NKN: a Scalable Self-Evolving and Self-Incentivized Decentralized Network

NKN Lab

www.nkn.org(Dated: March 13, 2018 Version: 1.0)

NKN (New Kind of Network) is a new generation of highly scalable, self-evolving and self-incentivized blockchain network infrastructure. NKN addresses the network decentralization andself-evolution by introducing Cellular Automata (CA) methodology [1, 2] for both dynamism andefficiency. NKN tokenizes network connectivity and data transmission capacity by a novel and use-ful Proof of Work. NKN focuses on decentralizing network resources, similar to how Bitcoin [3]and Ethereum [4] decentralize computing power as well as how IPFS [5] and Filecoin[6] decentralizestorage. Together, they form the three pillars of the Internet infrastructure for next generationblockchain systems. NKN ultimately makes the network more decentralized, efficient, equalized,robust and secure, thus enabling healthier, safer, and more open Internet.

CONTENTS

1. Challenges 21.1. Limitations of P2P Networks 21.2. Resource Utilization 21.3. Net Neutrality & Fragmentation 2

2. Vision 22.1. Objectives of NKN 22.2. The Third Pillar: Networking 32.3. Elementary Components 32.4. Networking toolkit for Fast and Painless DApp Development 4

3. Technology Foundations 43.1. Cellular Automata 43.2. Rules as Formulas 5

4. New Kind of Network 54.1. Next Generation Decentralized Network 54.2. A Useful Proof of Work 64.3. Network Topology and Routing 6

4.3.1. Dynamics 74.3.2. Self-Organization 74.3.3. Self-Evolution 8

4.4. Efficient Decentralization 8

5. Cellular Automata Powered Consensus 85.1. Mainstream Consensus 85.2. Cellular Automata Powered Consensus 9

5.2.1. Scalability Issue of BFT and PBFT 95.2.2. Consensus in Cellular Automata Described by Ising Model 95.2.3. Ising Model 95.2.4. Link Between Cellular Automata and Ising Model 105.2.5. Majority Vote Cellular Automata as a Consensus Algorithm 105.2.6. Randomized Neighbors 105.2.7. Simulations of CA Consensus Algorithm 115.2.8. Extension to Asynchronous and Unreliable Networks 11

5.3. Proof of Relay 115.4. Potential Attacks 12

6. Conclusions 13

References 14

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1. CHALLENGES

After years of transmutation, the Internet is in dan-ger of losing its original vision and spirit. For exam-ple, Network Neutrality is overturned [7]; spectrum andbandwidth are not efficiently utilized; information is frag-mented and can be censored; privacy protection is lim-ited. These signal that the network needs a reform.

Existing solutions are not suitable for next generationblockchain systems due to the following reasons:

• Utilize a centralized approach to improve efficiency.

• Sacrifice the scalability of the network to speed upconsensus.

• Limit participation rate of nodes or require autho-rization to increase “security”.

• Use purely financial motivations or trusted thirdparties to solve problems which should be solvedby mathematics and technology.

1.1. Limitations of P2P Networks

Peer-to-peer (P2P) networks currently face several ma-jor challenges, which are the opportunities for NKN.First static network topology is vulnerable to faulty andmalicious attack. Second, there is no economic self-incentivized scheme for network connectivity and datatransmission. Finally, network scalability is widely sacri-ficed to enhance controllability. These are all to be solvedby the NKN as shown in Fig. 1.

FIG. 1. Feature comparisons between existing solutions andNKN.

1.2. Resource Utilization

A highly reliable, secure and diverse Internet is essen-tial to everyone. Yet, huge inefficiency exists in the cur-rent network when providing global connectivity and in-formation transmission. It’s time to rebuild the networkwe want, not just patch the network we have. A fullydecentralized and anonymous peer-to-peer system offershuge potential in terms of improved efficiency, sustain-ability and safety for industry and society.

1.3. Net Neutrality & Fragmentation

When the Federal Communications Commission(FCC) approved a measure to remove the net neutral-ity rules by the end of 2017 [7], a demand of ending ourreliance on big telecommunication monopolies and build-ing decentralized, affordable, locally owned Internet in-frastructure becomes ever stronger. The unrestricted andprivate Internet access environment is becoming unsus-tainable under an endless stream of attacks and blockage,leading to selective and biased information propagation.Without a proper incentivizing engagement scheme, itis almost impossible to maintain a constant and securedinformation propagation channel.

Furthermore, Internet has become fragmented due tovarious reasons. This not only exacerbates separation butalso negatively impacts innovation of science, technologyand economy.

2. VISION

NKN intends to revolutionize the entire network tech-nology and business. NKN wants to be the Uber orAirbnb of the trillion-dollar communication service busi-ness, but without a central entity. NKN aspires to freethe bits, and build the Internet we always wanted.

2.1. Objectives of NKN

NKN sets the following objectives:

• Any node can connect to this fully open networkfrom any place

• Promote network sharing

• Secure net neutrality from network layer innova-tions

• Always keep network open and scalable

• Perform efficient and dynamic routing

• Tokenize network connectivity and data transmis-sion assets and incentivize participating nodes

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• Design and build the next generation of blockchainnetwork

2.2. The Third Pillar: Networking

By blockchainizing the third and probably the lastpillar of Internet infrastructure, NKN will revolutionizethe blockchain ecosystem by innovating on the networklayer, after Bitcoin [3] and Ethereum [4] blockchainizedcomputing power as well as IPFS [5] and Filecoin[6]blockchainized storage. The next generation blockchainsbased on NKN are capable of supporting new kind of de-centralized applications (DApp) which have much morepowerful connectivity and transmission capability. Thevision of NKN is not only to revolutionize the decentral-ized network layers, but also to develop core technologiesfor the next generation blockchain.

Core Building Blocks of Compute Infrastructure

Compute:

Bitcoin

Ethereum

Storage:

IPFS/

Filecoin

Network:

NKN

FIG. 2. NKN as the 3rd pillar of blockchainized Internetinfrastructure.

2.3. Elementary Components

NKN builds upon several innovative elementary com-ponents that are different from existing solutions, asshown in Fig. 3.

Application Layer: DApps & Smart Contracts

Incentive Layer:

Transmission & Connectivity Tokenized

Consensus Layer:

More Useful Proof of Work: Proof of Relay

Networks Layer:

Cellular Automata Rules & Dynamic Topology

Block Structure, Cryptography etc.

FIG. 3. NKN elementary components.

1. Blockchainizing the remaining core buildingblocks of computing infrastructure: NKN in-

troduces the concept of decentralized data trans-mission network (DDTN) scheme and utilizes trulydecentralized blockchain to provide network con-nectivity and data transmission capability by us-ing massive independent relay nodes to solve theproblem of precipitation of redundant data on thenetwork.

2. Cellular Automata powered DDTN: NKN in-troduces the idea of using Cellular Automata toreconstruct the network layer. The intrinsic char-acteristics of Cellular Automata such as decentral-ization, peer equivalence and concurrency enable usto build a truly decentralized blockchain network.

3. Cellular Automata driven consensus: NKNachieves consensus efficiently with high fault tol-erance in large scale distributed systems based onCellular Automata, which is essential for decentral-ized systems without trusted third parties.

4. Proof of Relay, A Useful Proof of Work: NKNproposes Proof of Relay (PoR), a mechanism thatencourages participants to contribute to blockchainnetwork by sharing their connectivity and band-width to get rewards, enhancing network connec-tivity and data transmission capacity. PoR is auseful Proof of Work (PoW).

5. Tokenization of network connectivity anddata transmission capability: NKN tokenizesnetwork connectivity and data transmission capa-bility by encouraging participants to share theirconnectivity and bandwidth in exchange for tokens.Idle network resources can be better used throughsuch sharing mechanism. NKN improves the uti-lization of network resources and the efficiency ofdata transmission. Refer to our paper on economicsmodel for details [8].

6. Networking toolkit for fast and painlessDApp development: With NKN, DApp devel-opers now have a new networking toolkit to buildtruly decentralized applications quickly and eas-ily. DApp developers can focus entirely on cre-ativity, innovation, user interface / user experi-ence and business logic. This networking toolkitis entirely complimentary to the toolkit by otherblockchain projects working on identity, machinelearning, payment, storage, and etc.

NKN utilizes Cellular Automata methodologies toachieve full decentralization. All nodes are equal, trulypeer to peer, and each is capable of sending, receiving,and relaying data. Cellular Automata makes it possibleto have simple local rules that can generate highly dy-namical and highly scalable global network overlay topol-ogy that is independent of the underlying physical andlogical infrastructure. The simplicity and locality of rulesmake it possible to have cost efficient implementation

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on all types of network devices, from Internet of Things(IoT), smart phones, all the way to routers. Despite itsseemingly simplicity, Cellular Automata enabled routingcan be highly random and unpredictable, thus providingsuperior security and privacy.

NKN nodes get rewarded for providing connectivityand transmission power, resulting in a fully competitivemarketplace optimized for maximizing the entire networkcapacity. For existing networks, NKN will increase theutilization of connectivity and data transmission capacityby sharing the unused bandwidth of participating nodes.More and more new nodes will join the network to earnreward, thus quickly bootstrapping and expanding theNKN network. Existing nodes are incentivized to up-grade and increase data transmission capacity. All ofabove will further boost overall network capacity, as wellas improve the dynamic topology since the network hasmuch more degrees of freedom in choosing the route.

In addition, NKN proposes a novel and more usefulproof of work. Unlike traditional hashing computationtype Proof of Work that provides no additional utility,NKN introduces Proof of Relay based on many useful ac-tivities including staying on-line for extended period, ex-panding amount of peer connection, providing high speedand low latency relay, etc. Even the consensus algorithmis designed from ground up to improve efficiency and fair-ness, while converge deterministically and globally basedon local knowledge.

Furthermore, NKN is intended to promote networksharing and network ownership by its users. NKN’s eco-nomic model and governance model will reflect this indesign and in implementation. These technology andeconomic model innovations complement each other andtogether will amplify the power of NKN network.

2.4. Networking toolkit for Fast and PainlessDApp Development

With NKN, DApp developers now have a new net-working toolkit to build truly decentralized applicationsrapidly and painlessly. DApp developers can focus en-tirely on the ideas and innovation, UI (user interface)/UX (user experience), and business logic that make theirproduct successful to the end users. They no longer needto wade through the wild jungle of blockchain, cryptog-raphy, consensus mechanism, identity and security beforethey even write one line of code for their users.

For example, in traditional app development with cen-tralized SaaS (Software as a Service) offerings, one canhost app on cloud computing platforms, store data oncloud storage, use web services for text message, phonecall and payment. In the decentralized blockchain world,it is already conceivable today to build a new kind ofFacebook by using Ethereum [4] /NEO [9] for comput-ing, IPFS [5] for storage, and NKN for networking. Thebeauty of this new paradigm is that users will personallyown their identity and data, and can be both consumer

and provider in the entire system as well. On top of that,at each layer there are built-in self-incentivized mecha-nism to maximize the network effect and bootstrap theentire community.

NKN will be one of the three foundational elementsand play a critical role in this decentralized paradigm.

3. TECHNOLOGY FOUNDATIONS

In this whitepaper, we take selective elements of theNKS (New Kind of Science) [2] as inspiration. NKN uti-lizes microscopic rules based on Cellular Automata todefine network topology, achieves self-evolution behav-iors, and explores Cellular Automata driven consensus,which is fundamentally different from existing blockchainnetwork layer.

As a powerful tool to study complex systems, CellularAutomaton is closely linked to philosophical categoriessuch as simple and complex, micro and macro, local andglobal, finite and infinite, discrete and continuous, etc.

3.1. Cellular Automata

Cellular Automata

Dynamic

Peer Equal

Decentralized

Open

Parallel

Simple

FIG. 4. Properties of Cellular Automata.

Cellular Automata (CA) is a state machine with a col-lection of nodes, each changing its state following a localrule that only depends on its neighbors. Each node onlyhas a few neighbor nodes. Propagating through localinteractions, local states will eventually affect the globalbehavior of CA. The desired openness of network is deter-mined by the homogeneity of Cellular Automata whereall nodes are identical, forming a fully decentralized P2P(peer-to-peer) network. Each node in the NKN networkis constantly updating based on its current state as wellas the states of neighbors. The neighbors of each node arealso dynamically changing so that the network topologyis also dynamic without changing its underlying infras-tructure and protocols.

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NKN utilizes CA to achieve efficient, decentralized,and dynamical topology such that information and datacan be transmitted efficiently and dynamically withoutcentralized connectivity.

3.2. Rules as Formulas

The Cellular Automata programming formula is called“local rule”, which is an indispensable rule for next gen-eration network of NKN and has an important influenceon the network topology [2, 10–13].

Proper choice of local rules leads to Cellular Automatawith complex but self-organized behaviors on the bound-ary between stability and chaos. Rules are essential be-cause they are formulas to program Cellular Automataand Automata Networks. The static characteristics of aCellular Automaton is a discrete dynamic system definedas

CA = (S,N,K, f) (1)

Finite number of nodes interact in a regular network.S represents states of nodes, where each node has a lo-cal state. The state of all nodes determines the globalstate. N denotes the number of nodes in network. K de-notes neighbor set, i.e. which neighbor nodes are takeninto account in local state transitions. f denotes a statetransition function, which has a dramatic impact on theglobal evolution of the system.

The dynamic characteristics of a Cellular Automatonis illustrated in Fig. 5. Dynamic evolution starts froman initial state. Nodes change their states based on theircurrent states and the states of their neighbor nodes. Theglobal state is fully determined by local states of all nodesand evolves accordingly.

Cellular Automata Characterization

Static

Dimension

Local State of Cells

State Transitions

Neighborhood

Dynamic

Dynamic Evolution

Initial Local State

Current State of a Cell

States of Neighbor Cells

Evolution Correlation

Local States Evolution

Global States Evolution

Dynamics of State Transitions

Synchronous

Asynchronous

Stochastic

FIG. 5. Characteristics of Cellular Automata.

The NKN team believes CA-based or CA-driven sys-tems are more natural and organic than current ap-

proaches utilizing static and fully connected topology.Complex systems with such a simple structure are closerto natural systems, thus enabling self-evolution.

4. NEW KIND OF NETWORK

NKN is the next generation of peer to peer networkinfrastructure built upon blockchain technology backedby Cellular Automata theory aiming at revolutionizingthe Internet with true decentralization and native tokenincentive mechanism.

4.1. Next Generation Decentralized Network

As the current leaders in blockchain, Bitcoin andEthereum tokenize computational power through Proofof Work (PoW). IPFS [5], Filecoin [6], Sia [14] and Storj[15], on the other hand, tokenize storage. Yet, few sys-tems blockchainize network connectivity and data trans-mission power, the third essential building block in theInternet. NKN is designed to tokenize network connec-tivity and data transmission capability as a useful PoW.

NKN solves the “efficiency” problem of blockchain byequalizing all nodes in the network. Each node follows arule of Cellular Automaton and updates its state basedon local rules. Proposed by Von Neumann in 1940s, Cel-lular Automaton (CA) is a generic term for a type ofmodel, a state machine characterized by discrete time,space and interaction [16, 17]. It is a discrete system thatevolves locally according to specific rules and is provento be able to emulate the evolution of complex systems.Cellular Automaton has the characteristics of decentral-ization, peer equality and concurrency. For the first time,NKN proposed Cellular Automata as the fundamental el-ement of the network layer for blockchain, so as to ensurethat the entire network layer can benefit from it.

Updating formulas in Cellular Automata are called “lo-cal rules”, which are found to be the critical factor thatcontrols the transition of Cellular Automaton betweenstability and chaos [2]. As an indispensable part of NKN,rules are one of the main factors impacting the networktopology.

NKN introduced the concept of Decentralized DataTransmission Network (DDTN). DDTN combines mul-tiple independent and self-organized relay nodes to pro-vide clients with connectivity and data transmission ca-pability. This coordination is decentralized and does notrequire trust of any involved parties. The secure opera-tion of NKN is achieved through a consensus mechanismthat coordinates and validates the operations performedby each node. DDTN provides a variety of strategies fordecentralized application (DApp).

In contrast to centralized network connectivity anddata transmission, there are multiple efficient paths be-tween nodes in DDTN, which can be used to enhance

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data transmission capacity. Native tokens can incen-tivize the sharing of network resources, and eventuallyminimize wasted connectivity and bandwidth. Such aproperty is termed “self-incentivized”.

4.2. A Useful Proof of Work

As the pioneering cryptocurrency, Bitcoin [3] is gen-erated by mining, a Proof of Work mechanism that in-centivizes miners to verify transactions by solving diffi-cult hashing problems. The downside of Bitcoin miningis that efficient mining requires specialized and expen-sive hardware and consumes a lot of energy. Accord-ing to Digiconomist, Bitcoin energy consumption rate isclose to 50 TWh/year at mid February 2018 and still in-creasing, while the number is close to 14 TWh/year forEthereum. Electricity consumed by these two cryptocur-rencies combined has surpassed the electricity usage ofmany countries.

A way to prove the work while avoiding waste of re-sources is highly desired. NKN proposes an alternative tothe current PoW by providing a more decentralized, dy-namically evolving, self-organizing and self-evolving net-work infrastructure and designing a whole new set of con-sensus mechanisms. The novel PoW does not result in awaste of resources. Instead, it is a peer-to-peer sharingmechanism at blockchain level. Participants receive re-wards by contributing more network resources than theyconsume. NKN uses Proof of Relay mechanism to guar-antee network connectivity and data transmission capac-ity.

4.3. Network Topology and Routing

Cellular Automata on Networks (CAoN) is a natu-ral extension of Cellular Automata [10, 11, 18] that isable to model networks with non-geometric neighbor con-nections. It is powerful when modeling networks whosetopology is evolving based on local rules. As the goal isto build a decentralized blockchain system with dynamictopology, CAoN is a natural model for the system.

We consider a dynamic P2P network with N nodes.The network connections at time t can be described byan N ×N adjacency matrix A(t) that evolves with time.Connections between nodes can be added, removed, oraltered at each time step. If the dynamics of A is Marko-vian, the updating process can be written as

A(t+ 1) = f [A(t)], (2)

where f is the updating rule of network topology. To keepthe updating rule local, f should be chosen such that onlyinformation of the neighbors of each node is used whenupdating its connections. The updating rule above doesnot contain states of nodes, so the topology evolution isindependent of the state of any node. A more general

Markovian updating rule should take both topology ofthe network and states of nodes into consideration suchthat

A(t+ 1) = f [A(t), S(t)]

S(t+ 1) = g[A(t+ 1), S(t)](3)

where S(t) is a vector representing the states of all nodesin the network at time t, f is the topology updating rule,and g is the state updating rule. Similarly, f and g shouldbe chosen such that only information of current neigh-bors are used when updating. The state could containhistorical information. An example state in blockchainsystem is all the blocks that a node stores locally. Notethat although we describe the system formally using theglobal state S and global connectivity A, each node i onlyneeds to know and store its local state Si and neighbors{j|Aij 6= 0}.

Consider a CAoN in a blockchain system where blocksare being generated. Each time a block is received, thenode updates its state and send the block to neighborswith digital signature. The neighbors will decide whetherto forward the message depending on their states like ifit has received the block, if the block is valid, or conflictwith other block in state, effectively affecting the topol-ogy of the entire network without changing the physicallayer or the underlying protocol.

As an example to illustrate how we model the network,one can consider a general Network Automaton that al-lows an arbitrary number of neighbors. For simplicity,a minimalist approach is adopted to emulate blockchainexpanding and data relay from a small set of microscopicrules. Initially (at time zero) the network is a 3D cubicstructure with 8 nodes, each has 3 neighbors, as shownin Fig. 6.

XY

Z

FIG. 6. An example of Network Automata with 8 nodes form-ing a cubic network in 3D space at initial state.

Starting from the simple network in Fig. 6, the systemis extended by adding nodes to it following various up-dating rules. The resulting topology can be dramaticallydifferent when different rules are used, as shown in Fig. 7.

NKN will bridge network evolution and blockchainfunctions using similar network models with microscopicrules. The simple local rules make replication straight-forward, simplifying and accelerating system implemen-tations.

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(b)(a)

FIG. 7. Some examples of complex blockchain networktopologies with various simple rule sets (a) ring topology, rule1655146, time step 1573; (b) pseudo-random topology, rule1655185, time step 1573.

4.3.1. Dynamics

Dynamics in CAoN are purely local: each node eval-uates the state transition independently of other nodesand changes its state accordingly [19]. Node state can bedriven by either the interaction between nodes, or exter-nal information, as shown in Fig. 8.

Be Commanded by an External Entity

Autonomously, Based on Some Internal Autonomous

Decision Making

FIG. 8. Possible conditions for a node to change its state inCAoN.

Rules are crucial to the resulting topology in CAoN.Network topology would be very different given smallchanges in the updating rules, as shown in Fig. 9.

Although in the mathematical description discretetime step was used for convenience, CAoN does not re-quire nodes have any global time or discrete time. In-stead, each node performs the update asynchronously[19]. This is a more general and realistic description ofreal blockchain networks.

4.3.2. Self-Organization

The global dynamics of Cellular Automata can be clas-sified into 4 types [2]: steady, periodic, chaotic, and com-plex. Our focus is in the complex type (Class 4), alsoknown as the edge of chaos, where all initial patternsevolve into structures that interact in complex ways, with

(b)

(a)

(c)

FIG. 9. Dynamics of network topology by rewriting rulesof Cellular Automata at the same time step index, (a) rule1655163, time step 1573; (b) rule 1655175, time step 1573; (c)rule 1655176, time step 1573.

the formation of local structures that can survive for longperiods of time. Wolfram speculates that although notall of the Class 4 Cellular Automata are capable of uni-versal computation, many of them are Turing-complete.This view has been successfully proven by the Rules 110[2, 20] and Conway’s Game of Life [21]. Complex, self-organizing and dynamical structures emerge spontaneousin Class 4 CA, providing us an ideal candidate for the ba-sis of decentralized systems.

Edges of ChaosStability Periodic Behavior Chaos

0.0 0.1 0.2 0.3 0.4 0.5 Langton’s λClass-1Global

Uniform Patterns

Class-2Periodic, Regular Patterns

Class-4Complex, Self-organized Behavior

Class-3Seemingly Random

Rule110 Rule30Rule04Rule248

FIG. 10. Wolfram’s 4 classes of behaviors versus Langton’s λparameter on 1D Cellular Automata.

A quantitative measure of the rule that can explainand predict the behavior type of the CA is the Lang-ton’s λ parameter defined by the fraction of rule tableentries that results in active state. As λ increases from

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0, the system will transit from steady state to periodicstate, then to complex state, and finally to chaos state,as shown in Fig. 10. In the classic 1D CA with nearestneighbor interaction, Class 4 behavior emerges when λ isaround 0.3. Langton’s λ parameter provides us a theo-retical guide on how to find the desired updating rules,which is essential for high dimensional systems.

4.3.3. Self-Evolution

CAoN is inherently self-evolving due to its simple butpowerful local dynamics. The updating rule essentiallysets the direction of evolution, and the system evolvescontinuously towards the direction, regardless of the ini-tial states or how nodes are added to the network. Fig. 11shows an example of the self-evolution in CAoN.

(c)(a) (b)

FIG. 11. Self-evolution of a 3D CAoN model on rule 1655185at various time step index (a) 100; (b) 1000; (c) 10000.

4.4. Efficient Decentralization

Due to the dynamical nature of NKN, network topol-ogy between nodes is constantly updating. Proper up-dating mechanism is critical to achieve decentralizationof the resulting topology. If, for example, the updatingmechanism is chosen such that a newly joined node hashigher chance to choose node with more neighbors to beits neighbor, and the probability to choose a node is pro-portional to the degree of that node, then the resultingnetwork will be scale-free [22]: the degree distributionfollows a power law form. Such networks have central-ized hubs defined by nodes with huge degree. Althoughhubs could potentially increase efficiency, they make net-work less robust as the failure of hubs will have muchlarger impact than the failure of other nodes.

One of the NKN’s goals is to design and build net-works that are decentralized while still being efficient ininformation transmission. This should be done by usinga proper topology updating mechanism that considersboth algorithm and incentive. On the algorithm side,neighbors should be sampled and chosen randomly; onthe incentive side, reward for data transmission shouldbe sublinear (grows slower than linear function) so that

hubs are discouraged. Sparse random network is one pos-sible topology that could be generated from such mech-anism. It is decentralized and thus robust to the failureof any node, while still being efficient in routing due toits small network diameter [12].

5. CELLULAR AUTOMATA POWEREDCONSENSUS

Nodes in blockchain are peers due to the decentral-ized nature of blockchain. The inherent lack of trustin blockchain systems is particularly noteworthy becauseany node can send any information to any nodes in theblockchain. Peers must evaluate information and makeagreement on their actions for blockchain to work prop-erly [23].

NKN is designed to be a futuristic blockchain infras-tructure that requires low latency, high bandwidth, ex-tremely high scalability and low cost to reach consensus.These properties are crucial for future DApps. Thus,NKN needs new consensus algorithms that could satisfysuch high requirements.

5.1. Mainstream Consensus

Currently there are several approaches to reach con-sensus in blockchain: Byzantine fault tolerance algorithm(BFT) [24], practical Byzantine fault tolerance algorithm(PBFT) [25], Proof of Work algorithm (PoW) [3], proofof stake algorithm (PoS) [26, 27], and delegated Proof ofStake algorithm (DPoS) [28].

1. Practical Byzantine Fault Tolerant (PBFT):Byzantine fault tolerance is a model that LeslieLamport proposed in 1982 to explain the issue ofconsensus. It discusses the consensus under the sce-nario where some nodes could be evil (the messagemay be forged) and provides a worst-case guaran-tee [24]. In Byzantine fault tolerance, let the totalnumber of nodes be N and the number of bad nodesbe F , If N ≥ 3F+1, then the problem can be solvedby the Byzantine Fault Tolerant (BFT) algorithm.Lamport proved that there is a valid algorithm suchthat when the fraction of bad nodes does not ex-ceed one-third, good nodes could always reach con-sensus no matter what messages bad nodes send.Practical Byzantine Fault Tolerant (PBFT), firstproposed by Castro and Liskov in 1999, was thefirst BFT algorithm to be widely used in practice[25]. PBFT is much more efficient and works in anasynchronized way, while it can still tolerate samenumber of faulty nodes as BFT, making it morepractical to use in real systems.

2. Proof of Work (PoW): Bitcoin blockchain net-work introduced an innovative Proof of Work(PoW) algorithm [3]. The algorithm limits the

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number of proposals by increasing the cost of them,and relax the need for final confirmation of con-formity by agreeing that everyone will accept thelongest-known chain. In this way, anyone who triesto vandalism will pay a great economic cost. Thatis, to pay more than half the system computingpower. Later, various “PoX” series algorithms areproposed following this thought, using economicpenalties to restrict the spoilers. PoW is the con-sensus used by Bitcoin and is also the earliest usedin blockchain system. In brief, PoW means howmuch work a miner pays and how much it gains.The work here is the computing power and timewhich a miner provides contribute to the blockchainsystem. The process of providing such services is“mining”. In PoW, the mechanism to allocate re-ward is that the mining income is proportional tothe computing power. The more powerful miningmachine used, the more expected reward minerswill get.

3. Proof of Stake (PoS): Initially, Proof of Stake re-duces the difficulty of calculating hash according tothe amount of tokens held. PoS is similar to finan-cial assets in bank, which distribute financial returnproportional to the amount of assets that stake-holder holds in a given period. Similarly in PoS,the blockchain system allocates “interests” accord-ing to stakeholder’s token amount and hold time[26, 27]. In Delegated Proof of Stake (DPoS), notevery stakeholder is able to create block. Instead,nodes vote for trustees that represent them to en-ter the parliament and create blocks. Users whowould like to become trustees need to go throughcommunity canvassing in order to gain trust of thecommunity [28].

5.2. Cellular Automata Powered Consensus

5.2.1. Scalability Issue of BFT and PBFT

It is challenging to get consensus in large distributedsystems using BFT and PBFT algorithm. In BFT al-gorithm, the total number of messages to be sent in thesystem is O(N !)[24], making it not practical. PBFT al-gorithm reduced the total message count to O(N2)[25],which is tractable but not scalable when N is large. Inaddition, both BFT and PBFT requires every node tohave a list of all other nodes in the network, which ishard for dynamical network.

5.2.2. Consensus in Cellular Automata Described by IsingModel

Cellular Automata (CA) is naturally a large dis-tributed system with only local connections. The asymp-

totic behavior of the system is controlled by its updatingrule. It is possible to achieve guaranteed global consen-sus in CA using message passing algorithm based onlyon sparse local neighbors for a set of updating rules.

Using the mathematical framework originally devel-oped for Ising model [29] in physics, we found and provedthat a class of CA rules will guarantee to reach consen-sus in at most O(N) iterations using only states of sparseneighbors by an exact map from CA to zero temperatureIsing model. Some studies investigated the fault toler-ance of Cellular Automata and how to increase robust-ness in Cellular Automata-Based systems [30–32]. Wefurther showed that the result is robust to random andmalicious faulty nodes and compute the threshold whendesired consensus cannot be made.

5.2.3. Ising Model

Ising model is a model of spin systems with pairwise in-teraction under external magnetic field [29]. The Hamil-tonian (energy) of the system without external magneticfield can be written as

H(s) = −∑i,j

Jijsisj , (4)

where si = ±1 is the spin of node i, and Jij is the inter-action between node i and node j. We consider the casewhere Jij can only be 1 (ferromagnetic interaction) or0 (no interaction). The probability that the system willbe in state s under equilibrium follows the Boltzmanndistribution

p(s) =1

Ze−βH(s) =

1

Zeβ

∑i,j Jijsisj , (5)

where Z =∑s e−βH(s) is the partition function, β =

1kBT

with kB being Boltzmann constant and T being thetemperature, representing noise level of the system. Theunits where kB = 1 will be used for simplicity.

Ising model on lattice has been extensively studied [29,33]. For the Ising model on a D dimensional lattice withnearest neighbor interaction, a phase transition occursat finite critical temperature Tc except for D = 1 wherethe critical temperature Tc = 0. When T < Tc, thesystem collapse into one of the two states where nodeshave a preferred spin (spontaneous magnetization), whilethe system does not have a preferred spin when T > Tc.

For example, for a 2D square lattice with nearest neigh-bor interaction, the exact solution of the Ising model canbe obtained. The critical temperature is

Tc =2

ln(1 +√

2)≈ 2.27, (6)

and the spontaneous magnetization is

〈s〉 = ±[1− (sinh 2β)−4

] 18 . (7)

10

All of the spins will become the same (either 1 or -1)when T → 0.

If the distributed system of interest can be mathemat-ically described by an Ising model, then the system isguaranteed to achieve consensus (all nodes have the samestates) when temperature is zero. Finite temperatureplays the role of failure by adding randomness to statetransition, and finite critical temperature leads to robust-ness to such failure.

5.2.4. Link Between Cellular Automata and Ising Model

Cellular Automata (CA) is closely related to IsingModel. A CA is characterized by its updating rule

p(st+1|st) =∏i

p(st+1i |s

t) (8)

that represents the probability of the system to transferto state st+1 at time t+ 1 given system state st at timet. The transfer probability is conditional independentbecause every node in CA updates its state solely de-pending on the previous system state. For deterministicCA, the transfer probability p(st+1|st) is a delta func-tion. If a Hamiltonian of the form H(s) = −

∑i,j Jijsisj

can be defined for a CA such that

p(st+1i |s

t) ∝ e−βH(st+1i |st) = eβ

∑j Jijs

t+1i stj , (9)

where H(st+1i |st) is the Hamiltonian of the system given

state sj = stj ,∀j 6= i and si = st+1i . The transfer proba-

bility becomes

p(st+1|st) ∝ eβ∑

i,j Jijst+1i stj . (10)

We now define a new state St which is a joint state ofst−1 and st such that p(St) ≡ p(st−1, st). The transferprobability of St is now proportional to the Boltzmanndistribution

p(St+1|St) = p(st+1|st) ∝ eβ∑

i,j Jijst+1i stj = e−βH(St+1),

(11)with Hamiltonian H(St) ≡ −

∑i,j Jijs

t−1i stj where the

interaction within st and within st−1 is zero. Thus, theCA is mapped to an Ising model with state S. The sta-tionary distribution of S follows the Boltzmann distribu-tion

p(S) =1

Ze−βH(S), (12)

while the stationary distribution of s is given by

p(s) =1

Z

∑s∗

eβ∑

i,j Jijsis∗j (13)

Deterministic CA can be mapped to Ising model atzero temperature, where T → 0, β → ∞, p(S) and p(s)is nonzero only at state(s) with lowest energy. In thecase of Jij = 1 or 0 which we are interested in, onlytwo states (si = 1,∀i or si = −1,∀i) are allowed at zerotemperature.

5.2.5. Majority Vote Cellular Automata as a ConsensusAlgorithm

Majority Vote Cellular Automata (MVCA) is a Cellu-lar Automata using majority vote as updating rule. Itcan be formalized as

st+1i = sign

∑j

Jijstj

, (14)

where Jij = 1 if node i and j are connected, otherwise0. sign(x) = 1 if x > 0, or −1 if x < 0. sign(0) = 1or −1 with equal probability. The definition of sign(0)does not have any impact if each node has odd number(k) of connections, which is true for D dimensional Cel-lular Automata with nearest neighbor connections andself connection. Only odd k is considered for simplicity.

The Hamiltonian can be defined asH = −∑i,j Jijsisj .

One can check that the majority vote rule satisfies the

mapping condition p(st+1i |st) ∝ eβ

∑j Jijs

t+1i stj with zero

temperature (β → ∞). According to the previous sec-tion, when MVCA reaches equilibrium, all nodes willhave the same state which depends on initial condition.

To show that MVCA will converge to its equilib-rium, we use the equation derived in previous section

p(St+1|St) ∝ e−βH(St+1). Since β → ∞, p(St+1|St)is nonzero only when H(St+1) is minimized. Fromthe definition of H(S) we get −

∑i,j Jijs

t+1i stj ≤

−∑i,j Jijsis

tj ,∀si, where equal is possible only when

st+1 = s since st+1 is uniquely determined by st whenevery node has odd number of connections. Specifically,for s = st−1 we have H(St+1) ≤ H(St), where equalholds only when st+1 = st−1, i.e. system in equilib-rium or two state oscillation. The latter one can beavoided when J is dynamic so we ignore it for now. SoH(St+1) < H(St) before MVCA reaches its equilibrium.On the other hand, we note that H(S) can only be inte-gers that change in step of 2 and −kN ≤ H(S) ≤ kN ,where N is the total number of nodes in the system andk is the number of connections each node has. ThusMVCA guarantees to converge to consensus state in atmost kN iterations for any initial state. Similarly, if theinitial state has m “incorrect” values, it takes at mostkm iterations to correct those “incorrect” values.

Although in the derivation above we use CA as themodel, we did not assume local connectivity. In fact, theresults are valid for any network topology with symmetricconnectivity matrix J .

5.2.6. Randomized Neighbors

Cellular Automata and Ising model are both latticebased system with interaction strength mostly dependson Euclidean distance. Such kind of models are mathe-matically easier to solve, while not practical to implement

11

in distributed systems, especially when nodes are dynam-ical, unreliable, and uncontrollable. Here we propose thatrandom network should be a better topology for consen-sus in distributed system with dynamical nodes. Theconsensus algorithm we proposed works in random net-works without any modification so that every node doesnot need to maintain a specific connectivity. It shouldbe mentioned that the random network discussed here ispurely an overlay network, regardless of how the nodesare physically connected. In a distributed system wherenode does not have a list of other nodes, one can usealgorithms like peer sampling to achieve random connec-tivity.

A critical parameter that controls how fast informationpropagates and thus consensus could be made is the net-work diameter which is defined as the shortest distancebetween the two most distant nodes in the network. Fora random network where each node has k neighbors andk is O(logN), the diameter of the network is at mostO(logN) [12], much smaller than a lattice based system.This is expected since random network could have longrange connections, which is not possible in lattice sys-tems. As a result, random networks converge faster toconsensus states. It is also shown that increase k leadsto smaller diameter [12], as one may expect.

Wolfram Class 4 Cellular Automata is ideal to con-struct the randomized network for superior consensusperformance. In Class 4 CA, the connectivity is effec-tively unpredictable, self-organized and self-evolved.

5.2.7. Simulations of CA Consensus Algorithm

To show the performance of our consensus algorithm,we apply it to a simulated network with N = 1, 000, 000nodes. Each node has k neighbors randomly selectedfrom the network. At each iteration, its state is updatedbased on the states of its k neighbors plus its own stateusing MVCA rule as proposed above. Neighbors are onedirectional so that J is not guaranteed to be symmetric.Initially (iteration 0), the state of each node is indepen-dently chosen to be 1 or -1 with some probability. Thesimulation is run for several iterations with different k, asshown in Fig. 12. One can see that the MVCA convergesto global consensus state in just a few steps even withk = 10, much faster than the theoretical upper boundkN . Note that consensus will be reached even when theinitial state contains equal number of 1 and -1 nodes.Larger k leads to faster convergence.

It should be mentioned that when N is large, the topol-ogy of the random network will be closer to its typicalcase as the probability to have any specific connectivitydecreases exponentially as N increases. Thus, one shouldlook at mean convergence time rather than worst casewhen (and only when) N is large, as in our simulations.

We further simulate the scenario where a fraction ofnodes are malicious. In this case correct nodes have ini-tial state 1, while malicious nodes have initial state -1

and does not update their states regardless of the statesof their neighbors. The goal of the correct nodes is toreach consensus on state 1, while the malicious nodes tryto reach consensus on state -1. From the results (Fig. 13)it can be seen that there is a transition between collapsingto the wrong state (-1) and keeping most correct nodesat the correct state (1). For N = 1, 000, 000 and k = 10,the critical fraction of the malicious nodes is around 30%,which is significant considering the size of N . The criticalfraction also depends on k, as shown in Fig. 13. Larger khas two effects: more malicious nodes can be tolerated,and less correct nodes will be affected by malicious nodes.

Results in Fig. 12 and Fig. 13 combined show the upperbound and lower bound of the network dynamics withfaulty initial states: the former one simulates the casewhere nodes with incorrect initial state are not malicious,while the latter one simulates the case where nodes withincorrect initial state are all malicious and want the restof the network to agree on the incorrect state. Networkdynamics fall between these two curves with the sameinitial states whatever strategy faulty nodes (the oneswith faulty initial state) take.

5.2.8. Extension to Asynchronous and Unreliable Networks

One advantage of using Ising model to describe thesystem is the natural extension to noisy and unreliablecommunication channels. The temperature parameter inIsing model controls the amount of noise in the system,and in our case is the randomness in the updating rule.At zero temperature, the updating rule is deterministic,while the rule becomes more random when temperatureincreases, and eventually becomes purely random whentemperature goes to infinity. By including a default state,probabilistic failure of message delivery can be modeledby finite temperature in Ising model. Thus, consensuscan still be made as long as noise is under the thresh-old, as discussed above. The threshold can be computednumerically given the statistics of network connectivity.Asynchronous state update can also be modeled by suchnoise when communication timeout is added, making itpractical for implementation.

5.3. Proof of Relay

Consensus in NKN is driven by Proof of Relay (PoR),a useful Proof of Work (PoW) where the expected re-wards a node gets depend on its network connectivityand data transmission power. Node proves its relay work-load by adding digital signature when forwarding data,which is then accepted by the system through consensusalgorithm.

PoR is not a waste of resources since the work per-formed in PoR benefits the whole network by providingmore transmission power. The “mining” is redefined ascontributing to the data transmission layer, and the only

12

0 2 4 6 8 10Iteration

1.0

0.5

0.0

0.5

1.0Av

erag

e St

ate

k = 10

0 2 4 6 8 10Iteration

1.0

0.5

0.0

0.5

1.0

Aver

age

Stat

e

k = 100

FIG. 12. Average state of the system converges to either 1 or -1, both representing global consensus. MVCA converges toconsensus state which is the state of the majority nodes in just a few steps even with only 10 neighboring nodes in a 1,000,000nodes network. Increasing the number of neighbors accelerates convergence. Note that when exactly half of the nodes are inone state while the other half in the other state, the converged state could be either one.

0 5 10 15 20Iteration

0.0

0.2

0.4

0.6

0.8

Frac

tion

of C

orre

ct N

odes

k = 10

0 5 10 15 20Iteration

0.0

0.2

0.4

0.6

0.8

Frac

tion

of C

orre

ct N

odes

k = 100

FIG. 13. Fraction of correct nodes (state 1) under the attack of malicious nodes (state -1) that does not update their states.There is a transition between whether the system will collapse to the wrong state when the initial fraction of malicious nodeschanges.

way to get more rewards is providing more transmissionpower. The competition between nodes in the networkwill eventually drive the system towards the direction oflow latency, high bandwidth data transmission network.

PoR is used for both token mining and transactionverification. On the one hand, token will be rewardedto nodes for data transmission; on the other hand, theexpected reward for transaction verification may also de-pend on PoR, either through election or difficulty adjust-ment.

For detailed algorithms and economic model, please re-fer to our separate technical yellow paper [34] and paperon economic model [8].

5.4. Potential Attacks

Since NKN is designed with attack prevention in mind,it is necessary to review related attack types. Attack

13

analysis and mitigation will be one of the important as-pects of NKN development and future work, and will beincluded in the technical yellow paper [34].

1. Double spending attack: double spending at-tack refers to the case where the same token is spentmore than once. In classic blockchain systems,nodes prevent double-spending attack by consen-sus to confirm the transaction sequence.

2. Sybil Attacks: Sybil attack refers to the casewhere malicious node pretends to be multiple users.Malicious miners can pretend to deliver more copiesand get paid. Physical forwarding is done by creat-ing multiple Sybil identities, but only transmittingdata once.

3. Denial-of-Service (DoS) Attacks: an off-lineresource centric attack is known as a denial of ser-vice attack (DoS). For example, an attacker maywant to target a specific account and prevent theaccount holder from posting transactions.

4. Quality-of-Service (QoS) Attacks: some at-tackers want to slow down the system performance,potentially reducing the amount of network connec-tivity and data transfer speed.

5. Eclipse attack: attacker controls the P2P com-munication network and manipulates a node’sneighbors so that it only communicates with ma-licious nodes. The vulnerability of the network toeclipse attack depends on the peer sampling algo-rithm, and can be reduced by carefully choosingneighbors.

6. Selfish Mining Attacks: in a selfish mining strat-egy, the selfish miners maintain two blockchains,one public and one private. Initially, the privateblockchain is the same as the public blockchain.The attacker always mine on the private chain, un-less the length of the private chain is being caughtup by the public chain, in which case the attackerpublishes the private chain to get rewards. The at-tack essentially lower the threshold of 51% attackas it may be more efficient for other miners to minethe private chain than the public chain. Yet, as aneconomic attack, selfish mining attack needs to beannounced in advance to attract miners.

7. Fraud Attacks: malicious miners can claim largeamounts of data to be transmitted but efficientlygenerate data on-demand using applets. If the ap-plet is smaller than the actual amount of relay data,it increases the likelihood of malicious miners get-ting block bonus.

6. CONCLUSIONS

This whitepaper presents a clear and cohesive path to-wards the construction of NKN system. We considerthis work to be a starting point for future research ondecentralized network connectivity and data transmis-sion. Future work include, but not limited to, Cellular-Automata-driven routing, Cellular-Automata-based con-sensus, Proof of Relay etc. NKN has several advantagescompared to current platforms.

First, NKN is an ideal networking platform for devel-oping decentralized applications. DApp developers canbe completely focused on the creative ideas and innova-tions that make their products successful for end users,as well as business logic. They no longer need to worryabout details of network infrastructure.

Second, NKN incentive model encourages more peopleto join the network to share and enhance network connec-tivity and data transmission, changing the entire networkstructure and creating a huge market. NKN is targetingthe trillion-dollar telecommunications business, and aimto provide better connectivity to everyone by incentivizethe sharing of unused networking resources, expandingand revolutionize the sharing network.

Compare to current systems, NKN blockchain plat-form is more suitable for peer-to-peer data transmissionand connectivity. In the meantime, this self-incentivizedmodel encourages more nodes to join the network, builda flat network structure, implement multi-path routing,and create a new generation of network transmissionstructure.

From the perspectives of computing infrastructure in-novation, NKN will revolutionize the blockchain ecosys-tem by blockchainizing the third and probably thelast pillar of Internet infrastructure, after Bitcoin andEthereum blockchainized computing power as well asIPFS and Filecoin blockchainized storage. Complement-ing the other two pillars of the blockchain revolution,NKN will be the next generation decentralized networkthat is self-evolving, self-incentivized, and highly scal-able.

NKN is a strategic exploration and innovation of thegeneral network layer infrastructure delivering the nextgeneration network to other fields. A highly reliable, se-cure and decentralized Internet is essential so that everyindividual and every industry can achieve their full po-tential in the digital world. NKN will offer tremendouspotential for achieving a fully decentralized peer-to-peersystem to make the Internet more efficient, sustainableand secure.

The current network has huge inefficiencies for provid-ing universal connectivity and access for all informationand applications. It’s time to rebuild the network wereally need instead of constantly patching the networkswe already own. Let’s start building the future Internet,today.

14

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