighbor Selection Problem
(NSP) for public-permissionless BCs by proposing a Dynamic Op-
timized Neighbor Selection protocol called DONS. As a first step
of the DONS protocol, a leader needs to be elected in order to
perform additional computations. To this end, we proposed an
Anonymized Leader Election protocol called AnoLE, that aims at
electing a leader in a distributed fashion, without any previous
knowledge of the network size or nodes private identities. By the
end of the AnoLE protocol, a leader is announced to perform the
following computations. Meanwhile, neither the elected leader
nor the nodes know the identities of each other (except for their
original knowledge about their neighbors). The elected leader
constructs an anonymized network topology, from which it com-
putes the Minimum Spanning Tree (MST) of the network. An
Optimized Neighbor Selection (ONS) is then derived from the MST
by the leader and the rest of network nodes, in a private manner.
Each node utilizes its derived ONS to communicate with the least
number of neighbors, but with optimized communications paths.
We analyzed the security and privacy of our proposed protocols,
and we provided the time and message complexities of their
algorithms. Additionally, we provided publicly available imple-
mentations of both protocols, which we used to experimentally
validate our approach. Our experiments showed significant en-
hancement of message propagation for different network models
and sizes, in terms of finality and fidelity, compared to similar
networks utilizing state-of-the-art methods.
In the future, we plan to investigate the multi-leader scenario
and its implications on the security and the efficiency of the DONS
protocol. As our current proposal of the AnoLE protocol does not
utilize a compatible privacy-aware leader incentivization mecha-
nism, we plan to investigate and deploy a suitable mechanism,
and evaluate the trade-offs that need to be tuned. We will focus
on some interesting previous works solving similar challenges,
e.g. [7478]. We also plan to investigate and implement a suitable
reputation mechanism compliant with the conditions discussed
in Section 5.1. The deployed mechanism shall, of course, adhere to
the security measures expected from DONS and AnoLE protocols,
e.g. as described in [79]. Finally, we will research the possibility
of upgrading the purpose of the DONS and AnoLE protocols into a
comprehensive consensus protocol for public-permissionless BCs,
turning a PoW-based BC into a PoUW-based BC.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgments
This research work was supported by the Hungarian Scientific
Research Fund under the grant number OTKA FK 131793, and by
the TruBlo project of the European Union’s Horizon 2020 research
and innovation program under grant agreement No. 957228, and
by the National Research, Development and Innovation Office
within the framework of the Artificial Intelligence National Labo-
ratory Programme, and by the University of Szeged Open Access
Fund under the grant number 5544.
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Hamza Baniata is a Ph.D. candidate at the Doctoral
School of Computer Science at University of Szeged,
Hungary. He is a member of the IoT-Cloud research
group, Department of Software Engineering, the Fog-
Block4Trust sub-grant project of the TruBlo EU H2020
project, and the OTKA FK 131793 project. He received
his B.Sc. degree in Computer and Military Sciences from
Mutah University-Jordan (2010), And his M.Sc. degree
with excellence in Computer Science from the Uni-
versity of Jordan (2018). Prior to starting his doctoral
studies in 2019, Hamza had served in the Jordan Armed
Forces for 12 years, and was promoted to the rank of Captain in 2017. His work
experience includes different roles in the domains of ICT and Security, inside
and outside the military. His current research interests fall in the domains of
Security, Privacy and Trust of Blockchain, Cloud/Fog Computing, and Internet of
Things systems.
Ahmad Anaqreh is a Ph.D. candidate at the Doc-
toral School of Computer Science at University of
Szeged, Hungary. His research interests include opti-
mization for graph problems using standard methods,
metaheuristics, and heuristics. He received the B.Sc. de-
gree in Computer Information Systems from Yarmouk
University (Jordan, 2010), and the M.Sc. degree in
Computer Science from University of Szeged (Hungary,
2019). Prior to starting the Ph.D., he worked as HCM
functional consultant and HCM specialist for 6 years.
Attila Kertesz is currently with the University of
Szeged, Szeged, Hungary. He is an associate professor
at the Department of Software Engineering, leading the
IoT-Cloud research group. He graduated as a program-
designer mathematician in 2005, received his Ph.D.
degree at the SZTE Doctoral School of Computer Science
in 2011, and habilitated at the University of Szeged
in 2017. His research interests include the federative
management of Blockchain, IoT, Fog and Cloud systems,
and interoperability issues of distributed systems in
general. He is the leader of the FogBlock4Trust sub-
grant project of the TruBlo EU H2020 project, and the OTKA FK 131793 national
project financed by the Hungarian Scientific Research Fund, and a work package
leader in the GINOPIoLT project, financed by the Hungarian Government and
the European Regional Development Fund. He is also a Management Committee
member of the CERCIRAS and INDAIRPOLLNET Cost Actions. He has more than
100 publications with more than 1000 citations.
90
... Therefore, research consideration should be given to multiple controllers to help the network scale up. Baniata et al. [84] used a hybrid architecture to manage the P2P network of blockchain, as shown in Figure 8. One peer is voted into a leadership role to take charge of topology management. ...
... However, this approach has significant network management overhead and does not easily lend itself to a dynamic reconfiguration. Therefore, to make P2P management more flexible and minimize its management overhead, researchers could consider developing intelligent semi-distributed techniques [84] to manage the P2P of blockchain networks. Thus, some peers in the blockchain are assigned special responsibilities. ...
... Semi-Distributed Topology Management Scheme used by Baniata et al.[84]. ...
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