NKN Whitepaper

Friday, June 15, 2018
Buy NKN coin
Save for later
Add to list
Whitepaper.io is a project of OpenBook

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 and self-evolution by introducing Cellular Automata (CA) methodology [1, 2] for both dynamism and efficiency. 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] decentralize storage. Together, they form the three pillars of the Internet infrastructure for next generation blockchain systems. NKN ultimately makes the network more decentralized, efficient, equalized, robust and secure, thus enabling healthier, safer, and more open Internet. CONTENTS 1. Challenges 2 1.1. Limitations of P2P Networks 2 1.2. Resource Utilization 2 1.3. Net Neutrality & Fragmentation 2 2. Vision 2 2.1. Objectives of NKN 2 2.2. The Third Pillar: Networking 3 2.3. Elementary Components 3 2.4. Networking toolkit for Fast and Painless DApp Development 4 3. Technology Foundations 4 3.1. Cellular Automata 4 3.2. Rules as Formulas 5 4. New Kind of Network 5 4.1. Next Generation Decentralized Network 5 4.2. A Useful Proof of Work 6 4.3. Network Topology and Routing 6 4.3.1. Dynamics 7 4.3.2. Self-Organization 7 4.3.3. Self-Evolution 8 4.4. Efficient Decentralization 8 5. Cellular Automata Powered Consensus 8 5.1. Mainstream Consensus 8 5.2. Cellular Automata Powered Consensus 9 5.2.1. Scalability Issue of BFT and PBFT 9 5.2.2. Consensus in Cellular Automata Described by Ising Model 9 5.2.3. Ising Model 9 5.2.4. Link Between Cellular Automata and Ising Model 10 5.2.5. Majority Vote Cellular Automata as a Consensus Algorithm 10 5.2.6. Randomized Neighbors 10 5.2.7. Simulations of CA Consensus Algorithm 11 5.2.8. Extension to Asynchronous and Unreliable Networks 11 5.3. Proof of Relay 11 5.4. Potential Attacks 12 6. Conclusions 13 References 14

2 1. CHALLENGES 1.2. Resource Utilization After years of transmutation, the Internet is in dan- A highly reliable, secure and diverse Internet is essen- ger of losing its original vision and spirit. For exam- tial to everyone. Yet, huge inefficiency exists in the cur- ple, Network Neutrality is overturned [7]; spectrum and rent network when providing global connectivity and in- bandwidth are not efficiently utilized; information is frag- formation transmission. It’s time to rebuild the network mented and can be censored; privacy protection is lim- we want, not just patch the network we have. A fully ited. These signal that the network needs a reform. decentralized and anonymous peer-to-peer system offers Existing solutions are not suitable for next generation huge potential in terms of improved efficiency, sustain- blockchain systems due to the following reasons: ability and safety for industry and society. • Utilize a centralized approach to improve efficiency. 1.3. Net Neutrality & Fragmentation • Sacrifice the scalability of the network to speed up When the Federal Communications Commission consensus. (FCC) approved a measure to remove the net neutral- ity rules by the end of 2017 [7], a demand of ending our • Limit participation rate of nodes or require autho- reliance on big telecommunication monopolies and build- rization to increase “security”. ing decentralized, affordable, locally owned Internet in- frastructure becomes ever stronger. The unrestricted and • Use purely financial motivations or trusted third private Internet access environment is becoming unsus- parties to solve problems which should be solved tainable under an endless stream of attacks and blockage, by mathematics and technology. leading to selective and biased information propagation. Without a proper incentivizing engagement scheme, it is almost impossible to maintain a constant and secured information propagation channel. 1.1. Limitations of P2P Networks Furthermore, Internet has become fragmented due to various reasons. This not only exacerbates separation but also negatively impacts innovation of science, technology Peer-to-peer (P2P) networks currently face several ma- and economy. jor challenges, which are the opportunities for NKN. First static network topology is vulnerable to faulty and malicious attack. Second, there is no economic self- 2. VISION incentivized scheme for network connectivity and data transmission. Finally, network scalability is widely sacri- ficed to enhance controllability. These are all to be solved NKN intends to revolutionize the entire network tech- by the NKN as shown in Fig. 1. nology and business. NKN wants to be the Uber or Airbnb of the trillion-dollar communication service busi- ness, but without a central entity. NKN aspires to free the 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 network from any place • Promote network sharing • Secure net neutrality from network layer innova- tions • Always keep network open and scalable • Perform efficient and dynamic routing FIG. 1. Feature comparisons between existing solutions and NKN. • Tokenize network connectivity and data transmis- sion assets and incentivize participating nodes

3 • Design and build the next generation of blockchain troduces the concept of decentralized data trans- network mission network (DDTN) scheme and utilizes truly decentralized blockchain to provide network con- nectivity and data transmission capability by us- 2.2. The Third Pillar: Networking ing massive independent relay nodes to solve the problem of precipitation of redundant data on the By blockchainizing the third and probably the last network. pillar of Internet infrastructure, NKN will revolutionize the blockchain ecosystem by innovating on the network 2. Cellular Automata powered DDTN: NKN in- layer, after Bitcoin [3] and Ethereum [4] blockchainized troduces the idea of using Cellular Automata to computing power as well as IPFS [5] and Filecoin[6] reconstruct the network layer. The intrinsic char- blockchainized storage. The next generation blockchains acteristics of Cellular Automata such as decentral- based on NKN are capable of supporting new kind of de- ization, peer equivalence and concurrency enable us centralized applications (DApp) which have much more to build a truly decentralized blockchain network. powerful connectivity and transmission capability. The 3. Cellular Automata driven consensus: NKN vision of NKN is not only to revolutionize the decentral- achieves consensus efficiently with high fault tol- ized network layers, but also to develop core technologies erance in large scale distributed systems based on for the next generation blockchain. Cellular Automata, which is essential for decentral- ized systems without trusted third parties. Core Building Blocks of Compute Infrastructure 4. Proof of Relay, A Useful Proof of Work: NKN proposes Proof of Relay (PoR), a mechanism that Compute: Storage: encourages participants to contribute to blockchain Network: network by sharing their connectivity and band- Bitcoin IPFS/ width to get rewards, enhancing network connec- NKN Ethereum Filecoin tivity and data transmission capacity. PoR is a useful Proof of Work (PoW). 5. Tokenization of network connectivity and FIG. 2. NKN as the 3rd pillar of blockchainized Internet data transmission capability: NKN tokenizes infrastructure. network connectivity and data transmission capa- bility by encouraging participants to share their connectivity and bandwidth in exchange for tokens. Idle network resources can be better used through 2.3. Elementary Components such sharing mechanism. NKN improves the uti- lization of network resources and the efficiency of NKN builds upon several innovative elementary com- data transmission. Refer to our paper on economics ponents that are different from existing solutions, as model for details [8]. shown in Fig. 3. 6. Networking toolkit for fast and painless DApp development: With NKN, DApp devel- opers now have a new networking toolkit to build Application Layer: DApps & Smart Contracts truly decentralized applications quickly and eas- ily. DApp developers can focus entirely on cre- Incentive Layer: ativity, innovation, user interface / user experi- Transmission & Connectivity Tokenized ence and business logic. This networking toolkit Consensus Layer: is entirely complimentary to the toolkit by other More Useful Proof of Work: Proof of Relay blockchain projects working on identity, machine Networks Layer: learning, payment, storage, and etc. Cellular Automata Rules & Dynamic Topology NKN utilizes Cellular Automata methodologies to Block Structure, Cryptography etc. achieve full decentralization. All nodes are equal, truly peer to peer, and each is capable of sending, receiving, and relaying data. Cellular Automata makes it possible FIG. 3. NKN elementary components. to 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 and 1. Blockchainizing the remaining core building logical infrastructure. The simplicity and locality of rules blocks of computing infrastructure: NKN in- make it possible to have cost efficient implementation

4 on all types of network devices, from Internet of Things and provider in the entire system as well. On top of that, (IoT), smart phones, all the way to routers. Despite its at each layer there are built-in self-incentivized mecha- seemingly simplicity, Cellular Automata enabled routing nism to maximize the network effect and bootstrap the can be highly random and unpredictable, thus providing entire community. superior security and privacy. NKN will be one of the three foundational elements NKN nodes get rewarded for providing connectivity and play a critical role in this decentralized paradigm. and transmission power, resulting in a fully competitive marketplace optimized for maximizing the entire network capacity. For existing networks, NKN will increase the 3. TECHNOLOGY FOUNDATIONS utilization of connectivity and data transmission capacity by sharing the unused bandwidth of participating nodes. In this whitepaper, we take selective elements of the More and more new nodes will join the network to earn NKS (New Kind of Science) [2] as inspiration. NKN uti- reward, thus quickly bootstrapping and expanding the lizes microscopic rules based on Cellular Automata to NKN network. Existing nodes are incentivized to up- define network topology, achieves self-evolution behav- grade and increase data transmission capacity. All of iors, and explores Cellular Automata driven consensus, above will further boost overall network capacity, as well which is fundamentally different from existing blockchain as improve the dynamic topology since the network has network layer. much more degrees of freedom in choosing the route. As a powerful tool to study complex systems, Cellular In addition, NKN proposes a novel and more useful Automaton is closely linked to philosophical categories proof of work. Unlike traditional hashing computation such as simple and complex, micro and macro, local and type Proof of Work that provides no additional utility, global, finite and infinite, discrete and continuous, etc. 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 speed 3.1. Cellular Automata and low latency relay, etc. Even the consensus algorithm is designed from ground up to improve efficiency and fair- ness, while converge deterministically and globally based on local knowledge. Dynamic Furthermore, NKN is intended to promote network sharing and network ownership by its users. NKN’s eco- nomic model and governance model will reflect this in Simple Peer Equal design and in implementation. These technology and economic model innovations complement each other and together will amplify the power of NKN network. Cellular Automata Parallel Decentralized 2.4. Networking toolkit for Fast and Painless DApp Development Open With NKN, DApp developers now have a new net- working toolkit to build truly decentralized applications rapidly and painlessly. DApp developers can focus en- tirely on the ideas and innovation, UI (user interface) FIG. 4. Properties of Cellular Automata. /UX (user experience), and business logic that make their product successful to the end users. They no longer need Cellular Automata (CA) is a state machine with a col- to wade through the wild jungle of blockchain, cryptog- lection of nodes, each changing its state following a local raphy, consensus mechanism, identity and security before rule that only depends on its neighbors. Each node only they even write one line of code for their users. has a few neighbor nodes. Propagating through local For example, in traditional app development with cen- interactions, local states will eventually affect the global tralized SaaS (Software as a Service) offerings, one can behavior of CA. The desired openness of network is deter- host app on cloud computing platforms, store data on mined by the homogeneity of Cellular Automata where cloud storage, use web services for text message, phone all nodes are identical, forming a fully decentralized P2P call and payment. In the decentralized blockchain world, (peer-to-peer) network. Each node in the NKN network it is already conceivable today to build a new kind of is constantly updating based on its current state as well Facebook by using Ethereum [4] /NEO [9] for comput- as the states of neighbors. The neighbors of each node are ing, IPFS [5] for storage, and NKN for networking. The also dynamically changing so that the network topology beauty of this new paradigm is that users will personally is also dynamic without changing its underlying infras- own their identity and data, and can be both consumer tructure and protocols.

5 NKN utilizes CA to achieve efficient, decentralized, proaches utilizing static and fully connected topology. and dynamical topology such that information and data Complex systems with such a simple structure are closer can be transmitted efficiently and dynamically without to natural systems, thus enabling self-evolution. centralized connectivity. 4. NEW KIND OF NETWORK 3.2. Rules as Formulas NKN is the next generation of peer to peer network The Cellular Automata programming formula is called infrastructure built upon blockchain technology backed “local rule”, which is an indispensable rule for next gen- by Cellular Automata theory aiming at revolutionizing eration network of NKN and has an important influence the Internet with true decentralization and native token on the network topology [2, 10–13]. incentive mechanism. Proper choice of local rules leads to Cellular Automata with complex but self-organized behaviors on the bound- ary between stability and chaos. Rules are essential be- cause they are formulas to program Cellular Automata 4.1. Next Generation Decentralized Network and Automata Networks. The static characteristics of a Cellular Automaton is a discrete dynamic system defined As the current leaders in blockchain, Bitcoin and as Ethereum tokenize computational power through Proof CA = (S, N, K, f ) (1) of Work (PoW). IPFS [5], Filecoin [6], Sia [14] and Storj [15], on the other hand, tokenize storage. Yet, few sys- Finite number of nodes interact in a regular network. tems blockchainize network connectivity and data trans- S represents states of nodes, where each node has a lo- mission power, the third essential building block in the cal state. The state of all nodes determines the global Internet. NKN is designed to tokenize network connec- state. N denotes the number of nodes in network. K de- tivity and data transmission capability as a useful PoW. notes neighbor set, i.e. which neighbor nodes are taken NKN solves the “efficiency” problem of blockchain by into account in local state transitions. f denotes a state equalizing all nodes in the network. Each node follows a transition function, which has a dramatic impact on the rule of Cellular Automaton and updates its state based global evolution of the system. on local rules. Proposed by Von Neumann in 1940s, Cel- The dynamic characteristics of a Cellular Automaton lular Automaton (CA) is a generic term for a type of is illustrated in Fig. 5. Dynamic evolution starts from model, a state machine characterized by discrete time, an initial state. Nodes change their states based on their space and interaction [16, 17]. It is a discrete system that current states and the states of their neighbor nodes. The evolves locally according to specific rules and is proven global state is fully determined by local states of all nodes to be able to emulate the evolution of complex systems. and evolves accordingly. Cellular Automaton has the characteristics of decentral- ization, peer equality and concurrency. For the first time, Dimension NKN proposed Cellular Automata as the fundamental el- Local State of Cells ement of the network layer for blockchain, so as to ensure Static that the entire network layer can benefit from it. State Transitions Updating formulas in Cellular Automata are called “lo- Neighborhood cal rules”, which are found to be the critical factor that controls the transition of Cellular Automaton between Initial Local State Cellular Automata stability and chaos [2]. As an indispensable part of NKN, Characterization Dynamic Current State of a Cell rules are one of the main factors impacting the network Evolution topology. States of Neighbor Cells NKN introduced the concept of Decentralized Data Local States Evolution Transmission Network (DDTN). DDTN combines mul- Evolution Dynamic Correlation tiple independent and self-organized relay nodes to pro- Global States Evolution vide clients with connectivity and data transmission ca- Synchronous pability. This coordination is decentralized and does not Dynamics of State require trust of any involved parties. The secure opera- Asynchronous Transitions tion of NKN is achieved through a consensus mechanism Stochastic that coordinates and validates the operations performed by each node. DDTN provides a variety of strategies for FIG. 5. Characteristics of Cellular Automata. decentralized application (DApp). In contrast to centralized network connectivity and The NKN team believes CA-based or CA-driven sys- data transmission, there are multiple efficient paths be- tems are more natural and organic than current ap- tween nodes in DDTN, which can be used to enhance

6 data transmission capacity. Native tokens can incen- Markovian updating rule should take both topology of tivize the sharing of network resources, and eventually the network and states of nodes into consideration such minimize wasted connectivity and bandwidth. Such a that property is termed “self-incentivized”. A(t + 1) = f [A(t), S(t)] (3) S(t + 1) = g[A(t + 1), S(t)] 4.2. A Useful Proof of Work where S(t) is a vector representing the states of all nodes in the network at time t, f is the topology updating rule, As the pioneering cryptocurrency, Bitcoin [3] is gen- and g is the state updating rule. Similarly, f and g should erated by mining, a Proof of Work mechanism that in- be chosen such that only information of current neigh- centivizes miners to verify transactions by solving diffi- bors are used when updating. The state could contain cult hashing problems. The downside of Bitcoin mining historical information. An example state in blockchain is that efficient mining requires specialized and expen- system is all the blocks that a node stores locally. Note sive hardware and consumes a lot of energy. Accord- that although we describe the system formally using the ing to Digiconomist, Bitcoin energy consumption rate is global state S and global connectivity A, each node i only close to 50 TWh/year at mid February 2018 and still in- needs to know and store its local state Si and neighbors creasing, while the number is close to 14 TWh/year for {j|Aij 6= 0}. Ethereum. Electricity consumed by these two cryptocur- Consider a CAoN in a blockchain system where blocks rencies combined has surpassed the electricity usage of are being generated. Each time a block is received, the many countries. node updates its state and send the block to neighbors A way to prove the work while avoiding waste of re- with digital signature. The neighbors will decide whether sources is highly desired. NKN proposes an alternative to to forward the message depending on their states like if the current PoW by providing a more decentralized, dy- it has received the block, if the block is valid, or conflict namically evolving, self-organizing and self-evolving net- with other block in state, effectively affecting the topol- work infrastructure and designing a whole new set of con- ogy of the entire network without changing the physical sensus mechanisms. The novel PoW does not result in a layer or the underlying protocol. waste of resources. Instead, it is a peer-to-peer sharing As an example to illustrate how we model the network, mechanism at blockchain level. Participants receive re- one can consider a general Network Automaton that al- wards by contributing more network resources than they lows an arbitrary number of neighbors. For simplicity, consume. NKN uses Proof of Relay mechanism to guar- a minimalist approach is adopted to emulate blockchain antee network connectivity and data transmission capac- expanding and data relay from a small set of microscopic ity. rules. Initially (at time zero) the network is a 3D cubic structure with 8 nodes, each has 3 neighbors, as shown in Fig. 6. 4.3. Network Topology and Routing Cellular Automata on Networks (CAoN) is a natu- ral extension of Cellular Automata [10, 11, 18] that is X Y able to model networks with non-geometric neighbor con- nections. It is powerful when modeling networks whose Z topology is evolving based on local rules. As the goal is to build a decentralized blockchain system with dynamic topology, 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 by an N × N adjacency matrix A(t) that evolves with time. Connections between nodes can be added, removed, or FIG. 6. An example of Network Automata with 8 nodes form- altered at each time step. If the dynamics of A is Marko- ing a cubic network in 3D space at initial state. vian, the updating process can be written as Starting from the simple network in Fig. 6, the system A(t + 1) = f [A(t)], (2) is extended by adding nodes to it following various up- dating rules. The resulting topology can be dramatically where f is the updating rule of network topology. To keep different when different rules are used, as shown in Fig. 7. the updating rule local, f should be chosen such that only NKN will bridge network evolution and blockchain information of the neighbors of each node is used when functions using similar network models with microscopic updating its connections. The updating rule above does rules. The simple local rules make replication straight- not contain states of nodes, so the topology evolution is forward, simplifying and accelerating system implemen- independent of the state of any node. A more general tations.

7 (a) (a) (b) FIG. 7. Some examples of complex blockchain network topologies with various simple rule sets (a) ring topology, rule 1655146, time step 1573; (b) pseudo-random topology, rule 1655185, time step 1573. (b) 4.3.1. Dynamics Dynamics in CAoN are purely local: each node eval- uates the state transition independently of other nodes and changes its state accordingly [19]. Node state can be driven by either the interaction between nodes, or exter- nal information, as shown in Fig. 8. (c) FIG. 9. Dynamics of network topology by rewriting rules of Cellular Automata at the same time step index, (a) rule 1655163, time step 1573; (b) rule 1655175, time step 1573; (c) Be Commanded by an External Entity rule 1655176, time step 1573. Autonomously, Based on Some the formation of local structures that can survive for long Internal Autonomous periods of time. Wolfram speculates that although not Decision Making all 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- FIG. 8. Possible conditions for a node to change its state in organizing and dynamical structures emerge spontaneous CAoN. in Class 4 CA, providing us an ideal candidate for the ba- sis of decentralized systems. Rules are crucial to the resulting topology in CAoN. Network topology would be very different given small Stability Periodic Behavior Edges of Chaos Chaos changes in the updating rules, as shown in Fig. 9. Although in the mathematical description discrete time step was used for convenience, CAoN does not re- quire nodes have any global time or discrete time. In- Rule110 Rule30 stead, each node performs the update asynchronously Rule248 Rule04 0.0 0.1 0.2 0.3 0.4 0.5 Langton’s λ [19]. This is a more general and realistic description of Class-1 Class-2 Class-4 Class-3 Global Periodic, Complex, Self- Seemingly real blockchain networks. Uniform Regular organized Random Patterns Patterns Behavior 4.3.2. Self-Organization FIG. 10. Wolfram’s 4 classes of behaviors versus Langton’s λ parameter on 1D Cellular Automata. The global dynamics of Cellular Automata can be clas- sified into 4 types [2]: steady, periodic, chaotic, and com- A quantitative measure of the rule that can explain plex. Our focus is in the complex type (Class 4), also and predict the behavior type of the CA is the Lang- known as the edge of chaos, where all initial patterns ton’s λ parameter defined by the fraction of rule table evolve into structures that interact in complex ways, with entries that results in active state. As λ increases from

8 0, the system will transit from steady state to periodic hubs are discouraged. Sparse random network is one pos- state, then to complex state, and finally to chaos state, sible topology that could be generated from such mech- as shown in Fig. 10. In the classic 1D CA with nearest anism. It is decentralized and thus robust to the failure neighbor interaction, Class 4 behavior emerges when λ is of any node, while still being efficient in routing due to around 0.3. Langton’s λ parameter provides us a theo- its small network diameter [12]. retical guide on how to find the desired updating rules, which is essential for high dimensional systems. 5. CELLULAR AUTOMATA POWERED CONSENSUS 4.3.3. Self-Evolution Nodes in blockchain are peers due to the decentral- CAoN is inherently self-evolving due to its simple but ized nature of blockchain. The inherent lack of trust powerful local dynamics. The updating rule essentially in blockchain systems is particularly noteworthy because sets the direction of evolution, and the system evolves any node can send any information to any nodes in the continuously towards the direction, regardless of the ini- blockchain. Peers must evaluate information and make tial states or how nodes are added to the network. Fig. 11 agreement on their actions for blockchain to work prop- shows an example of the self-evolution in CAoN. 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 satisfy such high requirements. 5.1. Mainstream Consensus (a) (b) (c) Currently there are several approaches to reach con- sensus in blockchain: Byzantine fault tolerance algorithm FIG. 11. Self-evolution of a 3D CAoN model on rule 1655185 (BFT) [24], practical Byzantine fault tolerance algorithm at various time step index (a) 100; (b) 1000; (c) 10000. (PBFT) [25], Proof of Work algorithm (PoW) [3], proof of stake algorithm (PoS) [26, 27], and delegated Proof of Stake algorithm (DPoS) [28]. 4.4. Efficient Decentralization 1. Practical Byzantine Fault Tolerant (PBFT): Byzantine fault tolerance is a model that Leslie Lamport proposed in 1982 to explain the issue of Due to the dynamical nature of NKN, network topol- consensus. It discusses the consensus under the sce- ogy between nodes is constantly updating. Proper up- nario where some nodes could be evil (the message dating mechanism is critical to achieve decentralization may be forged) and provides a worst-case guaran- of the resulting topology. If, for example, the updating tee [24]. In Byzantine fault tolerance, let the total mechanism is chosen such that a newly joined node has number of nodes be N and the number of bad nodes higher chance to choose node with more neighbors to be be F , If N ≥ 3F +1, then the problem can be solved its neighbor, and the probability to choose a node is pro- by the Byzantine Fault Tolerant (BFT) algorithm. portional to the degree of that node, then the resulting Lamport proved that there is a valid algorithm such network will be scale-free [22]: the degree distribution that when the fraction of bad nodes does not ex- follows a power law form. Such networks have central- ceed one-third, good nodes could always reach con- ized hubs defined by nodes with huge degree. Although sensus no matter what messages bad nodes send. hubs could potentially increase efficiency, they make net- Practical Byzantine Fault Tolerant (PBFT), first work less robust as the failure of hubs will have much proposed by Castro and Liskov in 1999, was the larger impact than the failure of other nodes. first BFT algorithm to be widely used in practice One of the NKN’s goals is to design and build net- [25]. PBFT is much more efficient and works in an works that are decentralized while still being efficient in asynchronized way, while it can still tolerate same information transmission. This should be done by using number of faulty nodes as BFT, making it more a proper topology updating mechanism that considers practical to use in real systems. both algorithm and incentive. On the algorithm side, neighbors should be sampled and chosen randomly; on 2. Proof of Work (PoW): Bitcoin blockchain net- the incentive side, reward for data transmission should work introduced an innovative Proof of Work be sublinear (grows slower than linear function) so that (PoW) algorithm [3]. The algorithm limits the

9 number of proposals by increasing the cost of them, totic behavior of the system is controlled by its updating and relax the need for final confirmation of con- rule. It is possible to achieve guaranteed global consen- formity by agreeing that everyone will accept the sus in CA using message passing algorithm based only longest-known chain. In this way, anyone who tries on sparse local neighbors for a set of updating rules. to vandalism will pay a great economic cost. That Using the mathematical framework originally devel- is, to pay more than half the system computing oped for Ising model [29] in physics, we found and proved power. Later, various “PoX” series algorithms are that a class of CA rules will guarantee to reach consen- proposed following this thought, using economic sus in at most O(N ) iterations using only states of sparse penalties to restrict the spoilers. PoW is the con- neighbors by an exact map from CA to zero temperature sensus used by Bitcoin and is also the earliest used Ising model. Some studies investigated the fault toler- in blockchain system. In brief, PoW means how ance of Cellular Automata and how to increase robust- much work a miner pays and how much it gains. ness in Cellular Automata-Based systems [30–32]. We The work here is the computing power and time further showed that the result is robust to random and which a miner provides contribute to the blockchain malicious faulty nodes and compute the threshold when system. The process of providing such services is desired consensus cannot be made. “mining”. In PoW, the mechanism to allocate re- ward is that the mining income is proportional to the computing power. The more powerful mining 5.2.3. Ising Model machine used, the more expected reward miners will get. Ising model is a model of spin systems with pairwise in- teraction under external magnetic field [29]. The Hamil- 3. Proof of Stake (PoS): Initially, Proof of Stake re- tonian (energy) of the system without external magnetic duces the difficulty of calculating hash according to field can be written as the amount of tokens held. PoS is similar to finan- cial assets in bank, which distribute financial return X H(s) = − Jij si sj , (4) proportional to the amount of assets that stake- i,j holder holds in a given period. Similarly in PoS, the blockchain system allocates “interests” accord- where si = ±1 is the spin of node i, and Jij is the inter- ing to stakeholder’s token amount and hold time action between node i and node j. We consider the case [26, 27]. In Delegated Proof of Stake (DPoS), not where Jij can only be 1 (ferromagnetic interaction) or every stakeholder is able to create block. Instead, 0 (no interaction). The probability that the system will nodes vote for trustees that represent them to en- be in state s under equilibrium follows the Boltzmann ter the parliament and create blocks. Users who distribution would like to become trustees need to go through community canvassing in order to gain trust of the 1 −βH(s) 1 P p(s) = e = eβ i,j Jij si sj , (5) community [28]. Z Z P −βH(s) where Z = se is the partition function, β = 1 5.2. Cellular Automata Powered Consensus kB T with kB being Boltzmann constant and T being the temperature, representing noise level of the system. The units where kB = 1 will be used for simplicity. 5.2.1. Scalability Issue of BFT and PBFT Ising model on lattice has been extensively studied [29, 33]. For the Ising model on a D dimensional lattice with It is challenging to get consensus in large distributed nearest neighbor interaction, a phase transition occurs systems using BFT and PBFT algorithm. In BFT al- at finite critical temperature Tc except for D = 1 where gorithm, the total number of messages to be sent in the the critical temperature Tc = 0. When T < Tc , the system is O(N !)[24], making it not practical. PBFT al- system collapse into one of the two states where nodes gorithm reduced the total message count to O(N 2 )[25], have a preferred spin (spontaneous magnetization), while which is tractable but not scalable when N is large. In the system does not have a preferred spin when T > Tc . addition, both BFT and PBFT requires every node to For example, for a 2D square lattice with nearest neigh- have a list of all other nodes in the network, which is bor interaction, the exact solution of the Ising model can hard for dynamical network. be obtained. The critical temperature is 2 Tc = √ ≈ 2.27, (6) 5.2.2. Consensus in Cellular Automata Described by Ising ln(1 + 2) Model and the spontaneous magnetization is Cellular Automata (CA) is naturally a large dis- 1 hsi = ± 1 − (sinh 2β)−4 8 .  tributed system with only local connections. The asymp- (7)

10 All of the spins will become the same (either 1 or -1) 5.2.5. Majority Vote Cellular Automata as a Consensus when T → 0. Algorithm If the distributed system of interest can be mathemat- ically described by an Ising model, then the system is Majority Vote Cellular Automata (MVCA) is a Cellu- guaranteed to achieve consensus (all nodes have the same lar Automata using majority vote as updating rule. It states) when temperature is zero. Finite temperature can be formalized as plays the role of failure by adding randomness to state   transition, and finite critical temperature leads to robust- X ness to such failure. st+1 i = sign  Jij stj  , (14) j 5.2.4. Link Between Cellular Automata and Ising Model where Jij = 1 if node i and j are connected, otherwise 0. sign(x) = 1 if x > 0, or −1 if x < 0. sign(0) = 1 Cellular Automata (CA) is closely related to Ising or −1 with equal probability. The definition of sign(0) Model. A CA is characterized by its updating rule does not have any impact if each node has odd number Y (k) of connections, which is true for D dimensional Cel- p(st+1 |st ) = p(st+1 i |st ) (8) lular Automata with nearest neighbor connections and i self connection. Only odd k is considered forPsimplicity. that represents the probability of the system to transfer The Hamiltonian can be defined as H = − i,j Jij si sj . to state st+1 at time t + 1 given system state st at time One can check that the majority vote P rule satisfies the t. The transfer probability is conditional independent β j Jij st+1 stj mapping condition p(st+1 i |s t ) ∝ e i with zero because every node in CA updates its state solely de- temperature (β → ∞). According to the previous sec- pending on the previous system state. For deterministic tion, when MVCA reaches equilibrium, all nodes will CA, the transfer probability p(st+1 |st ) is a P delta func- have the same state which depends on initial condition. tion. If a Hamiltonian of the form H(s) = − i,j Jij si sj To show that MVCA will converge to its equilib- can be defined for a CA such that rium, we use the equation derived in previous section P t+1 t+1 |st ) Jij st+1 stj p(S t+1 |S t ) ∝ e−βH(S ) . Since β → ∞, p(S t+1 |S t ) p(st+1 i |st ) ∝ e−βH(si = eβ j i , (9) is nonzero only when H(S t+1 ) is minimized. From where H(st+1 |st ) is the Hamiltonian of the system given the definition of H(S) we get − i,j Jij st+1 t P i i s j ≤ state sj = stj , ∀j 6= i and si = st+1 i . The transfer proba- P t − i,j Jij si sj , ∀si , where equal is possible only when bility becomes st+1 = s since st+1 is uniquely determined by st when P p(st+1 |st ) ∝ eβ i,j Jij st+1 i stj . (10) every node has odd number of connections. Specifically, for s = st−1 we have H(S t+1 ) ≤ H(S t ), where equal We now define a new state S t which is a joint state of holds only when st+1 = st−1 , i.e. system in equilib- t−1 s and st such that p(S t ) ≡ p(st−1 , st ). The transfer rium or two state oscillation. The latter one can be probability of S t is now proportional to the Boltzmann avoided when J is dynamic so we ignore it for now. So distribution H(S t+1 ) < H(S t ) before MVCA reaches its equilibrium. P Jij st+1 stj t+1 On the other hand, we note that H(S) can only be inte- p(S t+1 |S t ) = p(st+1 |st ) ∝ eβ i,j i , = e−βH(S ) gers that change in step of 2 and −kN ≤ H(S) ≤ kN , (11) where N is the total number of nodes in the system and with Hamiltonian H(S t ) ≡ − i,j Jij st−1 stj where the P i k is the number of connections each node has. Thus t t−1 interaction within s and within s is zero. Thus, the MVCA guarantees to converge to consensus state in at CA is mapped to an Ising model with state S. The sta- most kN iterations for any initial state. Similarly, if the tionary distribution of S follows the Boltzmann distribu- initial state has m “incorrect” values, it takes at most tion km iterations to correct those “incorrect” values. 1 Although in the derivation above we use CA as the p(S) = e−βH(S) , (12) Z model, we did not assume local connectivity. In fact, the while the stationary distribution of s is given by results are valid for any network topology with symmetric connectivity matrix J. 1 X β Pi,j Jij si s∗j p(s) = e (13) Z s∗ Deterministic CA can be mapped to Ising model at 5.2.6. Randomized Neighbors zero temperature, where T → 0, β → ∞, p(S) and p(s) is nonzero only at state(s) with lowest energy. In the Cellular Automata and Ising model are both lattice case of Jij = 1 or 0 which we are interested in, only based system with interaction strength mostly depends two states (si = 1, ∀i or si = −1, ∀i) are allowed at zero on Euclidean distance. Such kind of models are mathe- temperature. matically easier to solve, while not practical to implement

11 in distributed systems, especially when nodes are dynam- and does not update their states regardless of the states ical, unreliable, and uncontrollable. Here we propose that of their neighbors. The goal of the correct nodes is to random network should be a better topology for consen- reach consensus on state 1, while the malicious nodes try sus in distributed system with dynamical nodes. The to reach consensus on state -1. From the results (Fig. 13) consensus algorithm we proposed works in random net- it can be seen that there is a transition between collapsing works without any modification so that every node does to the wrong state (-1) and keeping most correct nodes not need to maintain a specific connectivity. It should at the correct state (1). For N = 1, 000, 000 and k = 10, be mentioned that the random network discussed here is the critical fraction of the malicious nodes is around 30%, purely an overlay network, regardless of how the nodes which is significant considering the size of N . The critical are physically connected. In a distributed system where fraction also depends on k, as shown in Fig. 13. Larger k node does not have a list of other nodes, one can use has two effects: more malicious nodes can be tolerated, algorithms like peer sampling to achieve random connec- and less correct nodes will be affected by malicious nodes. tivity. Results in Fig. 12 and Fig. 13 combined show the upper A critical parameter that controls how fast information bound and lower bound of the network dynamics with propagates and thus consensus could be made is the net- faulty initial states: the former one simulates the case work diameter which is defined as the shortest distance where nodes with incorrect initial state are not malicious, between the two most distant nodes in the network. For while the latter one simulates the case where nodes with a random network where each node has k neighbors and incorrect initial state are all malicious and want the rest k is O(logN ), the diameter of the network is at most of the network to agree on the incorrect state. Network O(logN ) [12], much smaller than a lattice based system. dynamics fall between these two curves with the same This is expected since random network could have long initial states whatever strategy faulty nodes (the ones range connections, which is not possible in lattice sys- with faulty initial state) take. tems. As a result, random networks converge faster to consensus states. It is also shown that increase k leads to smaller diameter [12], as one may expect. 5.2.8. Extension to Asynchronous and Unreliable Networks Wolfram Class 4 Cellular Automata is ideal to con- struct the randomized network for superior consensus One advantage of using Ising model to describe the performance. In Class 4 CA, the connectivity is effec- system is the natural extension to noisy and unreliable tively unpredictable, self-organized and self-evolved. communication channels. The temperature parameter in Ising model controls the amount of noise in the system, and in our case is the randomness in the updating rule. 5.2.7. Simulations of CA Consensus Algorithm At zero temperature, the updating rule is deterministic, while the rule becomes more random when temperature To show the performance of our consensus algorithm, increases, and eventually becomes purely random when we apply it to a simulated network with N = 1, 000, 000 temperature goes to infinity. By including a default state, nodes. Each node has k neighbors randomly selected probabilistic failure of message delivery can be modeled from the network. At each iteration, its state is updated by finite temperature in Ising model. Thus, consensus based on the states of its k neighbors plus its own state can still be made as long as noise is under the thresh- using MVCA rule as proposed above. Neighbors are one old, as discussed above. The threshold can be computed directional so that J is not guaranteed to be symmetric. numerically given the statistics of network connectivity. Initially (iteration 0), the state of each node is indepen- Asynchronous state update can also be modeled by such dently chosen to be 1 or -1 with some probability. The noise when communication timeout is added, making it simulation is run for several iterations with different k, as practical for implementation. shown in Fig. 12. One can see that the MVCA converges to global consensus state in just a few steps even with k = 10, much faster than the theoretical upper bound 5.3. Proof of Relay kN . Note that consensus will be reached even when the initial state contains equal number of 1 and -1 nodes. Consensus in NKN is driven by Proof of Relay (PoR), Larger k leads to faster convergence. a useful Proof of Work (PoW) where the expected re- It should be mentioned that when N is large, the topol- wards a node gets depend on its network connectivity ogy of the random network will be closer to its typical and data transmission power. Node proves its relay work- case as the probability to have any specific connectivity load by adding digital signature when forwarding data, decreases exponentially as N increases. Thus, one should which is then accepted by the system through consensus look at mean convergence time rather than worst case algorithm. when (and only when) N is large, as in our simulations. PoR is not a waste of resources since the work per- We further simulate the scenario where a fraction of formed in PoR benefits the whole network by providing nodes are malicious. In this case correct nodes have ini- more transmission power. The “mining” is redefined as tial state 1, while malicious nodes have initial state -1 contributing to the data transmission layer, and the only

12 k = 10 k = 100 1.0 1.0 0.5 0.5 Average State Average State 0.0 0.0 0.5 0.5 1.0 1.0 0 2 4 6 8 10 0 2 4 6 8 10 Iteration Iteration FIG. 12. Average state of the system converges to either 1 or -1, both representing global consensus. MVCA converges to consensus state which is the state of the majority nodes in just a few steps even with only 10 neighboring nodes in a 1,000,000 nodes network. Increasing the number of neighbors accelerates convergence. Note that when exactly half of the nodes are in one state while the other half in the other state, the converged state could be either one. k = 10 k = 100 0.8 0.8 Fraction of Correct Nodes Fraction of Correct Nodes 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 5 10 15 20 0 5 10 15 20 Iteration Iteration 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 nodes changes. way to get more rewards is providing more transmission For detailed algorithms and economic model, please re- power. The competition between nodes in the network fer to our separate technical yellow paper [34] and paper will eventually drive the system towards the direction of on economic model [8]. low latency, high bandwidth data transmission network. PoR is used for both token mining and transaction verification. On the one hand, token will be rewarded to nodes for data transmission; on the other hand, the 5.4. Potential Attacks expected reward for transaction verification may also de- pend on PoR, either through election or difficulty adjust- Since NKN is designed with attack prevention in mind, ment. it is necessary to review related attack types. Attack

13 analysis and mitigation will be one of the important as- 6. CONCLUSIONS pects of NKN development and future work, and will be included in the technical yellow paper [34]. This whitepaper presents a clear and cohesive path to- wards the construction of NKN system. We consider 1. Double spending attack: double spending at- this work to be a starting point for future research on tack refers to the case where the same token is spent decentralized network connectivity and data transmis- more than once. In classic blockchain systems, sion. Future work include, but not limited to, Cellular- nodes prevent double-spending attack by consen- Automata-driven routing, Cellular-Automata-based con- sus to confirm the transaction sequence. sensus, Proof of Relay etc. NKN has several advantages compared to current platforms. 2. Sybil Attacks: Sybil attack refers to the case First, NKN is an ideal networking platform for devel- where malicious node pretends to be multiple users. oping decentralized applications. DApp developers can Malicious miners can pretend to deliver more copies be completely focused on the creative ideas and innova- and get paid. Physical forwarding is done by creat- tions that make their products successful for end users, ing multiple Sybil identities, but only transmitting as well as business logic. They no longer need to worry data once. about details of network infrastructure. Second, NKN incentive model encourages more people 3. Denial-of-Service (DoS) Attacks: an off-line to join the network to share and enhance network connec- resource centric attack is known as a denial of ser- tivity and data transmission, changing the entire network vice attack (DoS). For example, an attacker may structure and creating a huge market. NKN is targeting want to target a specific account and prevent the the trillion-dollar telecommunications business, and aim account holder from posting transactions. to provide better connectivity to everyone by incentivize the sharing of unused networking resources, expanding 4. Quality-of-Service (QoS) Attacks: some at- and revolutionize the sharing network. tackers want to slow down the system performance, Compare to current systems, NKN blockchain plat- potentially reducing the amount of network connec- form is more suitable for peer-to-peer data transmission tivity and data transfer speed. and connectivity. In the meantime, this self-incentivized model encourages more nodes to join the network, build 5. Eclipse attack: attacker controls the P2P com- a flat network structure, implement multi-path routing, munication network and manipulates a node’s and create a new generation of network transmission neighbors so that it only communicates with ma- structure. licious nodes. The vulnerability of the network to From the perspectives of computing infrastructure in- eclipse attack depends on the peer sampling algo- novation, NKN will revolutionize the blockchain ecosys- rithm, and can be reduced by carefully choosing tem by blockchainizing the third and probably the neighbors. last pillar of Internet infrastructure, after Bitcoin and Ethereum blockchainized computing power as well as 6. Selfish Mining Attacks: in a selfish mining strat- IPFS and Filecoin blockchainized storage. Complement- egy, the selfish miners maintain two blockchains, ing the other two pillars of the blockchain revolution, one public and one private. Initially, the private NKN will be the next generation decentralized network blockchain is the same as the public blockchain. that is self-evolving, self-incentivized, and highly scal- The attacker always mine on the private chain, un- able. less the length of the private chain is being caught NKN is a strategic exploration and innovation of the up by the public chain, in which case the attacker general network layer infrastructure delivering the next publishes the private chain to get rewards. The at- generation network to other fields. A highly reliable, se- tack essentially lower the threshold of 51% attack cure and decentralized Internet is essential so that every as it may be more efficient for other miners to mine individual and every industry can achieve their full po- the private chain than the public chain. Yet, as an tential in the digital world. NKN will offer tremendous economic attack, selfish mining attack needs to be potential for achieving a fully decentralized peer-to-peer announced in advance to attract miners. system to make the Internet more efficient, sustainable and secure. 7. Fraud Attacks: malicious miners can claim large The current network has huge inefficiencies for provid- amounts of data to be transmitted but efficiently ing universal connectivity and access for all information generate data on-demand using applets. If the ap- and applications. It’s time to rebuild the network we plet is smaller than the actual amount of relay data, really need instead of constantly patching the networks it increases the likelihood of malicious miners get- we already own. Let’s start building the future Internet, ting block bonus. today.

14 [1] Stephen Wolfram. Statistical mechanics of cellular au- The byzantine generals problem. ACM Transactions tomata. Reviews of modern physics, 55(3):601, 1983. on Programming Languages and Systems (TOPLAS), [2] Stephen Wolfram. A new kind of science, volume 5. Wol- 4(3):382–401, 1982. fram media Champaign, 2002. [25] Miguel Castro and Barbara Liskov. Practical byzan- [3] Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic tine fault tolerance and proactive recovery. ACM Trans- cash system. 2008. actions on Computer Systems (TOCS), 20(4):398–461, [4] Vitalik Buterin et al. A next-generation smart con- 2002. tract and decentralized application platform. white paper, [26] Pavel Vasin. Blackcoins proof-of-stake protocol 2014. v2. URL: https://blackcoin. co/blackcoin-pos-protocol- [5] Juan Benet. Ipfs-content addressed, versioned, p2p file v2-whitepaper. pdf, 2014. system. arXiv preprint arXiv:1407.3561, 2014. [27] Sunny King and Scott Nadal. Ppcoin: Peer-to-peer [6] Protocol Labs. Filecoin: A decentralized storage net- crypto-currency with proof-of-stake. self-published paper, work, 2017. August, 19, 2012. [7] Federal Communications Commission. Restoring internet [28] BitShares. Delegated proof-of-stake consensus, 2013. freedom, 2017. [29] Ernst Ising. Beitrag zur theorie des ferromagnetismus. [8] NKN. NKN Economic Model and Roadmap. nkn.org, Zeitschrift für Physik, 31(1):253–258, 1925. 2018. [30] Mark McCann and Nicholas Pippenger. Fault tolerance [9] NEO. Neo white paper: A distributed network for the in cellular automata at high fault rates. Journal of Com- smart economy, 2017. puter and System Sciences, 74(5):910–918, 2008. [10] Xin-She Yang and Young ZL Yang. Cellular automata [31] Luděk Žaloudek and Lukáš Sekanina. Increasing fault- networks. Proceedings of Unconventional Computing, tolerance in cellular automata-based systems. In In- pages 280–302, 2007. ternational Conference on Unconventional Computation, [11] Carsten Marr, Mark Müller-Linow, and Marc-Thorsten pages 234–245. Springer, 2011. Hütt. Regularizing capacity of metabolic networks. Phys- [32] Ilir Çapuni and Peter Gács. A turing machine resist- ical Review E, 75(4):041917, 2007. ing isolated bursts of faults. In International Conference [12] Fan Chung and Linyuan Lu. The diameter of sparse on Current Trends in Theory and Practice of Computer random graphs. Advances in Applied Mathematics, Science, pages 165–176. Springer, 2012. 26(4):257–279, 2001. [33] Lars Onsager. Crystal statistics. i. a two-dimensional [13] Ali Mohammad Saghiri and Mohammad Reza Meybodi. model with an order-disorder transition. Physical Review, A closed asynchronous dynamic model of cellular learn- 65(3-4):117, 1944. ing automata and its application to peer-to-peer net- [34] NKN. NKN Yellow Paper. nkn.org, 2018. works. Genetic Programming and Evolvable Machines, [35] Benoit B Mandelbrot. The fractal geometry of nature, 18(3):313–349, 2017. volume 173. WH freeman New York, 1983. [14] David Vorick and Luke Champine. Sia: simple decentral- [36] Michael Abd-El-Malek, Gregory R Ganger, Garth R ized storage, 2014. Goodson, Michael K Reiter, and Jay J Wylie. Fault- [15] Shawn Wilkinson, Tome Boshevski, Josh Brandoff, and scalable byzantine fault-tolerant services. ACM SIGOPS Vitalik Buterin. Storj a peer-to-peer cloud storage net- Operating Systems Review, 39(5):59–74, 2005. work. 2014. [37] Kevin Driscoll, Brendan Hall, Michael Paulitsch, Phil [16] John Von Neumann. The general and logical theory of Zumsteg, and Hakan Sivencrona. The real byzantine automata. Cerebral mechanisms in behavior, 1(41):1–2, generals. In Digital Avionics Systems Conference, 2004. 1951. DASC 04. The 23rd, volume 2, pages 6–D. IEEE, 2004. [17] John Von Neumann, Arthur W Burks, et al. Theory of [38] Cynthia Dwork and Moni Naor. Pricing via processing self-reproducing automata. IEEE Transactions on Neural or combatting junk mail. In Annual International Cryp- Networks, 5(1):3–14, 1966. tology Conference, pages 139–147. Springer, 1992. [18] David MD Smith, Jukka-Pekka Onnela, Chiu Fan Lee, [39] Adam Back. A partial hash collision based Mark D Fricker, and Neil F Johnson. Network automata: postage scheme (1997). URL http://www. hashcash. Coupling structure and function in dynamic networks. org/papers/announce. txt, 2016. Advances in Complex Systems, 14(03):317–339, 2011. [40] Vitalik Buterin. What proof of stake is and why it mat- [19] B Chopard and M Droz. Cellular automata. Springer, ters. Bitcoin Magazine, August, 26, 2013. 1998. [41] Rodney J Baxter. Exactly solved models in statistical [20] Matthew Cook. Universality in elementary cellular au- mechanics. Elsevier, 2016. tomata. Complex systems, 15(1):1–40, 2004. [42] Catarina Cosme, JM Viana Parente Lopes, and João [21] John Conway. The game of life. Scientific American, Penedones. Conformal symmetry of the critical 3d ising 223(4):4, 1970. model inside a sphere. Journal of High Energy Physics, [22] Albert-László Barabási and Réka Albert. Emergence of 2015(8):22, 2015. scaling in random networks. science, 286(5439):509–512, [43] Bertrand Delamotte, Matthieu Tissier, and Nicolás 1999. Wschebor. Scale invariance implies conformal invariance [23] Arati Baliga. Understanding blockchain consensus mod- for the three-dimensional ising model. Physical Review els. Technical report, Tech. rep., Persistent Systems Ltd, E, 93(1):012144, 2016. Tech. Rep, 2017. [44] Sheer El-Showk, Miguel F Paulos, David Poland, Slava [24] Leslie Lamport, Robert Shostak, and Marshall Pease. Rychkov, David Simmons-Duffin, and Alessandro Vichi.

15 Solving the 3d ising model with the conformal bootstrap. cellular automata for system-under-test in distributed Physical Review D, 86(2):025022, 2012. computing. Journal of Convergence Information Tech- [45] Leemon Baird. The swirlds hashgraph consensus algo- nology, 9(6):55, 2014. rithm: Fair, fast, byzantine fault tolerance. Techni- [47] Steven Janke and Matthew Whitehead. Practical fault cal report, Swirlds Tech Report SWIRLDS-TR-2016-01, tolerant 2d cellular automata. available online, http://www. swirlds. com/developer- [48] Yoshihiko Kayama. Complex networks derived from cel- resources/whitepapers, 2016. lular automata. arXiv preprint arXiv:1009.4509, 2010. [46] Arnab Mitra, Anirban Kundu, Matangini Chattopad- hyay, and Samiran Chattopadhyay. A novel design with