Access to this full-text is provided by American Association for the Advancement of Science.
Content available from Space: Science and Technology
This content is subject to copyright. Terms and conditions apply.
Li et al. 2024 | https://doi.org/10.34133/space.0143 1
RESEARCH ARTICLE
The Node Security Access Authentication
Method for Mega-Constellation based on
Sharding Blockchain
Zongling Li1,2, Teng Long1, Baojun Zhao1, and Wangjie Qiu3*
1School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China. 2Institute
of Spacecraft System Engineering, China Academy of Space Technology, Beijing 100094, China. 3China
Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing
100191, China.
*Address correspondence to: wangjieqiu@buaa.edu.cn
The mega-constellation is a major future development direction for space-based technologies in
communications, navigation,remote sensing, and other fields. However, there are marked security threats
to the mega-constellation. Traditional password-based security protection techniques are inefficient for
vast node access authentication because they lack a unified management system and methodology.
To address the aforementioned issues, this work presents a mega-constellation node security access
authentication technique based on sharding blockchain via the “1 + N + 1” mega-constellation security
and trustworthiness architecture. We build a distributed node security access authentication system
based on functional domains and functional cross-domains, and we develop mathematical models for
the complexity of messaging and space, the throughput of transactions, and the overall estimation of
sharding blockchain systems. The results demonstrate that every indicator outperforms conventional
blockchain techniques, which has major implications for mega-constellation by creating a complete link
security and trustworthiness system. A universal solution for the number of consensus nodes I and the
number of shards N is found, which can be used to guide parameter design in mega-constellation sharding
blockchain systems.
Introduction
e mega-constellation composed of over 10,000 satellite nodes
is the future development direction of space-based system with
applications of communication, navigation, remote sensing, and
other elds. e United States and Europe are vying to start
large-scale networked constellation construction [1] and achieve
low cost, high elasticity, and high quality of service for full-time
and area integrated sensing, networking, computing, and storage
capabilities [2], and have successively launched plans such as
Iridium, Star-link, Black-jack, and Star-shield [3]. ere are two
parts to the mega-constellation system: a ground segment and
a space segment [4]. e ground segment consists of the primary
control center, monitoring center, and signal station, while the
space segment includes constellations, satellite-to-satellite links,
and satellite-to-ground links. e satellite-to-ground link trans-
mits, forwards, and exchanges data and signals using microwave,
laser, and other communication payloads. e space segment
has open communication links, a highly dynamic topology, and
massive data information sharing [5]. As the central component
of the system, it is vulnerable to numerous threats, including
distributed denial of service (DDoS), replay attacks, spoong
attacks, routing attacks, and malware attacks. Due to the unique
character of the spatial environment and the constraints of on-
orbit hardware resources, ground network security protection
methods [6] cannot be directly applied to space systems.
Attack protection and security credibility of satellite systems
have long been research priorities [7,8]. Koroniotis et al. [9]
proposed a deep learning-based network forensics framework
for detecting and tracking network attack activities against
intelligent satellite networks. To increase the time security of
global navigation satellite networks, Gao et al. [10] presented
a time synchronization service approach of separate clock dri
matching lters. Guo et al. [11] developed a blockchain-based
distributed collaborative entrance defense system that consists
of distributed detection and digesting processes, abstract virtual
aggregation processes, and entry control mechanisms, which
can defend satellite networks against DDoS attacks. Sun et al.
[12] devised an incentive-based air ground mobility manage-
ment collaborative blockchain and presented a collaborative
blockchain architecture for air space integrated networks in
order to manage various resources securely and eectively.
Wullems et al. [13] suggested an authentication technique for
mobile satellite communication systems, which has the funda-
mental qualities and security specications that mobile satellite
communication system authentication schemes should take
Citation: LiZ, LongT, ZhaoB,
QiuW. The Node Security Access
Authentication Method for Mega-
Constellation based on Sharding
Blockchain. Space Sci. Technol.
2024;4:Article 0143. https://doi.
org/10.34133/space.0143
Submitted 20 August 2023
Accepted 29 February 2024
Published 30 May 2024
Copyright © 2024 Zongling Li etal.
Exclusive licensee Beijing Institute of
Technology Press. No claim to original
U.S. Government Works. Distributed
under a Creative Commons
Attribution License 4.0 (CC BY 4.0).
Li et al. 2024 | https://doi.org/10.34133/space.0143 2
into account. e ground control center is used as a trusted
third party in Zhang et al.’s [14] public key authentication
method, which lessens the load of certicate management on
other nodes.
e conventional password-based method of protecting
satellite security does not account for the unied authentica-
tion and interconnection control of complicated heterogeneous
and multidomain interconnection scenarios in constellation
networking. ere are problems with a lack of trust between
nodes, a signicant chance of single-point failure, and diculty
assuring global data consistency. Because the protection tech-
nology does not communicate with one another, ensuring
global system security is dicult. ere is still a lack of a uni-
form management system and mechanism. Blockchain tech-
nology can be used to create a constellation node distributed
identity management and authentication mechanism to accom-
plish unied, mutual recognition, secure, and trusted access
authentication services. Due to its decentralized, distributed,
safe, and trusted properties, it can be used to establish the rst
line of defense and address a variety of security risks. However,
in the face of the future of mega-constellations with diverse
functional domains such as communication, navigation, and
remote sensing, where there is currently a problem with com-
plex node authentication, strict permission control, diculty
in cross-domain collaboration, and a lack of trust systems,
among other things, which are limited by hardware resources
such as satellite networks, compute, and storage, traditional
blockchain technology is unable to meet the demands of
eciency.
To solve the diculties raised above, this paper proposes a
mega-constellation node access authentication approach based
on a sharding blockchain system for distributed and secure
access authentication of constellation node identities. We
conduct a multilayer distributed “1 + N + 1” security and
trustworthiness system architecture for the hierarchical and
domain-based application scenarios of mega-constellations
based on the consortium chain. With the severe restrictions
of on-orbit hardware resources, using blockchain technol-
ogy with sharding greatly reduces complexity and achieves
a good balance in scalability, security, and decentralization.
Furthermore, we present a blockchain-based secure access
authentication system and undertake functional validation and
performance analysis in terms of messaging complexity, stor-
age complexity, transaction throughput, and comprehensive
estimation. Finally, a universal solution for the number of
consensus nodes I and the number of shards N is obtained
before building the comprehensive estimate mathematical
model for system perform ance using relevant factors such as
the number of nodes M, the number of consensus nodes I, the
number of shards N, and the normalization coecient of sys-
tem messaging cost p.
We summarize our contribution as follows.
We introduce a novel “1 + N + 1” security and trustwor-
thiness architecture that realizes the security and trustwor-
thiness of the entire link while taking into mind the high
eciency, better utilizing the benets of blockchain technol-
ogy in mega-constellation application situations. In the set-
ting of severely constrained on-orbit hardware resources in
the mega-constellation constellation, we dramatically reduce
complexity by utilizing sharded blockchain technology to
achieve a good balance between scalability, security, and
decentralization.
We propose a blockchain-based secure access authentica-
tion system that implements different management policies
with different security levels based on node levels to avoid
data concentration of the identity of mega-constellation
nodes and to realize trustworthy data interactions between
satellite-to-ground and satellite-to-satellite. This system
outperforms existing methods in terms of messaging com-
plexity, storage complexity, transaction throughput, and
thorough estimation after functional validation and perfor-
mance analysis.
We performed a signicant number of experiments and built
a mathematical model for fully evaluating the system perfor-
mance, which allowed us to analyze the experimental results
more thoroughly from the theoretical level. e proposed
model’s generalizations can be used to direct the design of
parameters for mega-constellations, such as the choice of con-
sensus nodes and the number of shards on the partitioned
blockchain, which is crucial for the advancement of blockchain
technology in the eld of mega-constellations.
Sharding Blockchain Methods
Basic principles
Blockchain is a new distributed database combining cryptog-
raphy, P2P network system, consensus mechanism, smart
contract, and other technologies. According to the degree of
decentralization, blockchain is divided into three categories:
public blockchain, consortium blockchain, and private block-
chain [15]. Public blockchain is a completely decentralized
blockchain where any node in a distributed system can par-
ticipate in the process of data reading, writing, validation, and
consensus on the chain, and receive corresponding economic
incentives based on their contributions. Consortium chain is
a partially decentralized blockchain that is suitable for orga-
nizations or consortium composed of multiple entities, and its
data read and write permissions are controlled by a predened
set of nodes. Private chain is a fully centralized blockchain that
is suitable for internal data management and auditing of spe-
cic institutions, and its write permission is controlled by the
central institution, while read permission can be selectively
opened to the public according to needs.
e high trust foundation of blockchain is established on
the basis that all transactions require verication and storage
at each node, which wastes a lot of messaging and space, and
also leads to low throughput [16], high latency [17], and poor
scalability [18] problems in blockchain systems. To address
the above challenges, many experts and scholars have opti-
mized and innovated traditional blockchain technology based
on specic application scenarios. In 2016, Luu et al. [19] pro-
posed an Elastico algorithm that combines database expan-
sion and sharding with blockchain technology. Since then,
many scholars have conducted extensive research on sharding
blockchain technology from the perspectives of distributed
ledgers [20], consensus mechanisms [21], and sharding meth-
ods [22], achieving good application results. As one of the
mainstream methods of blockchain expansion [23], sharding
technology adopts an on-chain parallel architecture, which
can achieve high performance on-chain expansion without
reducing the degree of blockchain decentralization, thereby
solving the problems of insufficient scalability and low
throughput of blockchain. It is a way to ensure blockchain
Li et al. 2024 | https://doi.org/10.34133/space.0143 3
security and stability while also improving the transaction
speed of blockchain systems [24].
“1 + N + 1” security and trustworthiness architecture
Focusing on the need to ensure the security and trustworthiness
of the global information of mega-constellations, combined
with the architecture and application characteristics of mega-
constellations based on functional domains, and considering
the limitations of hardware resources such as on-orbit net-
works, computing, and storage, consortium chain and sharding
blockchain are adopted as the underlying technology for the
security and trustworthiness of mega-constellations, and a
full link security and trustworthiness system based on the
“1 + N + 1” blockchain system architecture is constructed. As
shown in Fig. 1, the first “1” represents the Ground block-
chain; “N” represents the Functional blockchain for the mega-
constellation functional domain; the second “1” represents
the General blockchain for mega-constellations. e mega-
constellations will be divided into dierent functional domains
based on their application functions, and satellite nodes with
the same function are located within the same shard or multiple
shards that each shard has a cross-shard node. All the cross-
shard nodes form the General blockchain, and cross-shard
operations between dierent shards will be achieved through
consensus and synchronization of block information in the
General blockchain.
Within the functional domain, TBFT (Tendermint Byzantine
fault tolerance) consensus mechanism is used to achieve data
consistency within the domain and global data consistency
is achieved between functional domains through cross-chain
nodes forming a distributed autonomous system. e detailed
introduction is as follows:
1. Ground blockchain (“1”): Ground consensus network,
also known as Certicate Authority (CA) consensus network,
is the manager of the system and has functions such as network
management, data storage, and identity permission manage-
ment. e ground consensus network/CA consensus network
consists of at least four ground control stations/CA nodes, all
of which are consensus nodes and participate in consensus vot-
ing, transaction execution, block verication and block execu-
tion, and storing full data.
2. Functional blockchain (“N”): Divide mega-constellations
into N functional domains based on their functions, including
navigation, communication, remote sensing, and early warn-
ing, corresponding to N sharding blockchain networks. Each
shard contains a consensus network and a synchronization
network, consisting of at least one consensus master node, at
least three consensus subnodes, and M synchronization nodes,
with one synchronization node serving as a cross-shard node.
Considering both security and block network carrying capac-
it y, M should not exceed 196. The Functional blockchain can
independently complete consensus and data synchronization,
collaborate with ground nodes to complete new node access
authentication, and save abnormal node blacklists, global
chain node lists, and cross-shard node ranking lists for the
shard.
3. General blockchain (“1”): Designate a synchronous node
from each domain’s blockchain consensus network to form a
global blockchain network. e global blockchain network
consists of at least four consensus nodes and up to 196 syn-
chronization nodes. Due to the need for cross-shard nodes to
Fig. 1. The “1+N+1” sharding blockchain architecture for mega-constellation.
Li et al. 2024 | https://doi.org/10.34133/space.0143 4
undertake the tasks of both shard and global chains, nodes
with abundant hardware resources such as device computing,
storage, and network are selected as cross-shard nodes to form
a global blockchain network. e General blockchain is mainly
used to achieve consistency between shard nodes, saving abnor-
mal node blacklists, global chain node lists, and full block
header information. Once a node on the global chain is detected
as abnormal, the shard will replace it with a new node as a
cross-shard node to access the global chain.
Node type
Due to the limited hardware resources of satellite nodes, in order
to adapt to the special needs of satellite scenarios and dierent
functional satellites, and safely, eciently, reliably complete des-
ignated tasks with less occupation of satellite resources, three
types of blockchain nodes are designed: consensus, synchroniza-
tion, and cross-shard node. e detailed introduction is as
follows.
Consensus nodes: Consensus nodes participate in consensus
voting, transaction execution, block validation, and block execu-
tion in the blockchain network, storing the full amount of data
on the blockchain. In this system, consensus nodes are set up
on the ground control center/CA nodes and satellites. Among
them, there is one consensus master node and three consensus
subnodes in a consensus network. e consensus master node,
also known as a block node, is rotated within the consensus
network. For every h block submitted (h can be congured), the
consensus master node rotates to the next node.
Synchronous node: Due to the limitations of on-orbit latency
and data storage, some satellite nodes cannot participate in
decision-making as consensus nodes, but can act as synchronous
nodes to synchronize all data, including identity and permission
information. Supports data queries and simplied versions of
smart contracts that can be executed without the need for virtual
machines only when the searcher reaches the corresponding
security level can the data be queried.
Cross-shard node: In each shard, there is a synchronization
node that serves as the cross-shard node. As the synchroniza-
tion node of the functional shard, it needs to synchronize the
full amount of data within the shard, and as a cross-shard node
storing all blockchain header information for shard commu-
nication and collaboration. When a satellite is launched, it is
possible to choose whether to congure cross-shard function
-
ality. Satellite nodes with cross-shard function are listed in
order of launch time to form a list of cross-shard nodes.
Distributed Security Access Authentication
Process
Ensuring the legitimacy of the connected nodes and user ter-
minals is crucial for the security of the mega-constellation, and
it is necessary to ensure that the mega-constellation is “anti-
intrusion, anti-the, anti-takeover and anti-hijacking.” ere
are large-scale distributed nodes, and identity authentication
urgently needs to shi from a centralized architecture to a dis-
tributed architecture for mega-constellation. Dierent levels of
nodes should implement dierent security level management
strategies. In response to the above requirements, the paper
proposes a distributed security access authentication method
based on sharding blockchain technology to avoid the data
centralization of mega-constellation node identity and to
achieve the trusted data interaction among satellite-to-ground
or satellite-to-satellite.
Black and white list mechanism
e paper sets up a node security level list for users to record
the status of each node, mainly recording the current status,
number of consensus participation, and malicious actions of
each satellite node. Each functional domain needs to be main-
tained, which includes the following parts.
Node status
All satellite nodes in the functional domain are divided into
four categories: authenticated nodes, unauthenticated nodes,
frozen nodes, and malicious nodes. Authenticated and unau-
thenticated nodes belong to whitelist nodes, while frozen and
malicious nodes belong to blacklist nodes. Please refer to Table
1 for specic safety level classication methods.
Malicious behavior
e correct behavior of a node refers to its normal participa-
tion in communication within the functional domain, and
when its token expires, it will actively engage in access
authentication with nodes within the domain. e malicious
behavior of a node refers to its behavior of forging transac-
tions or communication information, and built-in protective
Table 1. Safety level classification
Node style
Security
level Description
Security
range
Authenticated
nodes
High Effective nodes
accessing the
functional
domain
(a, 1)
Unauthenticated
nodes
Medium Not connected
to functional
domain nodes or
nodes with
expired
authentication
(0.5, a]
Freeze
nodes
Lower Blacklist nodes
that have been
frozen after
detecting
abnormal
behavior
(b, 0.5]
Malicious
nodes
Lowest Blacklist nodes
confirmed and
revoked by the
ground CA
consensus
network
(0, b]
Li et al. 2024 | https://doi.org/10.34133/space.0143 5
equipment detects anomalies, sends alarm messages, and
updates them once. e alarm information will be synchro-
nized to all nodes within the functional domain and syn-
chronized to the ground CA organization for secondary
verication. At the same time, all nodes in the domain need
to undergo initial access authentication to investigate mali-
cious nodes again.
Security access authentication process
e key processes of the security and trustworthiness mecha-
nism of the mega-constellation based on the sharding block-
chain system include identity authentication, cross-domain
node replacement, blacklist update, and abnormal behavior
handling.
As shown in Fig. 2, the security access authentication pro-
cess is mainly divided into three parts, including the initializa-
tion, the initial access authentication, and the expired access
authentication. e initialization requires registration through
the ground CA consensus network to obtain a legal identity
for subsequent access authentication. e rst satellite only
needs to pass identity authentication through the ground con-
sensus network. Aer the second satellite is launched, it needs
to undergo initial access authentication with the rst satellite.
e third satellite needs to undergo access authentication with
the rst two satellites, and so on until four satellites success-
fully connect to the functional domain. e system defaults
to the rst four satellites becoming consensus nodes within
the functional domain. Aer the subsequent satellite launch,
an asymmetric encryption authentication mechanism with
initial access authentication will be adopted and only nodes
with successful authentication can access their functional
domain.
Within the access authentication period T, the protective
equipment of the satellite needs to send the alarm information
to other satellite nodes on the blockchain for consensus if
abnormal behavior is detected. e system will rst pull the
satellite node into the blacklist and mark the frozen eld. Aer
synchronizing with the blacklist information on the ground,
the certicate of satellite will be revoked and the frozen eld
in the blacklist will be revoked if the information is true, and
the satellite node will be removed from the blacklist if the
judgment information is incorrect. Aer the expiration of T,
the satellite needs to undergo expiration access authentication
in order to access its functional domain. e introduction is
as follows.
1. e authentication initialization process
① e CA consensus network sends the public key of the
CA institution to the functional domain blockchain network
to prepare for subsequent access authentication.
② Before satellite launch, satellite node A sends a registra-
tion request M to the CA consensus master node, where
M = ID
A
, and ID
A
contains entity ID, type, timestamp, physical
address number, domain, role, and check digit information and
“| |” represents the concatenation of messages.
③ Aer receiving the request, the CA consensus master
node will verify the information, generate the certicate CAA
and the private key SKA of node A aer conrmation, and
consensus the results in the ground consensus network, and
return the CAA and SKA to node A.
④ CA consensus network signs CA
A
to obtain certicate C.
en, the certicate C and the public key of the node A PKA
Fig.2.Security access authentication process for mega-constellation.
Li et al. 2024 | https://doi.org/10.34133/space.0143 6
will be sent to the functional domain blockchain network for
consensus.
e detailed algorithmic ow is given in Algorithm 3-1.
2. e initial access authentication process
⑤ Aer satellite launch, the initial access authentication of
the satellite adopts an asymmetric encryption authentication
mechanism. Satellite node A rst initiates a smart contract
request R1 to the access node of the corresponding functional
domain. Assuming that the authentication node is a synchro-
nous node, R1 = M1||S, S = SignSKA[H(M1)], M1 = M||T1,
H(M1) is the authentication code calculated by message M1
through the hash function, S is the signature of authentication
code H(M1) by A using its own private key, and T1 is the time-
stamp of satellite node A.
⑥ Due to the fact that the access node within the functional
domain is a synchronous node, the request R
1
will be forwarded
to the consensus node on the chain.
⑦ Aer receiving the request R
1
, the consensus node on the
chain decrypts the certicate C with the CA public key PK to
obtain the certicate CAA′ of A. If
CA
�
A
==CA
A
, the consensus
node will continue the next verication operation. e DPKA
[SignSKA[H(M1)] is decrypted with the A public key PKA to
obtain H(M1)′, and the hash operation is performed on the
message to obtain H(M1). en, the resolved H(M1)′ is com-
pared to the H(M1) to see if they are the same. If dierent,
discard the request. Set the eective authentication period T
for node A, and consensus the results among the four consensus
nodes. Finally, return the authentication results to synchronous
node 1.
⑧ Synchronous node 1 returns the authentication result
and authentication time T2 to satellite node A.
⑨ Within the T validity period, satellite node A sends a
communication request to any node in the domain and only
needs to send IDA and T2.
⑩ e authentication node veries whether the validity
period T of A is valid. If eective, it will be connected and
communicated normally.
e detailed algorithmic ow is given in Algorithm 3-2.
3. e expired access authentication process
⑪ When satellite node A determines the current time
t ≥ T + T2 on its own, it indicates that its identity has expired
on the chain and needs to be re authenticated. When A encoun-
ters the next satellite node that needs authentication, taking
synchronous node 2 as an example, expired access authentica-
tion will be performed.
⑫ e satellite sends an access authentication request R1 to
synchronous node 2 and repeats the initial access authentica-
tion steps in step ⑥. Follow the steps of ⑤ to ⑧.
e detailed algorithmic ow is given in Algorithm 3-3.
Consensus algorithm
e consensus process of sharding blockchain systems for
mega-constellation can be divided into two types: domain and
cross-domain. is article adopts the TBFT consensus algo-
rithm based on Tendermint in both domain and cross-domain
work processes [25], which diers from the traditional practical
Byzantine fault tolerance (PBFT) [26], where PBFT has a xed
master node to package transactions and will replace the master
node when the master node fails, and the master node is rotated,
and every time a certain number of blocks are submitted, the
master node will rotate to the next node in TBFT. erefore,
TBFT has better fairness than PBFT [27]. By utilizing the TBFT
consensus algorithm, the eciency and security of domain and
cross-domain consensus have been achieved, meeting the
Li et al. 2024 | https://doi.org/10.34133/space.0143 7
requirements of distributed authentication applications for
mega-constellation nodes.
Domain consensus process
When satellite nodes generate or receive data, it is rst neces-
sary to reach consensus intra-domain. e TBFT consensus
algorithm can ensure the safe operation of the system when
the number of Byzantine nodes (faulty nodes) is less than one-
third of the total number of consensus nodes. e specic con-
sensus process within the domain can be divided into six steps:
New-Round, Proposal, Prevote, Precommit, Commit, and
Synchronize. e following will be explained in Fig. 3, where
Sp is the consensus master node, Si, i = 1,2,3 is the consensus
subnode, and S1
', S2
' is the synchronization node.
1. New-Round
Clients Ci such as satellites and drones, as well as ground
control centers G, will send requests to Sp. If the transaction is
mistakenly sent to Si, it will be forwarded to Sp. During the
New-Round, the consensus state will be initialized. During the
implementation process, the consensus state dened includes
the following parameters: block height, voting round, step, pro-
posal, and validation proposal, which resets proposal and veri-
fying proposal to null. e signicance of the New-Round is
that the consensus node may timeout during the voting step.
If a consensus vote is not reached on the new block within the
timeout, it needs to enter the next round of voting round+1
and clear the proposal and verify the proposal, and vote again
until a consensus vote is reached on the new block.
2. Proposal
Aer Sp received the request of Ci, performing legal authen-
tication and duplicate checking on the received transaction, and
the veried transaction enters the packaging process, S
p
transac-
tions cached package into a group and reduce communication
overhead through batch processing; Finally, S
p
assigns a sequen-
tially increasing number to the packaged transactions to ensure
that S
i
is processed in the same order. Aer completing the trans-
action verication, packaging, and sorting process, S
p
broadcasts
the packaged transactions into blocks to Si. e information
exchange between nodes in the Proposal is as follows: Sp broad-
casts consensus status (block height, round, and proposal con-
tent) to Si; Si consensuses status messages will respond to prove
that they have received the message. us, Sp and Si have syn-
chronized a new Height with both (if this stage expires, a new
election will be held). During all information exchange processes,
each node needs to verify the message signatures of other nodes.
3. Prevote
Aer verifying the legality of the proposal, Si will generate
and sign a prevote for the block, and then broadcast own pre-
vote to other nodes. e information exchange between nodes
in the Prevote is as follows: Si broadcasts signed prevotes to
other consensus nodes, and receives prevoting messages from
other nodes and added to the voting set. At this step, Si only
validates the legality of proposed block.
4. Precommit
Sp and Si will verify whether the number of prevotes received
is greater than two-thirds of the number of nodes, and they will
generate a precommit vote and sign for the block if it meets the
requirements, and then broadcast its own precommit vote to
other nodes. e information exchange between nodes in the
prevote is as follows: nodes broadcast their signed consensus votes
to other consensus nodes. e node receives prevote messages
from other nodes and adds them to the voting set. At this step,
all consensus nodes verify whether the number of prevotes
received is greater than two-thirds of the number of nodes.
5. Commit
Sp and Si will verify whether the precommit vote is greater
than two-thirds, and if it is met, the blocks in the proposal are
submitted to the ledger and, aer successful submission, will
proceed to the next Height. At this step, Sp and Si will verify
whether the received precommit messages are greater than two-
thirds of the number of nodes.
6. Synchronize
S'
1 and S'
2 regularly request Height from Sp and Si, and if the
height of S'
1 and S'
2 is lower than the height of Sp and Si, then
S'
1 and S'
2 synchronize with the height of Sp and Si. e gener-
ated blocks within the domain S
p
are synchronized to the main
node of the ground consensus network GN
p
. When the ground
consensus network GN generates or receives new data, the con-
sensus process is the same as above, without a Synchronize.
Among the six consensus steps mentioned above, consensus
voting refers to the three steps of Proposal, Prevote, and
Precommit; the state of TBFT downtime can be restored
through the logs if it needs to be restarted; and it will be added
to the blacklist and can be replaced by modifying the congura-
tion if an exception occurs and is frozen.
Cross-domain consensus process
As shown in Fig. 4, the General blockchain is composed of cross-
domain nodes and global synchronization nodes from each
domain. Cross-domain nodes from each domain participate as
consensus nodes in the consensus process of the General block-
chain (S'
Bi) to support interdomain collaboration and achieve
global data consistency. e General blockchain also adopts the
TBFT consensus protocol, and the cross-domain consensus pro-
cess is divided into six steps: New-Round, Proposal, Prevote,
Precommit, Commit, and Synchronize. e general chain con-
sensus node SBi and the general chain synchronization node S'
Bi,
as well as the domain consensus node (S
p
,S
i
) and domain synchro-
nization node S'
i, operate the consensus process consistently.
In order to maintain the stability of cross-domain collabora-
tion, each functional domain Nbi will maintain a list CdList of
cross-domain node rankings within the domain and can choose
whether to congure cross-domain functionality when launch-
ing a satellite. Satellite nodes with cross-domain functionality
are listed in order orderlaunch of launch time to form a cross-
domain node ranking list CdList. When the protective equip-
ment of cross-domain nodes Sci detects abnormal nodes, a
replacement Sci process will be initiated within the domain.
① e protective equipment detects abnormal behavior of
the current cross-domain node Sc0 and records the node in the
blacklist.
② e new cross-domain node Sc1 is next in the ranking
list CdList of cross-domain nodes in the domain, and S
c1
veries
whether Sc0 is successfully recorded in the blacklist and then
initiates deletion Sc0 from the domain CdList.
③ Consensus and synchronize the modied local domain
CdList, and successfully switch between cross-domain nodes
within the domain.
④ Cross-domain nodes S
ci
initiate modication requests to
global cross-domain nodes Scj that are not on the blacklist.
⑤ e global chain consensus node SBi veries whether
the cross-domain node Sc1 has successfully switched within
the domain through block headers. Aer conrmation, the
consensus modies the list GcList of global chain nodes. e
Li et al. 2024 | https://doi.org/10.34133/space.0143 8
consensus process of the global chain follows the TBFT con-
sensus process.
⑥ e global chain consensus node SBi has synchronized
the consensus GcList with the synchronization node S'
Bi.
⑦ Each domain Nbi synchronizes the new domain CdList
to the ground network GN separately.
Results
Functional verication and performance analysis of the security
access authentication system based on sharding blockchain have
been conducted from the perspectives of messaging complexity,
spatial complexity, transaction throughput, and comprehensive
evaluation, and the results showed that the proposed security
access authentication method in the paper outperformed tradi-
tional blockchain methods in all the above aspects. By establish-
ing relevant factors such as the number of nodes M, the number
of consensus nodes I, the number of shards N, and the normal-
ization coecient of system messaging cost p, a comprehensive
evaluation of mathematical model for system performance is
constructed, where a universal solution for the number of con-
sensus nodes I and the number of shards N is obtained. e above
general solution can be used to guide the parameter design such
as the selection of consensus nodes and the number of shards on
sharding blockchain for mega-constellation.
Simulation and experiment design
We build the distributed safe access authentication system using
a process involving time data statistics based on the federation
chain and self-research satellite nodes with synchronized block
functions. We experiment with smart contracts in the go pro-
gramming language to simulate the access authentication pro-
cedure, and we use self-developed scripts to keep track of how
much time passes. Table 2 shows the hardware testing environ-
ment used in this experiment for system validation, which
includes CPU, memory, hard disk, and network capability
combinations.
e operating system, running environment and resource
monitoring tool versions in the testing soware environment
are shown in Table 3.
Fig. 3. Domain consensus flowchart.
Li et al. 2024 | https://doi.org/10.34133/space.0143 9
Our experiment aims to assess the performance of the
sharding-based blockchain system in the context of access
authentication, with a focus on important metrics including
messaging complexity, spatial complexity, and transaction
throughput. ese metrics are examined in conjunction with
mathematical models and data from simulation experiments.
Finally, we conduct a thorough analysis of the aforementioned
key indexes, compare the changes in the system with and with-
out sharding, and examine the trend of the system’s messaging
overhead in relation to the consensus node and sharding size.
Furthermore, we theoretically derive the mega-constellation
system’s design parameter generalizations.
e steps of this experiment are as follows:
Step 1: We utilize the script to construct chain proles for
4, 7, 10, and 13 dierent consensus nodes and then launch the
bottom chains of those nodes based on their proles.
Step 2: We use the script to launch 50, 100, 150, and 200
processes concurrently to simulate launching contracts to bot-
tom chains with varying numbers of consensus nodes. is
experiment employs a procedure that simulates a satellite node
performing an access authentication request (which may be
thought of as a synchronous node capable of launching the
contract), that is, the process of requesting the blockchain to
execute the contract.
Step 3: In this experiment, the access authentication con-
tract can be executed by a single chain if it is one shard, while
four chains can be initiated if they are four shards, allowing
for load-balanced contract execution. rough the aforemen-
tioned procedure, we do experiments to compare the perfor-
mance of sharded and unsharded systems.
Step 4: We use the self-developed satellite node program to
hit the data from the bottom chain and cross-chain. en, we
statistically count the messaging overhead of access authentica-
tion and cross-domain in intra-shard and inter-shard. ey are
used to calculate the key metrics of messaging complexity, spatial
complexity, and transaction throughput in this experiment.
e experimental scenarios comprise multiple combinations
of the number of consensus nodes in the chain (4, 7, 10, 13)
and satellite nodes (50, 100, 150, 200).
Modeling analysis
Messaging complexity
As shown in Eq. 1, the messaging of a distributed security
access authentication system Ctotal consists of two parts when
there is an access authentication request: one part
Cconsensus
total
is
the consensus messaging complexity, and the other part Csync
is the synchronization messaging complexity of the nodes aer
consensus.
Consensus messaging consists of two parts: shard and cross-
shard. First, the messaging complexity of node consensus shard
is analyzed. In a distributed security access authentication sys-
tem, there are N shards with consensus nodes Ii (i = 1,2,..., N)
within each shard. e expression for calculating the messaging
complexity of nodes within the shard is shown in Eq. 2:
In Eq. 2,
Ci
internal
is the number of communications within the i
shard,
Ci
proposal
is the number of communications during the
Proposal step of the TBFT consensus protocol within the shard,
Ci
prevote
is the number of communications during the Prevote step
of the TBFT consensus protocol within the shard, and
Ci
precommit
is the number of communications during the Precommit step of
the TBFT consensus protocol within the shard.
From the above calculation, it can be concluded that the
messaging complexity of the shard is
O(
I
2
i)
.
N shards correspond to N cross-domain nodes for consen-
sus, and the TBFT protocol is also used for consensus among
shards, where the messaging complexity calculation among
shards is shown in Eq. 3:
In Eq. 3, Ccross is the number of communication among
shards, Cproposal is the number of communication times during
the Proposal phase of the TBFT consensus protocol among
shards, Cprevote is the number of communication times during
the Prevote phase of the TBFT consensus protocol among
shards, and Cprecommit is the number of communications during
the Precommit step of the TBFT consensus protocol within the
shard. From the above calculation, it can be concluded that the
messaging complexity between node shards is O(N2).
By combining the messaging complexity within and among
shards, the total messaging complexity can be obtained
Cconsensus
total
,
as shown in Eq. 4:
(1)
Ctotal
=C
consensus
total
+C
sync
(2)
Ci
internale =C
i
proposal +C
i
prevote +C
i
precommit
=(
I
i
−1
)
+I
i(
I
i
−1
)
+I
i(
I
i
−1
)
=2I2
i
−I
i
−
1
(3)
C
cross
=C
proposal
+C
prevote
+C
precommit
=(N−1)+N(N−1)+N(N−1)=2N
2
−N−1
(4)
C
consensus
total =
N
i=1Ci
internal +Ccross
=
N
i=1
2I2
i−Ii−1
+
2N2−N−1
=O
N
i=1
I2
i+N2
Table 2. Testing hardware environment
Term Specification parameters
Server Think System SR650
CPU 80 Intel(R) Xeon(R) Gold 5218R CPU @ 2.10GHz
Memory 256G
Hard disk SSD 2Tbit
Network Gigabit
Table 3. Testing software environment
Term Version
Operating system Ubuntu 20.04.5 LTS (GNU/
Linux 5.15.0-72-generic x86_64)
Running environment Golang 1.17.0; Gcc 9.4.0
Resource monitoring tool VMware vSphere
Li et al. 2024 | https://doi.org/10.34133/space.0143 10
In Eq. 4, the average number of consensus nodes within the
shard is set to I,
I
=
∑k
iIi
N
, obtaining the overall complexity of
consensus messaging
Cconsensus
total
as shown in Eq. 5:
From the above formula, it can be seen that the number of
system shards N, the average number of consensus nodes I
within the shard, and the overall complexity of consensus mes-
saging
Cconsensus
total
are positively correlated in a quadratic curve.
According to the synchronization process of the consortium
chain, the synchronization messaging complexity can be expressed
as shown in Eq. 6:
In Eq. 6, N is the number of system shards, I represents the
average consensus nodes within the shard, M represents the
total number of satellite nodes in the system, and p is the nor-
malization coecient of system messaging cost.
By combining Eqs. 1 to 6, the messaging complexity of the
distributed secure access authentication system can be obtained
as shown in Eq. 7:
According to Eq. 7, the messaging complexity presented by
sharding in the access authentication scenario is shown in Eq. 8:
In the access authentication scenario non-shard, the mes-
saging complexity presented is actually N = 1, and the specic
expression is shown in Eq. 9:
Based on the above theoretical analysis, the time cost of the
distributed security access authentication system was simulated
and analyzed. Simulations were conducted based on four sce-
narios where the number of access nodes (including consensus
nodes and synchronization nodes) M was 50, 100, 150, and 200.
A comparative analysis was conducted on the access authenti-
cation methods of the “1 + N + 1” shard and non-shard block-
chain designed in the paper. Among them, the number of
shards N was designed as 4, and the number of consensus nodes
I was 4, 7, 10, and 13.
e experimental results are shown in Fig. 5, and the system
time cost is the average of three access times. When the number
(5)
Cconsensus
total
=O
(
NI
2
+N
2)
(6)
C
sync =
M−I∗N
I∗N
∗
p
(7)
C
total =Cconsensus
total +Csync =∑
N
i=1(2I2
i−Ii−1
)
+(
2N2−N−1
)
+M−I∗N
I∗N
∗p
(8)
C
total
=Cconsensus
total
+C
sync
=
O
2I2−I−1
N+
2N2−N−1
+M−I∗N
I∗N∗p
(9)
C
total =Cconsensus
total +Csync =
N
i=12I2
i−Ii−1
+M−I
I
∗
p=O
2I2−I−1+M−I
I
∗p
Fig. 4.Cross-domain consensus flowchart.
Li et al. 2024 | https://doi.org/10.34133/space.0143 11
of nodes is 50, with the number of consensus nodes increasing
from 4 to 13, the time cost of the non-shard scheme is 51.85,
51.21, 55.65, and 57.44 ms, while that of the Four-shard scheme
is 21.57, 25.42, 26.91, and 27.56 ms.
When the number of nodes is 100, with the number of con-
sensus nodes increasing from 4 to 13, the time cost of the Non-
shard scheme is 49.19, 55.20, 55.39, and 58.92 ms, while that
of the Four-shard scheme is 21.57, 25.42, 26.91, and 27.56 ms.
When the number of nodes is 150, with the number of con-
sensus nodes increasing from 4 to 13, the time cost of the Non-
shard scheme is 51.24, 51.42, 55.56, and 61.12 ms, while that
of the Four-shard scheme is 23.74, 23.89, 26.92, and 28.99 ms.
When the number of nodes is 200, with the number of
consensus nodes increasing from 4 to 13, the time cost of the
Non-shard scheme is 56.42, 57.23, 56.61, and 55.46 ms, while
that of the Four-shard scheme is 21.12, 21.71, 24.48, and
30.55 ms.
Generally, the average access authentication cost of the shard
method increases slightly overall with the increase of consensus
nodes, and more than twice the optimization of shard access
time overhead compared to non-shard. e impact of consen-
sus time and synchronization time on system time overhead
was analyzed separately. e comparison of the two costs in
dierent consensus nodes makes us realize that the choice of
the number of shards, the number of consensus nodes, and the
number of consensus nodes are needed to be considered in the
sharding solution.
According to Eq. 5, the consensus messaging complexity is
O(NI2 + N2), a quadratic function as the number of consensus
nodes N in shards increases, but the consensus time should not
increase sharply with the number of consensus nodes N because
every shard works parallelly. Consistent with this, the data in
Fig. 5 also indicate that as the number of consensus nodes
increases, the time cost increases slowly. Another reason for the
slow growth of time expenses is that a large amount of interme-
diate data needs to be stored during the experimental process.
For example, in order to ensure the consistency of consensus
state, each node needs to serialize voting information locally
aer receiving votes, which is also an important time cost and
weakens the impact of quadratic factors.
According to Eq. 6, the complexity of node synchronization
time is
O(
M−I∗N
I∗N)
, which is the total number of nodes M
multiplied by the number of shards N and the reciprocal of
the number of consensus nodes I within the shard. erefore,
as the number of consensus nodes and shards increases,
the synchronization time will correspondingly decrease. e
specic reason is that as the number of consensus nodes in
the system increases, node access after shard can achieve
consensus not only in shards but also among shards, greatly
increasing the concurrency of system consensus and improv-
ing eciency.
Based on the above analysis, it can be seen that sharding
operation can bring more than twice the performance improve-
ment within a certain range in the context of access authentica-
tion. However, it also introduces shard transactions, which
require a certain amount of time and require comprehensive
design optimization based on specic application scenarios.
Fig.5.Time cost for different number of access nodes.
Li et al. 2024 | https://doi.org/10.34133/space.0143 12
Spatial complexity
e spatial complexity of the sharding blockchain system is
quantied by analyzing the overhead of storage space. e
space overhead of non-shard is shown in Eq. 10:
e storage cost aer sharding is shown in Eq. 11:
In Eqs. 10 and 11, Costbase is the base storage, including the
size of the uplink contract and uplink ground public key certi-
cate. M is the number of satellite nodes; N is the number of
shards; Cost
average
represents the average space occupied by each
public key certicate; Cost
local
indicates the cost of not on chain
data, and this section mainly refers to the need for each satellite
node to save its own private key. In addition, a non-shard sys-
tem can be considered a special case when N = 1.
Consider that satellite storage space has an upper bound S
max
,
expressed as Costmax ≤ Smax; it can derive
N
≥
Cost
average
∗N
Smax
−
Costbase
≥
1
,
which will meet the storage cost of satellites Smax of the upper
bound of satellite storage.
Based on the above theoretical analysis, the spatial complex-
ity of the distributed security access authentication system is
quantied, using dierent numbers of satellite nodes for access
authentication and taking a typical “1 + N + 1” architecture as
an example, and designing an experiment with N = 4, there are
four functional domains to store the identity authentication
information required for satellite access authentication. Access
authentication is performed on satellite nodes with a total num-
ber of satellite nodes M of 50, 100, 150, and 200, and the storage
cost is calculated.
e experimental results are shown in Fig. 6. As the num-
ber of nodes increases from 50 to 200, the storage cost of the
Non-shard scheme changes from 1,239.33 KB to 2,216.17 KB,
while that of Four-shard scheme changes from 1,080.83 KB
to 1,320.19 KB. e trend of storage space overhead is con-
sistent regardless of whether it is shard or not, and it increases
with the number of connected satellites, but the dierence lies
in the slope of the curve. e slope aer shard is inversely
proportional to the number of shards, which is consistent with
the theoretical analysis of storage overhead. erefore, shard
can optimize and save system storage costs by at least 20%.
Transaction throughput
In blockchain systems, transaction throughput is usually repre-
sented by transaction volume per second. In sharding system,
transaction throughput is aected by cross-shard transactions.
On the one hand, to ensure cross sharding consistency, cross-
shard transactions require more conrmation and communica-
tion processes, which consume longer time; on the other hand,
cross-shard transactions can bring redundant transactions, which
is mentioned in classic sharding systems such as Rapidchain and
Monoxidide. Based on this, the transaction volume processed by
a shard in a time cycle can be calculated according to Eq. 12:
In Eq. 12, SB represents the size of a block, ST represents the
average size of the transaction, Cr represents the number of
rounds within a time cycle, and Rr indicates the number of
redundant transactions brought about by each cross-shard
transaction. Combining the consensus time of a time cycle can
provide the transaction throughput of a single shard as shown
in Eq. 13:
In Eq. 12, Tepoch represents the time of a single time cycle,
combined with the number of shards N, to obtain the overall
transaction throughput Ototal. As shown in Eq. 14:
Based on the above theoretical analysis, a quantitative analy-
sis of the throughput of the distributed secure access authen-
tication system is conducted, and using different numbers
of satellites for access authentication and taking the typical
“1 + N + 1” architecture as an example, the number of satellite
shards N = 4, 7, 10, 13. Experiments are designed with the
number of satellite consensus nodes I = 4, and access authen-
tication on satellite nodes is performed, where the total number
of satellite nodes M is 50, 100, 150, and 200 to calculate transac-
tion throughput.
e experimental results are shown in Fig. 7. When the
number of nodes is 50, with the number of consensus nodes
increasing from 4 to 13, the transaction throughput of the sys-
tem is 9,853.16, 15,121.77, 17,684.37, and 20,352.91. When the
number of nodes is 100, with the increase of the number of
consensus nodes, the transaction throughput of the system is
8,499.25, 15,737.54, 18,218.97, and 17,524.05. When the num-
ber of nodes is 150, with the increase of the number of consen-
sus nodes, the transaction throughput of the system is 9,451.75,
15,913.75, 18,704.41, and 21,389.98. When the number of
nodes is 200, with the increase of the number of consensus
nodes, the transaction throughput of the system is 9,227.06,
14,786.62, 18,751.37, and 21,389.98. It can be seen that in
sharding blockchain system, each shard can independently
process transactions, and the system throughput is equal to the
sum of single shard throughput. Due to the fact that the
throughput of shard transactions decreases as the number of
shards increases, while the throughput within the system
shard is basically the same as when it is non-shard, the num-
ber of shards cannot continue to increase. Overall, when the
(10)
C
ost
total
=Cost
base
+M∗
(
Cost
average
+Cost
local)
(11)
C
osttotal =Costbase +M∗
(Cost
average
N+Costlocal
)
(12)
Ω=
S
B
S
TCr
1
Rr
+
1
(13)
O
=
Ω
T
epoch
(14)
Ototal =NO
Fig.6.Storage overhead for different number of access nodes.
Li et al. 2024 | https://doi.org/10.34133/space.0143 13
transaction cost across shards is less than the throughput incre-
ment brought by shard, shard will be benecial for improving
system throughput.
Comprehensive evaluation
e previous text conducted a quantitative analysis based on
typical data on the messaging complexity, spatial complexity,
and transaction throughput of shard and non-shard systems.
It can be concluded that shard is benecial to the time and
storage costs as well as transaction throughput of blockchain
systems to a certain extent and within a certain range. is
section aims to derive general laws that aect blockchain per-
formance factors, providing theoretical support for the security
and trustworthiness system for mega-constellations.
e paper compares the messaging cost of shard and non-
shard systems, rst, by investigating the variation of messaging
complexity Ctotal of non-shard systems with consensus node I.
When non-shard, the number of shards N = 1. According to
the analysis of messaging complexity in the “Simulation and
experiment design” section, the consensus messaging complex-
ity within the shard is shown in Eq. 15:
us, system messaging complexity Ctotal as shown in Eq. 16:
Among them, I is the number of consensus nodes, M is the
total number of satellites (M set to 20,000), and p is the nor-
malization coecient between the average time required for a
single satellite node to synchronize each block of data and the
consensus time.
According to Eq. 16, a graph of the relationship between
system messaging complexity and the number of consensus
nodes is drawn, as shown in Fig. 8. e system messaging cost
rst decreases as the number of consensus nodes increases,
reaches a minimum of 1,735 when the consensus nodes are 17,
and then increases as the number of consensus nodes increases.
Because in the early step, as the number of consensus nodes
increases, although the consensus times increase linearly, as
the number of consensus nodes increases, the concurrency of
synchronization increases, resulting in a decrease in overall
times. Later, the impact of increasing consensus nodes is larger,
so the system messaging times increase as the number of con-
sensus nodes increases.
By establishing a mathematical model, the general relation-
ship between the number of consensus nodes I and the number
of satellites M without fragmentation is further analyzed. As
shown in Eq. 16, the total messaging cost can be regarded as a
quadratic function of one variable, and the rst derivative of
the variable can be calculated. e result is shown in Eq. 17:
Let
C′
total
= 0; the obtained results are shown in Eq. 18:
e equation of a univariate cubic function is solved, whose
solution is the minimum point of the function. Equation 18
can be converted into the general form of the Cardano formula.
By comparison, it can be obtained that a = 4, b = −1, c = 0,
d = −M*p. By using the substitution method, it can be converted
into a special form of the Cardano formula y3 + py + q = 0, and
the results can be obtained as shown in Eqs. 19 and 20:
According to Eq. 17, I > 0, the positive real number solution
of the function y
3
+ py + q = 0 is the meaningful solution, and
it can be seen that the positive real number solution is shown
in Eq. 21:
(15)
Ci
internal =C
i
proposal +C
i
prevote +C
i
precommit
=
(
I
i
−1
)
+I
i(
I
i
−1
)
+I
i(
I
i
−1
)
=2I2
i
−I
i
−
1
(16)
C
total =Cinrernal +Csync =2I2−I−1+
M−I
I
∗
p
(17)
C
�
total =4I2−1+
M∗p
I
2,M≥I,p>0, I>
0
(18)
4I3−I2−M∗p,M
≥
I,p
>
0, I
>
0
(19)
p=
3ac −b
2
3a
2
=−
1
48
(20)
q
=
27a
2
d−9abc+2b
3
27a
3=−
216M∗p+1
864
Fig. 7. System throughput result analysis.
Li et al. 2024 | https://doi.org/10.34133/space.0143 14
From Fig. 8, it can be seen that the function is a convex
function, and the minimum value of the convex function has a
unique solution, that is, at most one minimum value. Equation 21,
as the positive real number solution of the function y3 + py + q = 0,
is the maximum point of the function, which is the universal
solution of I.
By establishing a mathematical model, the general relation-
ship between the number of consensus nodes I, the number of
shards N, and the number of satellites M in the case of shard is
further analyzed.
To further enhance the universality of the model, the shard
consensus messaging cost (weighted value k1) and cross-shard
consensus messaging cost (weighted value k2) of the sharding
blockchain system in Eq. 7 in the “Simulation and experiment
design” section were weighted, and the results are shown in
Eq. 22:
where k1 + k2 = 1, N ≥ 1, I > 0, M ≥ I, p > 0. Based on the above
theoretical analysis, the messaging cost of the distributed secu-
rity access authentication system is simulated and visualized.
Among them, the number of consensus nodes I ranges from 1
to 100, the range of partition quantity N is 1 to 50, analyzing
the complexity of system messaging overhead as a function
of consensus nodes and shards, and the simulation results are
shown in Fig. 9:
From Fig. 9, it can be seen that the function Ctotal is convex,
and there is a unique solution to the minimum value within a
closed interval, that is, a strictly convex function on a convex
open set can only have at most one minimum value.
We formulated a gradient diagram delineating the equation
interrelation involving the number of consensus nodes, shard
count, and system time overhead, as illustrated in Fig. 10.
Employing the gradient descent method, we conducted an in-
depth analysis of the function’s gradient variations to ascertain
the minimal range of the function. Distinct colors within dif-
ferent regions signify the system time overhead under diverse
environmental congurations (consensus node count, shard
count). Darker hues denote lower values of system time over-
head, while star points symbolize theoretical optimal solutions
in the context of simulation experiments. e white dashed line
delineates a potential optimization trajectory achievable
through the application of the gradient descent method. In this
experimental context, the search step size was set to 0.001, the
search origin was positioned at (0, 0), and the threshold was
established at 0.00001. e analysis outcomes, depicted in Fig.
10, manifest that the most rapid gradient changes occur at the
two corners, leading to the determination of the equation’s
extremal point at (17.7946376800, 16.20847702026), situated
on the le segment of the diagram.
Further analysis of the theoretical universal solution, where
the function can be viewed as a multivariate function of I and
N, transforms the problem solving into nding the maximum
value of the multivariate function Ctotal.
e partial derivative of I for the function C
total
is calculated,
and the result is shown in Eq. 23:
e partial derivative of N for the function C
total
is calculated,
and the result is shown in Eq. 24:
Let Eq. 23 be equal to 0, and the equivalent result is as shown
in Eq. 25:
(21)
3
216M∗p+1
1728 +216M∗p+12
2999808 −
1
62208
+
3
216M∗p+1
1728
−
216M∗p+1
2
2999808
−
1
62208
+
1
12
(22)
C
total =k1∗
k
i=1Ci
internal +k2∗Ccross +Csync
=k1∗
2I2−I−1
N
+k2∗
2N2−N−1
+M−I∗N
I
∗
N
∗p
,
(23)
𝜕
f
𝜕I
=k1I
2
∗(4I−1)−M∗
p
NI
2
(24)
𝜕f
𝜕N
=−k1
(
2I
2
−I−1
)
+k2(4N−1)+M∗
p
IN
2
(25)
4k1I3
−
k1I2
−
Mp
=
0
Fig. 8. The relationship between system messaging complexity and consensus nodes.
Fig. 9.The complexity of system messaging overhead varies with the number of
consensus nodes and shards.
Li et al. 2024 | https://doi.org/10.34133/space.0143 15
Let Eq. 24 be equal to 0, and the equivalent result is as shown
in Eq. 26:
e equation of a univariate cubic function is solved, whose
solution is the minimum point of the function.
Equation 25 can be converted into the general form of the
Cardano formula. By comparison, a = 4k1, b = −k1, c = 0,
d = −M*p can be obtained and will be converted into a special
form y3 + py + q = 0 of the Cardano formula by using the sub-
stitution method, and the extreme value of I can be obtained
as shown in Eq. 27:
Equation 26 can be converted into the general form of the
Cardano formula. By comparison, a = 4k2I, b = −k2I, c = 0,
d = −k1I3 + k1I2 + k1I − Mp can be obtained and will be con-
verted into a special form y3 + py + q = 0 of the Cardano for-
mula by using the substitution method, and the extreme value
of N can be shown in Eq. 28:
It can be seen that Eq. 27 is the general solution of I, and
Eq. 28 is the general solution for N. e above general solution
can guide the parameter design such as the selection of con-
sensus nodes and the number of shards in sharding blockchain
systems for mega-constellation.
Conclusion
e paper proposes a multifunctional domain node security
access authentication based on sharding blockchain. First, for
the hierarchical and domain-based application scenarios of
mega-constellations, a multilayer distributed security and trust-
worthiness system of “1 + N + 1” is constructed based on the
consortium chain, and then, with a focus on the constraint
of on-orbit hardware resources, a distributed security access
authentication process for nodes within/among domains based
on consortium blockchain is proposed. Technical approaches
such as sharding blockchain and optimized TBFT consensus
algorithm process are adopted to signicantly reduce the com-
plexity of blockchain. Finally, functional verication and per-
formance analysis of the sharding blockchain system were
conducted from the perspectives of messaging complexity,
spatial complexity, transaction throughput, and comprehensive
evaluation. rough modeling analysis, it can be seen that
sharding technology improves and enhances the above perform-
ance indicators of the system.
By establishing relevant factors such as the number of nodes
M, the number of consensus nodes I, the number of shards N,
and the normalization coecient of system messaging cost p
that a comprehensive estimate mathematical model for system
performance is constructed, a universal solution for the num-
ber of consensus nodes I and the number of shards N is solved.
e above general solution can guide the parameter design such
(26)
4k2IN3
−
k2IN2
−
k1I3
+
k1I2
+
k1I
−
Mp
=
0
(27)
3
216Mp+k1
1728k1
+
216Mp+k12
2985984k2
1
−
1
2985984
+
3
216Mp+k1
1728k1
−
216Mp+k1
2
2985984k2
1
−
1
2985984 +
1
12
(28)
Fig. 10. The variation of system gradient with consensus nodes and shards.
Li et al. 2024 | https://doi.org/10.34133/space.0143 16
as the selection of consensus nodes and the number of shards
in sharding blockchain systems in scenarios with huge satellite
nodes.
Acknowledgments
Funding: is research received the specic grant from China’s
National Social Science Foundation (U23B2025 and U22B2014).
Author contributions: Z.L. have collectively written the manu-
script, T.L., J.Z. and W.Q. helped to revise the manuscript. All
Authors read and approved the manuscript.
Competing interests: e authors declare that they have no
competing interests.
Data Availability
e data used to support the ndings of this study are available
from the corresponding author upon reasonable request.
References
1. Neinavaie M, Khalife J, Kassas ZM. Acquisition, Doppler
tracking, and positioning with Starlink LEO satellites: First
results. IEEE Trans Aerosp Electron Syst. 2022;58(3):
2606–2610.
2. Patel H, Maynard IW, Rana L, Bernd C. Strategic forecasting
toward achieving defensible space architecture by year 2030.
J Spacecr Rocket. 2022;59(5):1437–1454.
3. Li Z, Song G, Wang L, etal. Research on key technologies of
high eciency management and intelligent application for
mega-constellation. Spacecra Eng. 2023;32(01):1–7.
4. Jia H, Jiang C, Kuang L, Lu J. An analytic approach for
modeling uplink performance of mega constellations.
IEEE Trans Veh Technol. 2023;72 (2):2258–2268.
5. Chen BS, Lin HY. Decentralized H∞ observer-based attack-
tolerant formation tracking network control of large-scale LEO
satellites via HJIE-reinforced deep learning approach. IEEE
Access. 2023;11:17165–17196.
6. Xie H, Zhan Y, Zeng G, Pan X. LEO mega-constellations for
6G global coverage: Challenges and opportunities. IEEE Access.
2021;9:164223–164244.
7. Usman M, Qaraqe M, Asghar MR, Ansari IS. Mitigating
distributed denial of service attacks in satellite networks. Trans.
Emerg. Telecommun. Technol. 2020;31(6):Article ett3936.
8. Mohorcic M, Werner M, Svigelj A, Kandus G. Adaptive routing
for packet-oriented intersatellite link networks: Performance
in various trac scenarios. EEE Trans Wirel Commun.
2002;1(4):808–818.
9. Koroniotis N, Moustafa N, Slay J. A new intelligent satellite
deep learning network forensic framework for smart satellite
networks. Comput Electr Eng. 2022;99:Article 107745.
10. Gao W, Li H, Zhong M, Lu M. e separate clock dri
matched lter to detect time synchronization attacks toward
global navigation satellite systems. IEEE Trans Ind Electron.
2023;70(6):6305–6315.
11. Guo W, Xu J, Pei Y, Yin L, Jiang C, Ge N. A distributed
collaborative entrance defense framework against DDoS
attacks on satellite internet. IEEE Internet ings J.
2022;9(17):15497–15510.
12. Sun W, Wang L, Wang P, Zhang Y. Collaborative blockchain for
space-air-ground integrated networks. IEEE Wirel Commun.
2020;27(6):82–89.
13. Wullems C, Pozzobon O, Kubik K. Signal authentication and
integrity schemes for next generation global navigation satellite
systems. Paper presented at: Proceedings of the European
Navigation Conference GNSS; 2005 Jul 19–22; Munich,
Ge rma ny.
14. Zhang Y, Chen J, Huang B. An improved authentication
scheme for mobile satellite communication systems. Int J Satell
Commun Netw. 2015;33(2):135–146.
15. Yong Y, Feiyue W. Blockchain theory and method. Beijing:
Tsinghua University Press; 2019. p. 1–35.
16. Wood G. Ethereum: A secure decentralised generalised
transaction ledger. Ethereum Project Yellow Paper.
2014;151(12):1–32.
17. Zhang PY, Zhou MC. Security and trust in blockchains:
Architecture, key technologies, and open issues. IEEE Trans
Comput Soc Syst. 2020;7(3):790–801.
18. Qi XD, Zhang Z, Jin CQ, Zhou A. BFT-Store: Storage partition
for permissioned blockchain via erasure coding. Paper
presented at: 2020 IEEE 36th International Conference on
Data Engineering (ICDE); 2020 Apr 20–24; Dallas, TX, USA.
19. Luu L, Narayanan V, Zheng C, Baweja K. A secure sharding
protocol for open blockchains. Paper presented at:
Proceedings of 2016 ACM SIGSAC Conference on Computer
and Communications Security; 2016: New York, USA.
20. Zhou QH, Huang HW, Zheng ZB, Bian J. Solutions to
scalability of blockchain: A survey. IEEE Access. 2020;8:
16440–16455.
21. Gao ZF, Zheng JL, Tang SY, Long Y, Liu Z-Q, Liu Z,
Gu D-W. State-of-the-art survey of consensus mechanisms
on DAG-based distributed ledger. J Softw. 2019;31(4):
1124–1142.
22. Huang H, Yue Z, Peng X, He L, Chen W, Dai H-N, Zheng Z,
Guo S. Elastic resource allocation against imbalanced transaction
assignments in sharding-based permissioned blockchains. IEEE
Trans Parallel Distrib Syst. 2022;33(10):2372–2385.
23. Bagui S, Nguyen LT. Database sharding: To provide fault
tolerance and scalability of big data on the cloud. Int J Cloud
Appl Comput. 2015;5(2):36–52.
24. Yun J, Goh Y, Chung JM. Trust-based shard distribution
scheme for fault-tolerant shard blockchain networks. IEEE
Access. 2019;7:135164–135175.
25. Qi X, Zhang Z, Jin C, Zhou A. A reliable storage partitioning
for permissioned blockchain. IEEE Trans. Knowl. Data Eng.
2021;33(1):14–27.
26. Garcia R, Ramachandran G, Ueyama J. Exploiting smart
contracts in PBFT-based blockchains: A case study in medical
prescription system. Comp Net. 2022;211(6):Article 109003.
27. Misic J, Misic VB, Chang X, Qushtom H. Adapting PBFT for
use with blockchain-enabled IoT systems. IEEE Trans Veh
Tech nol . 2021;70(1):33–48.
