We present detailed and in depth analysis of Elementary Cellular Automata (ECA) with periodic
cylindrical configuration. The focus is to determine whether Cellular Automata (CA) is suitable for the
generation of pseudo random number sequences (PRNs) of cryptographic strength. Additionally, we
identify the rules that are most suitable for such applications. It is found that only two sub-clusters of the
chaotic rule space are actually capable of producing viable PRNs. Furthermore, these two sub-clusters
consist of two majorly non-linear rules. Each sub-cluster of rules is derived from a cluster leader rule by
reflection or negation or the combined two transformations. It is shown that the members of each subcluster
share the same dynamical behavior. Results of testing the ECA running under these rules for
comprehensively large number of lattice lengths using the Diehard Test suite have shown that apart from
some anomaly, the whole output sequence can be potentially utilized for cryptographic strength pseudo
random sequence generation with sufficiently large number of p-values pass rates.
On Linear Complexity of Binary Sequences Generated Using Matrix Recurrence Re...ijdpsjournal
This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors over Z4 is generated from which random binary sequence is obtained. It is shown that such sequences have large linear complexity.
Secured wireless communication through simulated annealing guided traingulari...csandit
In this paper, simulated annealing guided traingularized encryption using multilayer perceptron
generated session key (SATMLP) has been proposed for secured wireless communication. Both
sender and receiver station uses identical multilayer perceptron and depending on the final
output of the both side multilayer perceptron, weights vector of hidden layer get tuned in both
ends. After this tunning step both perceptrons generates identical weight vectors which is
consider as an one time session key. In the 1st level of encryption process traingularized sub
key1 is use to encrypt the plain text. In 2nd level of encryption simulated annealing method
helps to generates sub key 2 for further encryption of 1st level generated traingularized
encrypted text. Finally multilayer perceptron generated one time session key is used to perform
3rd level of encryption of 2nd level generated encrypted text. Recipient will use same identical
multilayer perceptron guided session key for performing deciphering process for getting the
simulated annealing guided intermediate cipher text. Then using sub key 2 deciphering
technique is performed to get traingularized encrypted text. Finally sub key 1 is used to
generate the plain text. In this proposed technique session key is not transmitted over public
channel apart from few data transfers are needed for weight simulation process. Because after
synchronization process both multilayer perceptron generates identical weight vector which
acts as a session key. Parametric tests are done and results are compared in terms of Chi-
Square test, response time in transmission with some existing classical techniques, which shows
comparable results for the proposed system.
SECURED WIRELESS COMMUNICATION THROUGH SIMULATED ANNEALING GUIDED TRAINGULARI...cscpconf
In this paper, simulated annealing guided traingularized encryption using multilayer perceptron generated session key (SATMLP) has been proposed for secured wireless ommunication. Bothsender and receiver station uses identical multilayer perceptron and depending on the final output of the both side multilayer perceptron, weights vector of hidden layer get tuned in bothends. After this tunning step both perceptrons generates identical weight vectors which is consider as an one time session key. In the 1st level of encryption process traingularized sub key1 is use to encrypt the plain text. In 2nd level of encryption simulated annealing method helps to generates sub key 2 for further encryption of 1st level generated traingularized encrypted text. Finally multilayer perceptron generated one time session key is used to perform
3rd level of encryption of 2nd level generated encrypted text. Recipient will use same identical multilayer perceptron guided session key for performing deciphering process for getting the simulated annealing guided intermediate cipher text. Then using sub key 2 deciphering technique is performed to get traingularized encrypted text. Finally sub key 1 is used to generate the plain text. In this proposed technique session key is not transmitted over public channel apart from few data transfers are needed for weight simulation process. Because after synchronization process both multilayer perceptron generates identical weight vector which acts as a session key. Parametric tests are done and results are compared in terms of ChiSquare test, response time in transmission with some existing classical techniques, which shows comparable results for the proposed system.
RELIABILITY ASSESSMENT OF EMBEDDED SYSTEMS USING STOPWATCH PETRI NETSIJCSEA Journal
In this paper, we propose a reliability approach in which feared events define reliability requirements and
taking them into account allows to design systems which will be able to avoid the drift towards a feared
state. The description of feared scenarios since the system design phase enables us to understand the
reasons of the feared behavior in order to envisage the necessary reconfigurations and choose safe
architectures. In order to face the increasing complexity of embedded systems and to represent the
suspension and resumption of task execution we propose to extract directly feared scenarios from
Stopwatch Petri net model avoiding the generation of the associated reachability graph and the eternal
combinative explosion problem.
Improvement of Search Algorithm for Integral Distinguisher in Subblock-Based ...ijcisjournal
Integral distinguisher is the main factor of integral attack. Conventionally, higher order integral distinguisher is obtained as an extension of first order integral (conventional algorithm). The algorithm was applied to many subblock-based block ciphers, however, the conventional algorithm has some problems. We find other integral distinguisher of two sub block-based block ciphers, TWINE and LBlock, which are different from the conventional evaluations. As a solution, we propose a new algorithm to search for higher order integral distinguisher. The point of a proposal algorithm is exploitation of bijective and injective components of cipher functions. Applying the proposal algorithm to TWINE and LBlock, we confirm the results of the proposal algorithm are consistent with the results which are calculated from computer experiment. The results are the optimal distinguisher and the most advantageous one for the attackers. Our proposal algorithm contributes to development of stronger block ciphers by obtaining such integral distinguisher.
Derivative threshold actuation for single phase wormhole detection with reduc...ijdpsjournal
Communication in mobile Ad hoc networks is completed via multi
-
hop ways. Owing to the distributed
specification and restricted resource of nodes, MANET is a lot prone
to wormhole attacks i.e. wormhole
attacks place severe threats to each Ad hoc routing protocol and a few security enhancements. Thus,
so as
to discover wormholes, totally different techniques are in use. In all those techniques fixation of
threshold
is mer
ely by trial & error methodology or by random manner. Conjointly wormhole detection is in twin
part by putting the nodes that is higher than the edge in a suspicious set, however predicting the n
ode as a
wormhole by using some other algorithms. Our aim in
this paper is to deduce the traffic threshold level by
derivational approach for identifying wormholes in a very single phase in relay network having dissi
milar
characteristics.
Mobile ad hoc network (MANET) is an autonomous system of mobile nodes. Each node operates not only as an end system, but also as a router to forward packets. The nodes are free to move about and organize themselves into a network. These cause extra challenges on security. In this paper, evaluation of prominent on-demand routing protocol i.e. AODV,MAODV,RAODV has been done by varying the network size. An effort has been carried out to do the performance evaluation of these protocols using random way point model. The simulator used is NS 2.34. The performance of either protocol has been studied by using a self created network scenario with respect to pause time.
Mathematics Research Paper - Mathematics of Computer Networking - Final DraftAlexanderCominsky
1. The document discusses the mathematics behind various computer networking security protocols including Spanning Tree Protocol (STP), Secure Sockets Layer (SSL)/Transport Layer Security (TLS), and RSA encryption.
2. It explains how STP uses concepts from graph theory like trees, cycles, and Dijkstra's shortest path algorithm to create loop-free network topologies and ensure efficient routing.
3. It describes how SSL/TLS uses asymmetric and symmetric key cryptography, including RSA, to securely transmit data across networks by encrypting communications between devices.
On Linear Complexity of Binary Sequences Generated Using Matrix Recurrence Re...ijdpsjournal
This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors over Z4 is generated from which random binary sequence is obtained. It is shown that such sequences have large linear complexity.
Secured wireless communication through simulated annealing guided traingulari...csandit
In this paper, simulated annealing guided traingularized encryption using multilayer perceptron
generated session key (SATMLP) has been proposed for secured wireless communication. Both
sender and receiver station uses identical multilayer perceptron and depending on the final
output of the both side multilayer perceptron, weights vector of hidden layer get tuned in both
ends. After this tunning step both perceptrons generates identical weight vectors which is
consider as an one time session key. In the 1st level of encryption process traingularized sub
key1 is use to encrypt the plain text. In 2nd level of encryption simulated annealing method
helps to generates sub key 2 for further encryption of 1st level generated traingularized
encrypted text. Finally multilayer perceptron generated one time session key is used to perform
3rd level of encryption of 2nd level generated encrypted text. Recipient will use same identical
multilayer perceptron guided session key for performing deciphering process for getting the
simulated annealing guided intermediate cipher text. Then using sub key 2 deciphering
technique is performed to get traingularized encrypted text. Finally sub key 1 is used to
generate the plain text. In this proposed technique session key is not transmitted over public
channel apart from few data transfers are needed for weight simulation process. Because after
synchronization process both multilayer perceptron generates identical weight vector which
acts as a session key. Parametric tests are done and results are compared in terms of Chi-
Square test, response time in transmission with some existing classical techniques, which shows
comparable results for the proposed system.
SECURED WIRELESS COMMUNICATION THROUGH SIMULATED ANNEALING GUIDED TRAINGULARI...cscpconf
In this paper, simulated annealing guided traingularized encryption using multilayer perceptron generated session key (SATMLP) has been proposed for secured wireless ommunication. Bothsender and receiver station uses identical multilayer perceptron and depending on the final output of the both side multilayer perceptron, weights vector of hidden layer get tuned in bothends. After this tunning step both perceptrons generates identical weight vectors which is consider as an one time session key. In the 1st level of encryption process traingularized sub key1 is use to encrypt the plain text. In 2nd level of encryption simulated annealing method helps to generates sub key 2 for further encryption of 1st level generated traingularized encrypted text. Finally multilayer perceptron generated one time session key is used to perform
3rd level of encryption of 2nd level generated encrypted text. Recipient will use same identical multilayer perceptron guided session key for performing deciphering process for getting the simulated annealing guided intermediate cipher text. Then using sub key 2 deciphering technique is performed to get traingularized encrypted text. Finally sub key 1 is used to generate the plain text. In this proposed technique session key is not transmitted over public channel apart from few data transfers are needed for weight simulation process. Because after synchronization process both multilayer perceptron generates identical weight vector which acts as a session key. Parametric tests are done and results are compared in terms of ChiSquare test, response time in transmission with some existing classical techniques, which shows comparable results for the proposed system.
RELIABILITY ASSESSMENT OF EMBEDDED SYSTEMS USING STOPWATCH PETRI NETSIJCSEA Journal
In this paper, we propose a reliability approach in which feared events define reliability requirements and
taking them into account allows to design systems which will be able to avoid the drift towards a feared
state. The description of feared scenarios since the system design phase enables us to understand the
reasons of the feared behavior in order to envisage the necessary reconfigurations and choose safe
architectures. In order to face the increasing complexity of embedded systems and to represent the
suspension and resumption of task execution we propose to extract directly feared scenarios from
Stopwatch Petri net model avoiding the generation of the associated reachability graph and the eternal
combinative explosion problem.
Improvement of Search Algorithm for Integral Distinguisher in Subblock-Based ...ijcisjournal
Integral distinguisher is the main factor of integral attack. Conventionally, higher order integral distinguisher is obtained as an extension of first order integral (conventional algorithm). The algorithm was applied to many subblock-based block ciphers, however, the conventional algorithm has some problems. We find other integral distinguisher of two sub block-based block ciphers, TWINE and LBlock, which are different from the conventional evaluations. As a solution, we propose a new algorithm to search for higher order integral distinguisher. The point of a proposal algorithm is exploitation of bijective and injective components of cipher functions. Applying the proposal algorithm to TWINE and LBlock, we confirm the results of the proposal algorithm are consistent with the results which are calculated from computer experiment. The results are the optimal distinguisher and the most advantageous one for the attackers. Our proposal algorithm contributes to development of stronger block ciphers by obtaining such integral distinguisher.
Derivative threshold actuation for single phase wormhole detection with reduc...ijdpsjournal
Communication in mobile Ad hoc networks is completed via multi
-
hop ways. Owing to the distributed
specification and restricted resource of nodes, MANET is a lot prone
to wormhole attacks i.e. wormhole
attacks place severe threats to each Ad hoc routing protocol and a few security enhancements. Thus,
so as
to discover wormholes, totally different techniques are in use. In all those techniques fixation of
threshold
is mer
ely by trial & error methodology or by random manner. Conjointly wormhole detection is in twin
part by putting the nodes that is higher than the edge in a suspicious set, however predicting the n
ode as a
wormhole by using some other algorithms. Our aim in
this paper is to deduce the traffic threshold level by
derivational approach for identifying wormholes in a very single phase in relay network having dissi
milar
characteristics.
Mobile ad hoc network (MANET) is an autonomous system of mobile nodes. Each node operates not only as an end system, but also as a router to forward packets. The nodes are free to move about and organize themselves into a network. These cause extra challenges on security. In this paper, evaluation of prominent on-demand routing protocol i.e. AODV,MAODV,RAODV has been done by varying the network size. An effort has been carried out to do the performance evaluation of these protocols using random way point model. The simulator used is NS 2.34. The performance of either protocol has been studied by using a self created network scenario with respect to pause time.
Mathematics Research Paper - Mathematics of Computer Networking - Final DraftAlexanderCominsky
1. The document discusses the mathematics behind various computer networking security protocols including Spanning Tree Protocol (STP), Secure Sockets Layer (SSL)/Transport Layer Security (TLS), and RSA encryption.
2. It explains how STP uses concepts from graph theory like trees, cycles, and Dijkstra's shortest path algorithm to create loop-free network topologies and ensure efficient routing.
3. It describes how SSL/TLS uses asymmetric and symmetric key cryptography, including RSA, to securely transmit data across networks by encrypting communications between devices.
This document describes constructing a Monte Carlo model of a multi-population neural network to compare with mean field and population density methods. It summarizes modeling neural activity across populations with different physiological characteristics. Simulation results show the Monte Carlo method can accurately model population interactions and parameter variations, making it suitable for testing population density methods. The document concludes additional physiological variables should be included in future simulations.
Applying Deep Learning Machine Translation to Language ServicesYannis Flet-Berliac
Recurrent neural networks (RNNs) have been performing well for learning tasks for several decades now. The most useful benefit they present for this paper is their ability to use contextual information when mapping between input and output sequences.
A deep neural network for machine translation implies the use of a sequence-to-sequence model, consisting of two RNNs: an encoder that processes the input and a decoder that generates the output.
To meaningfully assess the model’s performances, texts from a translation company and thoughts from skilled experts about specialized topics will be tested.
This document discusses the use of probability in cryptography. It begins with introductions to cryptography and probability. Key probability terms and concepts like events, sample spaces, and Markov models are defined. Public key cryptography using Fermat's Little Theorem is explained. Applications of probability in cryptography are explored, including checksums and the birthday problem, pseudo-random number generators, and code breaking using the Metropolis-Hastings algorithm. The document concludes that probability and cryptography are important fields that help secure communications and protect society from cyber attacks.
This document presents methods for detecting encrypted code on confiscated hard drives. It proposes using the Barkman crypto indicator to measure how uniformly characters are distributed in code blocks, with a more even distribution suggesting encryption. It describes applying change point detection algorithms like CUSUM and Shiryaev to the indicator values over time to detect when encrypted code begins. The performance of these methods is evaluated based on their conditional expected delay and predictive value in detecting the change point while controlling the rate of false alarms.
Reduced Merge_FSM Pattern Matching Algorithm for Network Intrusion Detectionidescitation
Pattern matching is a significant issue in intrusion detection systems (IDS), as it
is required to identify and restrict certain virus patterns by matching them with the
patterns present in the database. The performance of an Intrusion Detection System is
dependent on two metrics that is throughput and the total number of patterns that can fit
on a device. Many hardware approaches are proposed to accelerate pattern matching.
Among hardware approaches, memory based architecture has attracted a lot of attention
because of its easy reconfiguration and scalability. In memory architecture approach. First,
the virus string patterns are compiled to a finite-state machine (FSM) whose output is
asserted when any substring of input strings matches the string patterns. The speed of
comparisons and memory required to store virus string patterns is evaluated through the
number of state transitions made. In this paper, a new pattern-matching algorithm
‘Reduced Merge_FSM’ is proposed which significantly reduce the memory requirement
and provides faster matching, by reducing the state transitions, than that of existing Finite
State Machine (FSM) based approaches. This reduction in states results in optimization of
memory and also the comparison time. To prove the efficiency of the proposed algorithm,
it is compared through experimentation with the existing AC-Algorithm and Merge_FSM.
Simulation of Quantum Cryptography and use of DNA based algorithm for Secure ...IOSR Journals
This document describes a simulation of quantum cryptography and the use of a DNA-based algorithm for secure communication. It discusses the fundamentals of quantum cryptography based on no-cloning theorem and Heisenberg's uncertainty principle. The document then proposes a system with modules for BB84 protocol-based key exchange and authentication, followed by encryption/decryption of messages using a DNA-based symmetric block cipher algorithm. Screenshots of a simulation of the system are provided along with analysis of its time and space complexity.
PREDICTION OF MALICIOUS OBJECTS IN COMPUTER NETWORK AND DEFENSEIJNSA Journal
The paper envisages defense of critical information used in Computer Networks those are using Network Topologies such as Star Topology. The first part of the paper develops a model to predict the malicious traffic from the incoming traffic by using Black Scholes Equations. MATLAB is used to simulate the developed model for realistic values. However, the second part of the problem provides a framework for the treatment of predicted malicious traffic with detailed discussion of security measures.
A new dna based approach of generating key dependent shift rows transformationIJNSA Journal
The use of key-dependent shiftRows can be considered as one of the applied methods for altering the quality of a cryptographic algorithm. This article describes one approach for changing the ShiftRows transformation employed in the algorithm AES. The approach employs methods inspired from DNA processes and structure which depended on the key while the parameters of the created new ShiftRows have characteristics identical to those of the original algorithm AES in addition to increase its resistance against attacks. The proposed new ShiftRows were tested for coefficient correlation for dynamic and static independence between the input and output. The NIST Test Suite tests were used to test the randomness for the block cipher that used the new transformation
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The document discusses analyzing information flow in a computer simulated cortical neural network model. It describes how transfer entropy was used to quantify information flow within and between neurons in the model. The presence of information flow contributed to validating the neural network reconstruction by suggesting information is not randomly created and destroyed at each node. Generally, the document describes analyzing information flow in the cortical neural network model and why it is important.
WEAKNESS ON CRYPTOGRAPHIC SCHEMES BASED ON REGULAR LDPC CODESIJNSA Journal
We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. As application of these methods is a cryptographic schema using regular Low Density Parity Check (LDPC) Codes. This result prohibits the use of chained code and particularly regular LDPC codes on cryptography
Random Keying Technique for Security in Wireless Sensor Networks Based on Mem...ijcsta
The document proposes a random keying technique combined with memetics concepts to provide security in wireless sensor networks. It involves randomly selecting keys from ranges distributed from the base station to cluster heads and nodes. When a node communicates, it selects keys that undergo crossover and mutation to generate header and trailer keys. The receiving node verifies packets by applying the same operations to the header keys and comparing the results to the trailer keys. Simulations showed this technique effectively combats spoofing attacks while being energy efficient compared to cryptographic methods.
Secure Scan Design Using Redundant Scan RegisterIDES Editor
Cryptographic VLSI chip has a significant role to
resist the attacks which is the growing customer concern of
hardware security. Redundancy introduces a great amount of
randomness & non linearity in any kind circuitry
(combinational or sequential). We introduce a new type of
redundancy in sequential circuits to make redundant scan
registers that are indistinguishable with the original scan
registers. They are sequentially undetectable as well as
redundant, which makes it highly secured. The approach is
only to replace the original scan registers to modified
redundant scan registers called RScR.
1. Digital signatures provide authentication of digital documents by using asymmetric cryptography techniques. A digital signature is generated using a private key and can be verified by anyone using the corresponding public key.
2. There are various types of attacks against digital signature schemes like key-only attacks, generic chosen message attacks, and adaptive chosen message attacks. The security goals are to prevent total key breaks or the ability to forge signatures selectively or existentially.
3. A secure digital signature scheme must produce signatures that depend on the message, use secret information to prevent forgery and denial, be efficient to generate and verify, and make forgery computationally infeasible. Timestamps can be included to require message freshness.
Modeling the Behavior of Selfish Forwarding Nodes to Stimulate Cooperation in...IJNSA Journal
We study routing misbehavior in MANETs (Mobile Ad Hoc Networks) in this paper. In general, routing protocols for MANETs are designed based on the assumption that all participating nodes are fully cooperative. However, due to the open structure and scarcely available battery-based energy, node misbehaviors may exist.[1]. One such routing misbehavior is that some selfish nodes [2], will participate in the route discovery and maintenance processes but refuse to forward data packets. In this paper, we develop a game theoretic based cooperation model that observes the behavior of an intermediary node (selfish neighbors) while forwarding packets for others on a route between a source and a destination. It also allows formally study and analyze the impact of selfish behavior on the system performance.
SECURITY EVALUATION OF LIGHT-WEIGHT BLOCK CIPHERS BY GPGPUacijjournal
This document summarizes a research paper that proposes using GPUs to accelerate the security evaluation of lightweight block ciphers through integral attacks. The paper first provides background on integral attacks and discusses limitations of previous evaluation methods. It then proposes a new algorithm that uses both theoretical and experimental steps to iteratively search for higher-order integral distinguishers. In the experimental step, the algorithm executes computer experiments on candidate distinguishers using a GPU to accelerate the computations. When applied to several lightweight block ciphers, the proposed method obtained more advantageous results than previous approaches.
This document discusses recurrent neural networks (RNNs) and some of their applications and design patterns. RNNs are able to process sequential data like text or time series due to their ability to maintain an internal state that captures information about what has been observed in the past. The key challenges with training RNNs are vanishing and exploding gradients, which various techniques like LSTMs and GRUs aim to address. RNNs have been successfully applied to tasks involving sequential input and/or output like machine translation, image captioning, and language modeling. Memory networks extend RNNs with an external memory component that can be explicitly written to and retrieved from.
A novel cluster based wormhole avoidance algorithm for mobile adhoc networkscsandit
A severe type of network layer security attack called Wormhole attack can occur in MANET,
during which a malicious node captures packets from one location in the network, and tunnels
them to another colluding malicious node at a distant point, which replays them locally. This
paper presents a hierarchical cluster based Wormhole attack avoidance technique to avoid such
scenario. The concept of hierarchical clustering with a novel hierarchical 32-bit node
addressing scheme is used for avoiding the attacking path during the route discovery phase of
the DSR protocol, which is considered as the under lying routing protocol. Pinpointing the
location of the Wormhole nodes in the case of exposed attack is also given by using this method.
On The Application of Hyperbolic Activation Function in Computing the Acceler...iosrjce
1) The document discusses integrating a hyperbolic activation function into the Reverse Analysis method for data mining using a Hopfield neural network.
2) Reverse Analysis is a method that examines connection strengths in a neural network to deduce logical rules encoded in the database, while hyperbolic tangent is a smoother activation function compared to logistic.
3) Computer simulations showed the integrated method had faster processing times and was more efficient than the normal Reverse Analysis method as the network complexity increased with more neurons.
This document describes constructing a Monte Carlo model of a multi-population neural network to compare with mean field and population density methods. It summarizes modeling neural activity across populations with different physiological characteristics. Simulation results show the Monte Carlo method can accurately model population interactions and parameter variations, making it suitable for testing population density methods. The document concludes additional physiological variables should be included in future simulations.
Applying Deep Learning Machine Translation to Language ServicesYannis Flet-Berliac
Recurrent neural networks (RNNs) have been performing well for learning tasks for several decades now. The most useful benefit they present for this paper is their ability to use contextual information when mapping between input and output sequences.
A deep neural network for machine translation implies the use of a sequence-to-sequence model, consisting of two RNNs: an encoder that processes the input and a decoder that generates the output.
To meaningfully assess the model’s performances, texts from a translation company and thoughts from skilled experts about specialized topics will be tested.
This document discusses the use of probability in cryptography. It begins with introductions to cryptography and probability. Key probability terms and concepts like events, sample spaces, and Markov models are defined. Public key cryptography using Fermat's Little Theorem is explained. Applications of probability in cryptography are explored, including checksums and the birthday problem, pseudo-random number generators, and code breaking using the Metropolis-Hastings algorithm. The document concludes that probability and cryptography are important fields that help secure communications and protect society from cyber attacks.
This document presents methods for detecting encrypted code on confiscated hard drives. It proposes using the Barkman crypto indicator to measure how uniformly characters are distributed in code blocks, with a more even distribution suggesting encryption. It describes applying change point detection algorithms like CUSUM and Shiryaev to the indicator values over time to detect when encrypted code begins. The performance of these methods is evaluated based on their conditional expected delay and predictive value in detecting the change point while controlling the rate of false alarms.
Reduced Merge_FSM Pattern Matching Algorithm for Network Intrusion Detectionidescitation
Pattern matching is a significant issue in intrusion detection systems (IDS), as it
is required to identify and restrict certain virus patterns by matching them with the
patterns present in the database. The performance of an Intrusion Detection System is
dependent on two metrics that is throughput and the total number of patterns that can fit
on a device. Many hardware approaches are proposed to accelerate pattern matching.
Among hardware approaches, memory based architecture has attracted a lot of attention
because of its easy reconfiguration and scalability. In memory architecture approach. First,
the virus string patterns are compiled to a finite-state machine (FSM) whose output is
asserted when any substring of input strings matches the string patterns. The speed of
comparisons and memory required to store virus string patterns is evaluated through the
number of state transitions made. In this paper, a new pattern-matching algorithm
‘Reduced Merge_FSM’ is proposed which significantly reduce the memory requirement
and provides faster matching, by reducing the state transitions, than that of existing Finite
State Machine (FSM) based approaches. This reduction in states results in optimization of
memory and also the comparison time. To prove the efficiency of the proposed algorithm,
it is compared through experimentation with the existing AC-Algorithm and Merge_FSM.
Simulation of Quantum Cryptography and use of DNA based algorithm for Secure ...IOSR Journals
This document describes a simulation of quantum cryptography and the use of a DNA-based algorithm for secure communication. It discusses the fundamentals of quantum cryptography based on no-cloning theorem and Heisenberg's uncertainty principle. The document then proposes a system with modules for BB84 protocol-based key exchange and authentication, followed by encryption/decryption of messages using a DNA-based symmetric block cipher algorithm. Screenshots of a simulation of the system are provided along with analysis of its time and space complexity.
PREDICTION OF MALICIOUS OBJECTS IN COMPUTER NETWORK AND DEFENSEIJNSA Journal
The paper envisages defense of critical information used in Computer Networks those are using Network Topologies such as Star Topology. The first part of the paper develops a model to predict the malicious traffic from the incoming traffic by using Black Scholes Equations. MATLAB is used to simulate the developed model for realistic values. However, the second part of the problem provides a framework for the treatment of predicted malicious traffic with detailed discussion of security measures.
A new dna based approach of generating key dependent shift rows transformationIJNSA Journal
The use of key-dependent shiftRows can be considered as one of the applied methods for altering the quality of a cryptographic algorithm. This article describes one approach for changing the ShiftRows transformation employed in the algorithm AES. The approach employs methods inspired from DNA processes and structure which depended on the key while the parameters of the created new ShiftRows have characteristics identical to those of the original algorithm AES in addition to increase its resistance against attacks. The proposed new ShiftRows were tested for coefficient correlation for dynamic and static independence between the input and output. The NIST Test Suite tests were used to test the randomness for the block cipher that used the new transformation
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The document discusses analyzing information flow in a computer simulated cortical neural network model. It describes how transfer entropy was used to quantify information flow within and between neurons in the model. The presence of information flow contributed to validating the neural network reconstruction by suggesting information is not randomly created and destroyed at each node. Generally, the document describes analyzing information flow in the cortical neural network model and why it is important.
WEAKNESS ON CRYPTOGRAPHIC SCHEMES BASED ON REGULAR LDPC CODESIJNSA Journal
We propose a method to recover the structure of a randomly permuted chained code and how to cryptanalyse cryptographic schemes based on these kinds of error coding. As application of these methods is a cryptographic schema using regular Low Density Parity Check (LDPC) Codes. This result prohibits the use of chained code and particularly regular LDPC codes on cryptography
Random Keying Technique for Security in Wireless Sensor Networks Based on Mem...ijcsta
The document proposes a random keying technique combined with memetics concepts to provide security in wireless sensor networks. It involves randomly selecting keys from ranges distributed from the base station to cluster heads and nodes. When a node communicates, it selects keys that undergo crossover and mutation to generate header and trailer keys. The receiving node verifies packets by applying the same operations to the header keys and comparing the results to the trailer keys. Simulations showed this technique effectively combats spoofing attacks while being energy efficient compared to cryptographic methods.
Secure Scan Design Using Redundant Scan RegisterIDES Editor
Cryptographic VLSI chip has a significant role to
resist the attacks which is the growing customer concern of
hardware security. Redundancy introduces a great amount of
randomness & non linearity in any kind circuitry
(combinational or sequential). We introduce a new type of
redundancy in sequential circuits to make redundant scan
registers that are indistinguishable with the original scan
registers. They are sequentially undetectable as well as
redundant, which makes it highly secured. The approach is
only to replace the original scan registers to modified
redundant scan registers called RScR.
1. Digital signatures provide authentication of digital documents by using asymmetric cryptography techniques. A digital signature is generated using a private key and can be verified by anyone using the corresponding public key.
2. There are various types of attacks against digital signature schemes like key-only attacks, generic chosen message attacks, and adaptive chosen message attacks. The security goals are to prevent total key breaks or the ability to forge signatures selectively or existentially.
3. A secure digital signature scheme must produce signatures that depend on the message, use secret information to prevent forgery and denial, be efficient to generate and verify, and make forgery computationally infeasible. Timestamps can be included to require message freshness.
Modeling the Behavior of Selfish Forwarding Nodes to Stimulate Cooperation in...IJNSA Journal
We study routing misbehavior in MANETs (Mobile Ad Hoc Networks) in this paper. In general, routing protocols for MANETs are designed based on the assumption that all participating nodes are fully cooperative. However, due to the open structure and scarcely available battery-based energy, node misbehaviors may exist.[1]. One such routing misbehavior is that some selfish nodes [2], will participate in the route discovery and maintenance processes but refuse to forward data packets. In this paper, we develop a game theoretic based cooperation model that observes the behavior of an intermediary node (selfish neighbors) while forwarding packets for others on a route between a source and a destination. It also allows formally study and analyze the impact of selfish behavior on the system performance.
SECURITY EVALUATION OF LIGHT-WEIGHT BLOCK CIPHERS BY GPGPUacijjournal
This document summarizes a research paper that proposes using GPUs to accelerate the security evaluation of lightweight block ciphers through integral attacks. The paper first provides background on integral attacks and discusses limitations of previous evaluation methods. It then proposes a new algorithm that uses both theoretical and experimental steps to iteratively search for higher-order integral distinguishers. In the experimental step, the algorithm executes computer experiments on candidate distinguishers using a GPU to accelerate the computations. When applied to several lightweight block ciphers, the proposed method obtained more advantageous results than previous approaches.
This document discusses recurrent neural networks (RNNs) and some of their applications and design patterns. RNNs are able to process sequential data like text or time series due to their ability to maintain an internal state that captures information about what has been observed in the past. The key challenges with training RNNs are vanishing and exploding gradients, which various techniques like LSTMs and GRUs aim to address. RNNs have been successfully applied to tasks involving sequential input and/or output like machine translation, image captioning, and language modeling. Memory networks extend RNNs with an external memory component that can be explicitly written to and retrieved from.
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A severe type of network layer security attack called Wormhole attack can occur in MANET,
during which a malicious node captures packets from one location in the network, and tunnels
them to another colluding malicious node at a distant point, which replays them locally. This
paper presents a hierarchical cluster based Wormhole attack avoidance technique to avoid such
scenario. The concept of hierarchical clustering with a novel hierarchical 32-bit node
addressing scheme is used for avoiding the attacking path during the route discovery phase of
the DSR protocol, which is considered as the under lying routing protocol. Pinpointing the
location of the Wormhole nodes in the case of exposed attack is also given by using this method.
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1) The document discusses integrating a hyperbolic activation function into the Reverse Analysis method for data mining using a Hopfield neural network.
2) Reverse Analysis is a method that examines connection strengths in a neural network to deduce logical rules encoded in the database, while hyperbolic tangent is a smoother activation function compared to logistic.
3) Computer simulations showed the integrated method had faster processing times and was more efficient than the normal Reverse Analysis method as the network complexity increased with more neurons.
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It presents a two-step acquisition procedure where the first dwell examines only the first portion of the OOC code to test cells, and the second dwell fully examines cells that pass the first test. Closed-form expressions are derived to analyze the false alarm and detection probabilities of this method using GQ functions, showing it can achieve the same performance as the existing Multiple Shift algorithm with lower complexity. Numerical results validate the model and show the two-dwell method matches the performance of the Multiple Shift algorithm.
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We present the findings of analysis of elementary cellular automata (ECA) boundary conditions. Fixed and variable boundaries are attempted. The outputs of linear feedback shift registers (LFSRs) act as continuous inputs to the two boundaries of a one-dimensional (1-D) Elementary Cellular Automata (ECA) are analyzed and compared. The results show superior randomness features and the output string has passed the Diehard statistical battery of tests. The design has strong correlation immunity and it is inherently amenable for VLSI implementation. Therefore it can be considered to be a good and viable candidate for parallel pseudo random number generation
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Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two components 1) a set of cells and 2) a set of rules . Programmable Cellular Automata(PCA) employs some control signals on a Cellular Automata(CA) structure. Programmable Cellular Automata were successfully applied for simulation of biological systems, physical systems and recently to design parallel and distributed algorithms for solving task density and synchronization problems. In this paper PCA is applied to develop cryptography algorithms. This paper deals with the cryptography for a parallel AES encryption algorithm based on programmable cellular automata. This proposed algorithm based on symmetric key systems.
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In this paper, the proposed technique use high speed stream cipher approach because this approach is useful where less memory and maximum speed is required for encryption process. In this proposed approach Self Acclimatize Genetic Algorithm based approach is exploits to generate the key stream for encrypt / decrypt the plaintext with the help of key stream. A widely practiced approach to identify a good set of parameters for a problem is through experimentation. For these reasons, proposed enhanced Self Acclimatize Genetic Algorithm (GAKG) offering the most appropriate exploration and exploitation behavior. Parametric tests are done and results are compared with some existing classical techniques, which shows comparable results for the proposed system.
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Control of Nonlinear Industrial Processes Using Fuzzy Wavelet Neural Network ...IJRES Journal
Artificial intelligence control techniques, becomes one of the major control strategies and has received much attention as a powerful tool for the control of nonlinear systems. This paper presents a design of Fuzzy Wavelet Neural Network (FWNN) trained genetic algorithm (FWN-GA) for control of nonlinear industrial process. The FWNN is applied to approximate unknown dynamic of system and GA is used to train and optimize the FWNN parameters. In the proposed control scheme, neural control system synthesis is performed in the closed-loop control system to provide appropriate control input. For this, the error between desired system output and output of control object is directly utilized to tune the network parameters. The controller is applied to a highly nonlinear industrial process of continues stirred tank reactor (CSTR). Simulation results show that FWNN-GA controller has excellent dynamic response and adapt well to changes in reference trajectory and system parameters.
Neuro genetic key based recursive modulo 2 substitution using mutated charact...ijcsity
In this paper, a neural genetic key based technique for encryption (NGKRMSMC) has been proposed
through recursive modulo
-
2 substitution using mutated character code generation for online wireless
communication of data/information.
Both sender and receive
r get synchronized based on their final output
.
The length of the key depends on the number of input and output neurons. Coordinated matching weight
vectors assist to generate chromosomes pool. Genetic secret key is obtained using fitness function, which i
s
the hamming distance between two chromosomes. Crossover and mutation are used to add elitism of
chromosomes.
At first
mutated character code table
based encryption strategy get perform on plain text.
.
Then the intermediate cipher text is yet again encry
pted through recursive positional modulo
-
2 substitution
technique to from next level encrypted text. This 2nd level intermediate cipher text is again encrypted to
form the final cipher text through chaining and cascaded xoring of neuro genetic key with the
identical
length intermediate cipher text block.
Receiver will perform same symmetric operation to get back the plain
text using identical key
Power system transient stability margin estimation using artificial neural ne...elelijjournal
This paper presents a methodology for estimating the normalized transient stability margin by using the multilayered perceptron (MLP) neural network. The complex relationship between the input variables and output variables is established by using the neural networks. The nonlinear mapping relation between the normalized transient stability margin and the operating conditions of the power system is established by using the MLP neural network. To obtain the training set of the neural network the potential energy boundary surface (PEBS) method along with time domain simulation method is used. The proposed method is applied on IEEE 9 bus system and the results shows that the proposed method provides fast and accurate tool to assess online transient stability.
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effect precision in the chaotic dynamics used in the coupled technic and the chaotic map’s perturbation
technics used for the generation of a Pseudo-Random Number Generator (PRNGs).The use of the
pseudo- chaotic sequences coupled to the orbit perturbation method in the chaotic logistic map and the
NewPiece-Wise Linear Chaotic Map (NPWLCM). The pseudo random number generator’s originality
proposed from the perturbation of the chaotic recurrence. Furthermore the outputs of the binary sequences
with NPWLCM are reconstructed conventionally with the Bernoulli’s sequences shifts map to change the
shapes with the bitwise permetation then the results in simulation are shown in progress.After being
perturbed, the chaotic system can generate the chaotic binary sequences in uniform distribution and the
statistical properties invulnerable analysis. This generator also has many advantages in the possible useful
applications of spread spectrum digitalimages, such as sensitive secret keys, random uniform distribution
of pixels in Crypto system in secure and synchronize communication.
In this paper a novel intelligent soft computing based cryptographic technique based on synchronization of
two chaotic systems (CSCT) between sender and receiver has been proposed to generate session key using
Pecora and Caroll (PC) method. Chaotic system has some unique features like sensitive to initial
conditions, topologically mixing; and dense periodic orbits. By nature, the Lorenz system is very sensitive
to initial conditions meaning that the error between attacker and receiver is going to grow exponentially if
there is a very slight difference between their initial conditions. All these features make chaotic system as
good alternatives for session key generation. In the proposed CSCT few parameters ( , b , r , x1 ,y2 and z2 )
are being exchanged between sender and receiver. Some of the parameter which takes major roles to form
the session key does not get transmitted via public channel, sender keeps these parameters secret. This way
of handling parameter passing mechanism prevents any kind of attacks during exchange of parameters like
sniffing, spoofing or phishing.
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Study Of The Fault Diagnosis Based On Wavelet And Fuzzy Neural Network For Th...IJRES Journal
In the fault diagnosis of the motor, the vibration signals can fully reflect the status of the motor. In this paper, on the basis of wavelet packet fault feature extraction, a new approach for motor fault diagnosis based on wavelet packet analysis and fuzzy RBF neural network was presented.The method gains the energy of characteristic channel of bearing failure vibration signals of asynchronous motor, which adopts the technology of wavelet packet analysis. It also composes the characteristics of the vector as input of fuzzy RBF neural network, used to diagnose the induction motor bearing failures. The method overcomes the slow convergence, a long training time, local minimum problems when using BP neural network. Experimental results shows that using fuzzy RBF neural network can improve the accuracy of the motor fault diagnosis.
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One of the major issues in Target-coverage problem of wireless sensor network is to increase the network
lifetime. This can be solved by selecting minimum working nodes that will cover all the targets. This
paper proposes a completely new method, in which minimum working node is selected by modified Ant
colony Algorithm. Experimental results show that the lever of algorithmic complication is depressed and
the searching time is reduced, and the proposed algorithm outperforms the other algorithm in terms.
Energy-Efficient Target Coverage in Wireless Sensor Networks Based on Modifie...ijasuc
One of the major issues in Target-coverage problem of wireless sensor network is to increase the network
lifetime. This can be solved by selecting minimum working nodes that will cover all the targets. This
paper proposes a completely new method, in which minimum working node is selected by modified Ant
colony Algorithm. Experimental results show that the lever of algorithmic complication is depressed and
the searching time is reduced, and the proposed algorithm outperforms the other algorithm in terms.
Energy-Efficient Target Coverage in Wireless Sensor Networks Based on Modifie...ijasuc
One of the major issues in Target-coverage problem of wireless sensor network is to increase the network
lifetime. This can be solved by selecting minimum working nodes that will cover all the targets. This
paper proposes a completely new method, in which minimum working node is selected by modified Ant
colony Algorithm. Experimental results show that the lever of algorithmic complication is depressed and
the searching time is reduced, and the proposed algorithm outperforms the other algorithm in terms.
High - Performance using Neural Networks in Direct Torque Control for Asynchr...IJECEIAES
This article investigates solution for the biggest problem of the Direct Torque Control on the asynchronous machine to have the high dynamic performance with very simple hysteresis control scheme. The Conventional Direct Torque Control (CDTC) suffers from some drawbacks such as high current, flux and torque ripple, as well as flux control at very low speed. In this paper, we propose an intelligent approach to improve the direct torque control of induction machine which is an artificial neural networks control. The principle, the numerical procedure and the performances of this method are presented. Simulations results show that the proposed ANN-DTC strategy effectively reduces the torque and flux ripples at low switching frequency, compared with Fuzzy Logic DTC and The Conventional DTC.
Multilayer Perceptron Guided Key Generation through Mutation with Recursive R...pijans
In this paper, a multilayer perceptron guided key generation for encryption/decryption (MLPKG) has been
proposed through recursive replacement using mutated character code generation for wireless
communication of data/information. Multilayer perceptron transmitting systems at both ends accept an
identical input vector, generate an output bit and the network are trained based on the output bit which is
used to form a protected variable length secret-key. For each session, different hidden layer of multilayer
neural network is selected randomly and weights or hidden units of this selected hidden layer help to form
a secret session key. The plain text is encrypted using mutated character code table. Intermediate cipher
text is yet again encrypted through recursive replacement technique to from next intermediate encrypted
text which is again encrypted to form the final cipher text through chaining , cascaded xoring of multilayer
perceptron generated session key. If size of the final block of intermediate cipher text is less than the size of
the key then this block is kept unaltered. Receiver will use identical multilayer perceptron generated
session key for performing deciphering process for getting the recursive replacement encrypted cipher text
and then mutated character code table is used for decoding. Parametric tests have been done and results
are compared in terms of Chi-Square test, response time in transmission with some existing classical
techniques, which shows comparable results for the proposed technique.
Implementation of a stream cipher based on bernoulli's mapijcsit
A stream cipher was implemented on a FPGA. The keystream, for some authors the most important
element, was developed using an algorithm based on Bernoulli’s chaotic map. When dynamic systems are
digitally implemented, a normal degradation appears and disturbs their behavior; for such reason, a
mechanism was needed. The proposed mechanism gives a solution for degradation issue and its
implementation is not complicated. Finally, the implemented cipher includes 8 stages and 2 pseudo-random
number generators (PRNG), such cipher was tested using NIST testes. Once its designing stage, it was
implemented using a developing FPGA board.
Secured transmission through multi layer perceptron in wireless communication...ijmnct
In this paper, a multilayer perceptron guided encryption/decryption (STMLP) in wireless communication
has been proposed for exchange of data/information. Multilayer perceptron transmitting systems at both
ends generate an identical output bit and the network are trained based on the output which is used to
synchronize the network at both ends and thus forms a secret-key at end of synchronizations of the
networks. Weights or hidden units of the hidden layer help to form a secret session key. The plain text is
encrypted through chaining , cascaded xoring of multilayer perceptron generated session key. If size of the
final block of plain text is less than the size of the key then this block is kept unaltered. Receiver will use
identical multilayer perceptron generated session key for performing deciphering process for getting the
plain text. Parametric tests have been done and results are compared in terms of Chi-Square test, response
time in transmission with some existing classical techniques, which shows comparable results for the
proposed technique. Variation numbers of input vectors and hidden layers will increase the confusion
/diffusion of the schemeand hence increase the security. As a result variable energy based techniques may
be achieved which may be applicable devices/interface of the heterogeneous sizes of the network/device.
Search for a substring of characters using the theory of non-deterministic fi...journalBEEI
The paper proposed an algorithm which purpose is searching for a substring of characters in a string. Principle of its operation is based on the theory of non-deterministic finite automata and vector-character architecture. It is able to provide the linear computational complexity of searching for a substring depending on the length of the searched string measured in the number of operations with hyperdimensional vectors when repeatedly searching for different strings in a target line. None of the existing algorithms has such a low level of computational complexity. The disadvantages of the proposed algorithm are the fact that the existing hardware implementations of computing systems for performing operations with hyperdimensional vectors require a large number of machine instructions, which reduces the gain from this algorithm. Despite this, in the future, it is possible to create a hardware implementation that can ensure the execution of operations with hyperdimensional vectors in one cycle, which will allow the proposed algorithm to be applied in practice.
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ANALYSIS OF ELEMENTARY CELLULAR AUTOMATA CHAOTIC RULES BEHAVIOR
1. International Journal of Security, Privacy and Trust Management ( IJSPTM) Vol 2, No 6, December 2013
ANALYSIS OF ELEMENTARY CELLULAR
AUTOMATA CHAOTIC RULES BEHAVIOR
K. Salman
Middle Tennessee State University, Murfreesboro, Tennessee, U.S.A.
ABSTRACT
We present detailed and in depth analysis of Elementary Cellular Automata (ECA) with periodic
cylindrical configuration. The focus is to determine whether Cellular Automata (CA) is suitable for the
generation of pseudo random number sequences (PRNs) of cryptographic strength. Additionally, we
identify the rules that are most suitable for such applications. It is found that only two sub-clusters of the
chaotic rule space are actually capable of producing viable PRNs. Furthermore, these two sub-clusters
consist of two majorly non-linear rules. Each sub-cluster of rules is derived from a cluster leader rule by
reflection or negation or the combined two transformations. It is shown that the members of each subcluster share the same dynamical behavior. Results of testing the ECA running under these rules for
comprehensively large number of lattice lengths using the Diehard Test suite have shown that apart from
some anomaly, the whole output sequence can be potentially utilized for cryptographic strength pseudo
random sequence generation with sufficiently large number of p-values pass rates.
KEYWORDS
Elementary Cellular Automata, Pseudo Random Number Sequences, Diehard Test suite, Chaotic Rules, pvalues.
1. INTRODUCTION
The subject of security of data from a transmitting agent to a receiving agent is well researched in
both academia and professional research entities and may fall under encryption/decryption
schemes. The basic idea is to find a means of delivering a message from one side to another side
using public transmission media such that the message when interrupted during the transmission
interval display zero information to the non-intended receiver. Obviously, the message must
undergo some transformation in order to hide the message in a noise like background. Of course
a persistent or interesting third party may resort to extremely powerful means such as super
computers and good algorithms, depending on the importance of the content of the message, to
try to recover the message from the distorting means used. Many excellent textbooks have been
written to explain the various techniques used to encrypt and decrypt the message, such as [1].
One common and established scheme used in the art is the synchronous stream cipher, the basic
structure of which is depicted in figure 1. The message to be transmitted by the sender is usually
referred to as Plaintext denoted by is mixed with the output
(Random Sequence) of the
random number generator (RNG) by the exclusive-or primitive represented by the operation
symbol to yield the resultant which is the encrypted message and usually referred to as
ciphertext, thus: = . The mixing operation, usually referred to as encryption, will make the
ciphertext look like a random sequence and therefore an unintended third party (the
Eavesdropper) should not be able to use it in order to extract the original message . However,
the intended Receiver can easily recover the original message by applying the same mixing
DOI : 10.5121/ijsptm.2013.2601
1
2. operation on the ciphertext using the exact replica of the random number generator , thus =
. This operation is usually referred to as decryption. It should be noted that the mixing
operation, the exclusive-or, is a linear operation by means of which the recovery of the original
message is facilitated. In order for the two operations encryption and decryption to work properly
the random number generators at both sides should obviously be identical and use the exact same
seed. However, when the random number generator used is extracted from a natural noise source
then no matter what seed is used the two random sequences generated at both sides will not be the
same by virtue of the action of the random nature of the source. Therefore natural sources based
random number generators are precluded from utilization in stream ciphers. Mathematical based
algorithms can thus present themselves as a viable alternative. It should be easy to realize that any
algorithm based on mathematical means cannot be random, rather pseudo random and the
viability needs to be ascertained.
International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Figure 1. Typical Synchronous Stream Cipher.
In order for the Pseudo Random Number Generator (PRNG) to be strong it must produce a
sequence that has at least the following salient attributes which are intrinsic in the natural RNGs:
•
•
•
•
•
Uniformity of the output digits
Long cycle length.
No repeated patterns can be detected in the sequence.
The sequence is easy to generate but hard to reproduce or best described by the so called
the next bit unpredictability, i.e. the next bit cannot be predicted or extrapolated even
with the a priori knowledge of the whole sequence.
The algorithm must be simple and both operationally and computationally efficient.
Several algorithms were used in the past to generate PRNs, notably Linear Feedback Shift
Registers (LFSRs). These registers proved to be simple and efficient and were used quite
extensively until an algorithm developed by [2], showed that the linear complexity of such
registers can be reduced drastically to just two span lengths of the register and rendered such
devices unsuitable for encryption/decryption of the synchronous stream ciphers. The breakdown
of these registers is in principle due to the linear primitive used exclusively in the feedback path.
Non-linear Feedback Shift Registers, on the other hand, could prove neither efficient nor viable
for such applications. Recently, however, cellular automata have been utilized to generate strong
PRNs, [3]. To the knowledge of the author, in spite of the wealth of available research on cellular
automata and the different configurations published, no thorough analysis of the strength of
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3. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
periodic and uniform ECA for production of pseudo random number sequences seem to exist in
the open literature. This paper is intended to address this issue at the outset.
The focus of this paper is to test the quality of the randomness of the output of uniform
Elementary Cellular Automata to ascertain the strength of such novel means in utilization for
pseudo random sequence generation of cryptographic strength. Such strength is gauged in this
paper by the passing of the widely accredited state of the art Diehard Test Suite. The paper is
arranged as follows: section 2 will describe the theory of elementary cellular automata, followed
by the dynamics of ECA balanced chaotic rule equivalence in section 3, description of the
Diehard test suite use in testing the output data string in section 4 while section 5 gives an
account of the test data results with explanations, and finally the conclusions and suggestions for
further research.
2. THEORY OF ELEMENTARY CELLULAR AUTOMATA (ECA)
We
start
by
defining
our
ECA
structure 〈 , , , ( ), , , , , 〉, where:
•
•
•
•
•
•
by
a
nonuple
mathematical
∈ is the ECA span length and is made up of interconnected identical memory
cells
that are indexed spatially by ∈ and temporally by ∈ .
Σ is a finite set of states so that each memory cell
at location and time step
can occupy one element of the finite set.
∈ is the total time evolution of the ECA.
( ) ∈ is the neighbourhood of the memory cell where it expands equally and
spatially left and right at equal radius ∈ in which case it can be stated that
= 2 + 1.
is the global rule of the ECA which is defined by the mapping : → .
∈ is the local transition rule defined by the mapping : → where ℜ is
the ECA rule space and ∈ 2 .
is the global ECA state space defined by = .
={
} is the initial seed of the automaton at time step = 0 .
is the output function that works on the output string of the data generated by the
ECA to form the resultant pseudo random string output used in the stream cipher.
•
•
•
The ECA under consideration is one dimensional (1-D) implying that it consists of a linear finite
lattice of interconnected and identical cells of length K , K ∈ N . Each cell denoted mathematically
by
is interconnected with one cell to the right hand side denoted by
and another cell to
the left hand side denoted by
. The alphabet is defined to be {0,1} over , and the
neighbourhood id defined by = 2 + 1 = 3 where = 1 that follows immediately from the
definition of binary elementary cellular automata. The interconnection is symmetrically valid for
1 ≤ ≤ − 2 leaving the two extreme end cells
and
to be made adjacently
interconnected as depicted in figure 2(a). The whole ECA is made effectively circular and the
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4. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
shaded extreme end cells coloured blue and red are made adjacent as indicated by the thick black
demarcation line separating them in figure 2(b). The evolution of this circular (periodic)
automaton will eventually form cylindrical ECA automata.
c
t
0
c
t
K −1
c
t
c
K −2
t
k +1
c
t
k
c
t
c
k −1
t
1
c
t
0
c
t
K −1
(a)
(b)
The next state of a cell away from the two boundaries can be represented by
=
) under rule for 1 ≤ ≤ − 2. It follows that the next state of the extreme
(
, ,
end cells, the left hand cell and right hand cell or the boundary cells under the same rule are
) and
), respectively.
logically represented by
= ( ,
,
= ( , ,
The rule numbering used in this paper is implementation of the rule numbering scheme suggested
by Wolfram, [4], and is now widely used by those skilled in the art. The rule number is quoted in
the decimal number system and can be defined by = ∑
(2 ∗ ) , where
∈ denote
the minterms (as they are usually referred to in switching circuit theory) indexed by ∈ 2 or
∈ 2 which represents the row number in decimal of the truth table, as depicted in table 1. Since
the mapping is {0,1} → {0,1} it follows that each ECA rule will have a truth table the size of
which consists of 2 rows or 2 unique minters . It can be seen that the size of the ECA rule
space ℜ will therefore be 2 or 2 = 256 unique rules. They are , , … , , … , , as
depicted in figure 3. Each rule is uniquely determined by these minterms { }, which can either
be a form of a rule table:
{ , , , , , , , }
Figure 2- Illustration of periodic (circular) ECA configuration.
Or a rule number
the above string:
=∑
(2 ∗
(
), where
∈ that gives the decimal representation of
)
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5. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
x
t
ck
1
t
ck
t
ck
1
0
1
255
30
m0
m1
m2
m3
m4
m5
m6
m7
Figure 3- ECA rule space table.
Table 1- ECA Rule Minterms Table.
111 110 101 100 011 010 001 000
In order to realize the hardware of the ECA running under rule the logical expression of this
rule must be derived in minimum form. One common approach is by means of Karnaugh
mapping as illustrated in figure 4 for the two rules and .
ckt −1
ckt +1
ckt −1
ckt +1
Figure 4- Karnaugh-Maps of the two chaotic rules ∅
30
45
and ∅ .
=
( +
) for rule ∅ and as
=
( +
) for rule ∅
example of the realization of this expression for rule ∅ is illustrated in figure 5.
The next state minimized logical expression can be derived from the K-Map shown in figure 4 as
. An
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6. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
t
c k+1
Qk
Dk
t
ck
t
ck
45
t
c k +1
Figure 5- ∅
t
c k −1
logic circuit realization with memory cell at spatial index .
The evolution of the periodic ECA in a single time step is depicted in figure 6 while figure 7
illustrates the evolution of the periodic ECA running under ∅ with an arbitrary starting seed for
seven contiguous time steps. The random nature of the ECA output at the seventh time step is
apparent, which is not the case with all the ECA rule space.
t
cK
1
t
cK
2
t
ck
1
t
ck
t
ck
1
t
c k
1
1
c1t
t
c0
45
t
t
c K 11 c K 1 2
t
c k
1
1
t
c k
1
c1t
1
Figure 6- One time step evolution illustration using ∅
t
2
t
3
t
4
t
5
t
.
1
t
1
0
t
t
c 0
6
Figure 7- seven time-steps evolution of uniform periodic ECA with 8-cell span length using ∅
t
7
.
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7. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
The ECA rule space has been conjectured by [4] to be classified into four different classes:
•
•
•
•
Class I:
Class II:
Class III
Class IV
Evolution leads to homogeneous fixed points.
Evolution leads to periodic configurations.
Evolution leads to chaotic, aperiodic patterns.
Evolution produces persistent, complex patterns of localized structures.
Although this classification was based primarily on the phenomenological nature of the
spatiotemporal patterns of the ECA dynamics, more in depth studies, such as that attributed to [5],
inferred almost the same classification. The only class that can be useful for possible strong PRN
generation is class III when the ECA is run uniformly under one local rule. However, in order for
the output binary sequence to be useful it has to have at least some common attributes as listed in
the previous section. The first attribute, Uniformity of the output digits, can only be satisfied
when the local rule used has balanced minters. This means that the number of asserted minterms
must equal to the number of unasserted minterms. It can be seen that the sub-space of the ECA
rule space that satisfy this condition reduces to
!∗
!
= 70 unique rules, to be denoted
by . However, this sub-space, albeit satisfies the first randomness attribute as outlined
above does not contain purely chaotic rules of class III but rather other rules that belong to the
other three classes. It has been shown here that only some of these rules, exactly 16 rules and
denoted by , , are actually chaotic, belong to class III and may prove to be useful for
PRNs generation. These rules are:
, , , , , , ,
,
,
,
,
,
,
,
,
It can be seen that this sub-space consists of two groups, one group is dominated by non-linear
primitives in their logical expressions and will be denoted by
and consist of all
the constituent rules in the two cluster leaders and . The second half of the chaotic rules
sub-space relies only on linear primitives in their logical expressions, and is denoted
by
:
, ,
,
,
,
,
,
The following table 2 provides the Karnaugh Map based minimized logical expressions of the 16
rules based on the neighbourhood of the three cells,
, , and
. It can be seen that eight
rules are non-linear while the other eight rules are linear. The different colours associate the
clusters of the rules. The rules marked yellow belong to the cluster of , those marked with
green belong to , and these two clusters are the non-linear rules. The rules marked orange are
the cluster of rule , while the blue colour show the two rules and . The last two linear
rules
and are coloured pink. It can be seen that the cluster rules of and consist
of just two rules.
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8. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Table 2-Chaotic Rules sub-space Logic Expressions
Rule Cluster
Minterms
= {0,0,0,1,1,1,1,0}
Next State logical expression Rule Dynamics
=
= {0,1,0,1,0,1,1,0}
(
=
= {1,0,0,0,0,1,1,1}
+
(
=
(
= {1,0,0,1,0,1,0,1}
=
(
= {0,1,0,1,1,0,0,1}
=
+
(
= {0,0,1,0,1,1,0,1}
=
= {0,1,0,0,1,0,1,1}
(
=
= {0,1,1,0,0,1,0,1}
(
=
= {0,0,1,1,1,1,0,0}
= {0,1,1,0,0,1,1,0}
= {1,0,0,1,1,0,0,1}
=
=
=
= {1,1,0,0,0,0,1,1}
=
= {0,1,0,1,1,0,1,0}
=
= {0,0,0,1,1,1,1,0}
=
= {0,1,1,0,1,0,0,1}
=
= {1,0,0,1,0,1,1,0}
+
=
+
(
+
)
)
)
+
)
+
)
+
)
)
Non-Linear
)
Linear
Based on previous work, [6], the sixteen chaotic rules were shown to belong to clusters of rules
formed by the transformations, complementation, negation and reflection on any member rule of
the cluster as depicted in figure 8.
x
z
y
Figure 8- Basic transformations in Rule equivalence.
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9. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Suppose that the minterms of a generic rule are:
{
,
,
,
,
,
,
Then by reflection transformation of the minterms,
the minterms
{ ,
,
,
, ,
according to the scheme depicted in figure 9:
m7
m6
m5
m4
,
,
,
m2
m3
}
}
we obtain the rule
m1
with
m0
Figure 9-ECA Rule Reflection Scheme
Note that rule reflection transformation undergoes the exchange or swap of the unsymmetrical
minterms, thus: (
→
) or (
→
) and (
→
) or (
→
) as
well as (
→
) or (
→
) and (
→
) or (
→
) for the
generic rule . Similarly, rule negation transformation
with the minterms:
{
,
,
,
,
,
,
The two transformations reflection followed by negation
reverse order
{
,
,
}
results in forming
,
,
,
,
}
results in forming
or the
with the minterms:
These transformations are illustrated in table 3 for the generic rule generating rules , ,
and
noting that
and
are two representations of the same rule. Figure 10 shows
the formation of the rule cluster of generic rule hypercube. Taking a specific example
is represented by the minterms (00011110)2 change under rule reflection
transformation to the following minterms (01010110)2 which represents 86 . Similarly,
is represented by changing the minterms (00011110)2 under rule negation
transformation to the following minterms (10000111)2 and for 149 changing (00011110)2
into (10010101)2 under rule negation transformation followed by rule reflection transformation
or in reverse order, as illustrated in table 4.
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10. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Table 3- Generic Rule equivalence minterms modification
rules
minterms
x
x
x
N
x
R
xC
xC
xC
R N
N
xC
R
R N
Figure 10- Illustration of Rule equivalence Hypercube of the generic rule cluster 30
Table 4- 30 equivalence transformations minterms modification
rules
minterms
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
The cluster rules that are useful for PRN sequence generation are those of rules 30 , 45 , 60
and 90 as well as the two rules 105 and 150. However, the rules in the lower plane of the
hypercubes of rules 30 and 45 as illustrated in figure 11 that are formed by the complementation
transformation have been found to be inconsequential for the purposes of PRN sequence
generation except for the complementation transformation of rule 105 . Each of these two
hypercubes of rules 30 , and 45 consists of eight rules while the hypercube of 60 consists of
four rules and the last two rules 90 and 105 consists of just two rules. By virtue of the structure
of the minterms of rule 60 only two transformations and their succession can produce different
rules. The complementation transformation of rules 60 , 195 , 102 , 153 wrap around themselves.
The last two rules 90 and 105 produce different rules each with just one transformation. The
reduced number of rules in the rule cluster is referred to as collapsed clusters, [6].
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11. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Figure 11- Hypercube representation of balanced chaotic rule clusters.
3.
DYNAMICS OF
EQUIVALENCE
ECA
BALANCED
CHAOTIC
RULE
The dynamics of the 16 balanced chaotic rules identified in the previous section will be observed
by the phenomenological appearance of the spatio-temporal images of relatively short automaton
span length and limited time evolution. For example table 5 displays the spatio-temporal images
of the ECA running under the four chaotic rules of rule cluster for a span length = 61 and
time-steps evolution = 200 for the same seed that consists of a single one on the extreme right
hand cell and all the other cells are set at zero. In these images a black cell represents the state of
the cell at “1” and a white cell when the cell state is “0”. The similarity of the dynamical behavior
is clear from inspection of the images. The mirror reflection transformation of is clear by
inspecting the images of the two rules and or by inspecting the images of the two rules
and . Likewise the negation transformation of rule is also apparent when inspecting
the image of the two rules and
or by inspecting the images of the two rules
and . The image of rule is obtained by either reflection transformation followed by
negation transformation or the reverse order on the image of rule . It can be seen that the
appearance of the self similar fractals are the same in the images of all the four rules. It can be
said that the four rules behave dynamically in the same manner starting from the same seed.
Although the seed consists of a single one on the extreme right hand side the evolution of less
than one hundred time steps yields a fairly complex image. It is also observable that the spreading
of the patterns takes place at maximum speed which is usually referred to as the speed of light
that corresponds to the ±45o diagonal spreading. Therefore starting from a single cell the whole
lattice span = 61 of the ECA fills up after /2 time-steps. These four rules exhibit good speed
of spreading amongst the 16 chaotic rules. Although the self similar or fractals of the cluster rule
are different from the triangular like shapes of the self similar or fractals of cluster rule
but the complexity of the dynamics are not less random. The three transformations on
also behave similarly to the previous rule cluster . The images shown in table 6 illustrate
the role of the transformations on . The rule equivalence of rule cluster for the same seed
and number of evolution time steps likewise demonstrate the similarity of the dynamical behavior
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12. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
of the rules , ,
and . However, the dynamics are not as random as exhibited by
the rule equivalence of cluster rules and . Symmetrical behavior is quite prevalent in the
dynamics, a feature that is obviously undesirable for pseudo random sequence generation. The
same argument may apply to the rule equivalence of and . The symmetrical nature in the
dynamics of rule and its reflection transformation
highlight the possible linear
relationship in the mathematical expressions of the two rules. The same also applies to rule
and its complement transformation equivalent rule .
Table 5- Spatio-Temporal images of chaotic rule equivalence of
Chaotic Rule Equivalence of rule cluster
= 61, = 100
= 0000000000000000000000000000000000000000000000000000000000001
Table 6- Spatio-Temporal images of chaotic rule equivalence of
Chaotic Rule Equivalence of rule cluster
= 61, = 100
= 0000000000000000000000000000000000000000000000000000000000001
Table 7- Spatio-Temporal images of chaotic rule equivalence of
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13. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Chaotic Rule Equivalence of rule cluster
= 61, = 100
= 0000000000000000000000000000000000000000000000000000000000001
Table 8- Spatio-Temporal images of chaotic rule equivalence of
and
Chaotic Rule Equivalence of rule clusters and
= 61, = 100
= 0000000000000000000000000000000000000000000000000000000000001
4. DIEHARD TEST SUITE
As stated previously, the intended use of the ECA in this paper is for utilization as key generator
in a synchronous stream cipher. The key of the stream cipher is obtained from the seed originally
fed to the cellular automaton denoted by . The ECA then evolves with time and produce the
output stream that consists of the concatenation of { } conditioned by the output function .
Let the output key generated by the ECA represented by = ( { } ), then for this to be a
viable key for a cryptographic strength stream cipher we must be able to assess the strength of the
quality of its randomness. Fortunately, the Diehard test suite [?], has been available to use for
free and has been regarded as the most stringent test suite as of the writing of this paper. The
most recent version of this test suite consists of 22 individual tests as follows:
1.
2.
3.
4.
5.
6.
7.
8.
9.
The BIRTHDAY SPACINGS TEST (9+1)
The tough BIRTHDAY SPACINGS TEST (1)
The GCD TEST-(Big Crush)
The GORILLA TEST -(Big Crush)
The OVERLAPPING 5-PERMUTATION TEST-(Big Crush)
The BINARY RANK TEST for 31x31 matrices (1)
The BINARY RANK TEST for 32x32 matrices (1)
The BINARY RANK TEST for 6x8 matrices (25+1)
The BITSTREAM TEST (20)
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14. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
The OPSO TEST means Overlapping-Pairs-Sparse-Occupancy (23)
The OQSO TEST means Overlapping-Quadruples-Sparse-Occupancy (28)
The DNA TEST (31)
The COUNT-THE-1's TEST on a stream of bytes (1)
The COUNT-THE-1's TEST for specific bytes (25)
The PARKING LOT TEST (10+1)
The MINIMUM DISTANCE TEST (10+1)
The 3-D SPHERES TEST (20+1)
The SQUEEZE TEST (1)
The OVERLAPPING SUMS TEST (10+1)
The UP-DOWN RUNS TEST (3)
The CRAPS TEST (2)
the CRAPS TEST 2 with different dice (2)
The tests vary in the number of p-values they yield, as described above. The Diehard test suite
requires that the output stream to be tested must be converted to a binary form that is suitable for
the test suite. It also requires that the size of the unconverted data must exceed 80 mega bits for
19 of the 22 tests, hence the binary file produced must be greater or equal to 10 Mbytes. The
other three tests, 3, 4, and 5 require much larger data size, namely exceeding 2.7 Giga bits. These
three tests are dubbed as Big Crush [22], a name borrowed to indicate the difficulty in passing the
test. The other 19 tests likewise can be dubbed as Small Crush. When Diehard runs the small
crush it produces 230 p-values. Some of the p-values are produced by the Kolmogorov-Smirnov
test, as indicated by a plus sign in the above list. There is also an overall Kolmogorov-Smirnov
test p-value which can be considered as an indication of Pass/Fail criteria, [7-9]. This paper
reports the findings of running the Small Crush test while the Big Crush test will be the subject
matter for future publication.
5. ECA RULE SPACE DYNAMICS ANALYSIS
Following the discussion of section II above, the number of rules that need to be tested is reduced
to the chaotic rules sub-space , that consists of the 16 chaotic rules:
, , , , , , ,
,
,
,
,
,
,
,
,
These rules belong to the chaotic rules of class III where the λ parameter =0.5, [5]. All the other
rules that belong to the other three classes stand no chance in the testing simply because either the
global dynamics collapse to a very small attraction cycle (named so since any transient of states
reaching this cycle will be trapped in this cycle for eternity), this case applies to the two classes I
and II, or the global dynamics are rich with repeated patterns, as is the case with class IV. This
paper is concerned with testing the whole data generated by the ECA running under one chaotic
rule in contrast to the approach adopted by [3], and explores the ability of the data collected to be
utilized as strong cryptographic data. Since the Diehard test suite for good reasons is the test suite
of choice, it is thus required to collect contiguous concatenated output sequences of size
exceeding 80 Mbits without modifications or decimation. The output function is constructed to
output the data stream as illustrated in figure 12.
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15. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Figure 12 - Concatenation of the ECA output data stream by the output function .
It should be helpful if one could find an easy approach to qualify a sequence of pseudo random
numbers for testing prior to applying a suite of tests. It can be stated that one of the easiest tests is
the uniform distribution of 0’s and 1’s in the binary sequence under test which is attributed to
[10]. However, before attempting to find this distribution the length of the sequence or at least its
lower bound must be determined. Hence the data in the sequence must not repeat implying that
the period of the pseudo random sequence must be longer than the length of the sequence in use.
The LFSR can meet this requirement quite easily at the cost of low linear complexity. In
comparison the ECA can provide superior linear complexity but the length of the period is much
less than that provided by the LFSR. Hence the need to accommodate long periods is essential
when utilizing ECA in pseudo random number generation. The period
of the LFSR in its
maximum sequence mode is computed linearly and is represented by
= 2 -1, where ∈
is the span length of the LFSR. On the other hand the maximum period
attainable from ECA
is not an easy task to compute particularly when non-linear chaotic rules are used and does not
seem to follow any analytically discernible trend. One clear fact is that for the same span length
>
. Information about the periods of the ECA amongst a host of other features during
its time evolution are obtainable from study of the global dynamics of the ECA for arbitrary local
transition rule and span length. For example, figure 13 depicts the global dynamics and gives the
two state diagrams of the ECA running uniformly in a periodic boundary configurations under
for
= 5. Two cycles of attraction can be identified the maximum is of size 5-states and
the minimum of size 1-state. The minimum attraction cycle is only reachable by the state 3110 =
111112, while the maximum attraction cycle is reachable by the five states 310, 610, 1210, 1710, and
2410. All these six states, coloured green, are usually referred to as Garden Of Eden (GOE) states
signifying that they are unreachable which means that they have no pre-images or predecessors.
Additionally, the minimum attraction cycle has a transient trajectory of just one state; it is the
GOD state 3110, which is typical with , while the maximum attraction cycle can be reached by
any state in any one of the five transient branches. One can easily infer that the maximum number
of states to be traversed before the maximum attraction cycle begins to repeat is 5+5=10 states
while the minimum attraction cycle requires just one state before the ECA is locked in the
attraction cycle. Therefore the best scenario for this case of the ECA running uniformly under
rule for
= 5 is to limit the seeds to a repertoire of five GOE states excluding the GOE
state 3110. In comparison, the LFSR of span length 5 in a maximum cycle feedback configuration
can be seeded with any state from the state space of 25-1, i.e. all the span length permutations
excluding the all 0’s state, and runs for 2 5-1 = 31states before repeating.
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16. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
Figure 13- State Diagram of a periodic ECA running uniformly under rule
for
= 5.
We can arguably state that we are interested in the major trajectory from a GOE state, let its
length be denoted by α, usually referred to as a transient, to the major attraction cycle, let the
length of this cycle be denoted by β, as well as the minimum trajectory from a GOE state to the
minimum attraction cycle. Obviously, the best scenario here is to form a seed repertoire that
consists of a collection of GOE states that has the major transient to the major attraction cycle.
Let the total number of states traversed before the major cycle repeats be denoted by ,
giving = + , then for viable cryptographic applications the output string of data generated
by the ECA, denoted by∆, must not exceed ζ, i.e. ≥ . For large data requirements the ECA
must run with a sufficiently large span length , such that the above lower bounds can be
satisfied. Let represent the total number of the Garden of Eden states available for an arbitrary
chaotic rule , then ⊊ represents the proper subset of the Garden of Eden states that lead to
the largest attraction cycle or cycles because it excludes those Garden of Eden states that transit to
shorter cycle or cycles including such states as all 0’s or all 1’s for both even and odd span
lengths and the two states 1010… or 0101… for the even span lengths when using . This
subset should be the set available for use as seeds in any encryption/decryption setting that make
use of the whole ECA output to the stream cipher. This subset of states will be able to guarantee
the orbit of the longest transient evolution but at the cost of limited number of seeds, a case that
can be considered restrictive and inefficient for the utilization of cellular automata in
encryption/decryption applications.
The advantage of the LFSR cannot be overemphasized with the exception of computational
complexity where the ECA inherently gains the upper hand compared to the LFSR. All the
necessary information, such as the primitive polynomial and the feedback taps about the LFSR
can be derived from a collection of 2 ∗ contiguous bits from the output data stream, [**], the
ECA minimum complexity on the other hand asymptotically approaches ( ∗ 2 ∗ ), where
represents the cardinal of the rule sub-space applicable to the periodic configuration. Several
authors have researched the global dynamics of the ECA rule space, [4,6,11], most prominently
was that due to [6] that culminated in the publication of the atlas of global dynamics of cellular
automat. The main goal of all these attempts is to give a detailed account of the state transition
graphs or diagrams or as it is referred to by [6], the field of basin of attraction of the ECA rule
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17. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
space. The information that can be extracted from such data is of particular pertinence when
trying to study the viability of cellular automata in generating cryptographic pseudo random
number sequences. The results published in the above referenced atlas, however, gave details of
the state transition diagrams for ≤ 15 possibly due to the prohibitive computational expense in
the attempt beyond = 15 because the ECA has to run for the entire state space 2 , but of
course larger sizes of can lead to better understanding of the behavior of the ECA and can also
justify the viability of the use of ECA in pseudo random number generation. Excerpts of the data
from the atlas of global dynamics [6] for is tabulated and presented in the following table 9.
It can be seen that the periods of the maximum attraction cycles are inferior to the maximum
cycle lengths of the LFSR and do not follow a linear trend. In addition the LFSR can be seeded
with all states 2 except the all 0’s state while the ECA in the uniform periodic setting should be
seeded with those states that lead to the maximum attraction cycle in order to maximize the
period of the output sequence. Such conditions add severe restrictions to the collection of the
seeds available for the applications sought in this paper. For example the total number of states
available for seeding a uniform and periodic ECA running under when = 11 is 1551
which is the addition of the maximum attraction cycle length and all the transients leading to the
cycle as compared to 2047 for the LFSR for the same span length. Therefore there are two main
factors that influence the required data size; the cellular automaton span length
∈ and the
number of steps of the evolution time ∈ . Let denotes the output data size, then it is
required that the ECA under test should provide a data size of ≥ ∗ . It can be seen that the
number of time steps follows the assignment of the span length . The ECA selected chaotic
rule space was subjected to run on cellular automaton span length range 27 ≤ ≤ 1503. The
minimum span length
= 27 was selected based on the possible cycle length of the ECA
matching the maximum cycle length of the Linear Feedback Shift Register, albeit the ECA
maximum cycle length cannot reach the maximum cycle length of the same span length of the
LFSR as will be explained shortly. For = 80 Mbits the span length must satisfy ≥
/ 2. As explained previously, the ECA is a synchronous sequential circuit that evolves
according to the local transition rule , ∈ 2 therefore for each a group of state transition
diagrams must exist that covers all the states 2 for a span length ∈ . It can be seen that a
detailed compilation of such state diagrams for the range of used in this paper is presently
computationally too exhaustive.
The ECA was run for each span length in the range 27 ≤ ≤ 1503 for each of the 16 chaotic
rules mentioned above. Each output of size ≈ 80 M bits was tested individually by the Diehard
test suite to ensure the inclusion of all the 19 individual tests mentioned above. The results are
shown in the figures 14-19 and the following findings can be derived:
1. Cluster seems to outperform the other 12 rules.
2. Cluster ∅ is the second best.
3. Cluster , Rules 90 and 165 and Rules 105 and 150 seem to perform worst with low
passing rates compared to the two non-linear cluster rules 30 and 45.
The results of the four rules in cluster seem to be almost identical and the same apply to the
other clusters therefore it should suffice to show the results of the leading rules in the clusters. In
depth study of the results of shows that the range of results undergoes many regions. The
first region covers seed length range 27 ≤ ≤ 73 where the ECA failed to pass all the p-values.
However at
= 73 it passed 228 p-values and failed one p-value as well as the KS overall p17
18. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
value. In our criterion this is equivalent to failing the tests. In this way the first seed where the
ECA passed all the 230 p-values happened at = 109. If one considers the suitability of the
ECA for pseudo random generation based on passing all the p-values produced by the Diehard
test suite then the region just mentioned 27 ≤ ≤ 108 can be considered unsuitable for pseudo
random number generation when running uniformly under in the periodic configuration. One
important observation is the frequent dip in the number of p-values passed at 32-bit intervals.
Starting from = 30 with 32 number of p-values passed with a neighbour span lengths passing
more p-values, a clear dip in the number of p-values passed takes place at = 62 where the pvalues passed by the neighbour span lengths are 123 and 92. It repeats after another 32-bit
increment, i.e. at = 94 and = 126 and so on. The number of p-values passed increase after
the dip at = 287with the number of p-values passed equal 180, the next dip takes place at
= 319 with 210 number of p-values passed while at 2-bit neighbouring seeds the ECA fails
around just 2 p-values. Similar patterns but more condensed also observable with rule cluster 45.
In this cluster the dip happens more frequently and at span length differences of 4, 8, 16 and
32bits. The increase of the rate of failures is quite apparent. The intervals of failures with the
other rules also take place at similar span length differences as with rule cluster 45. There is no
clear explanation for the reason why such failures happen at the differences in span lengths
described above. However, since the numbers are powers of two and that the Diehard test suite is
in fact based on testing binary numbers of 32-bit wide, it may have some sensitivity to the results
obtained. Further research is obviously warranted for this problem. By inspecting the results of
the rest of the chaotic rules it seems that none of the other rules behave better than . From the
above results one can state that the data presented in table 9 may lead to the contention that
running the ECA with a random seed may probabilistically result in the failure of the output data
stream in passing the test suite. This should be clear from the results presented in this paper.
Table 9. State Diagrams Data for for span length range 3 ≤ ≤ 14.
LFSR
(span length L)
Rule 30
ECA
span
length
K
3
4
5
6
7
8
9
10
11
12
13
14
#of attractors
producing
Less than
Maximum
maximum
period
period
1
3
1
1
1
3
1
8
4
1
1
2
4
2
2
1
8
4
4
1
17
1
Maximum
Attractor
period
Total # of states in
the maximum
attractor state
diagrams
Total # of
GOE
states
8
5
63
40
171
15
154
102
832
1428
12
30
77
224
414
420
1551
975
2600
13818
3
5
6
12
10
33
57
56
136
91
964
1478
Maximum cycle
length
2 −1
7
15
31
63
127
255
511
1023
2047
4095
8191
16383
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19. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
#p-values passed
Rule 30
250
200
150
100
50
0
0
500
1000
1500
Seed Length K
Figure 14 – Diehard Results of ECA running uniformly under
2000
for span length range 27 ≤
≤ 1503
#p-values passed
Rule 45
250
200
150
100
50
0
0
500
1000
1500
2000
Seed Length K
Figure 15 – Diehard Results of ECA running uniformly under
for span length range 27 ≤
≤ 1503
Rule 60
#p-values passed
250
200
150
100
50
0
0
200
400
600
800
1000
1200
1400
1600
Seed Length K
Figure 16 – Diehard Results of ECA running uniformly under
for span length range 27 ≤
≤ 1503
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20. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
#p-values passed
Rule 90
250
200
150
100
50
0
0
200
400
600
800
1000
1200
1400
1600
Seed Length K
Figure 17 – Diehard Results of ECA running uniformly under
for span length range 27 ≤
≤ 1503
Rule 105
250
#p-values passed
200
150
100
50
0
0
200
400
600
800
1000
1200
1400
1600
Seed Length K
Figure 18 – Diehard Results of ECA running uniformly under
for span length range 27 ≤
≤ 1503
#p-values passed
Rule 150
250
200
150
100
50
0
0
200
400
600
800
1000
1200
1400
1600
Seed Length K
Figure 19 – Diehard Results of ECA running uniformly under
for span length range 27 ≤
≤ 1503
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21. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
6. CONCLUSIONS
It has been shown that if passing all the p-values generated by the Diehard test suite is considered
a good criterion to qualify a sequence of pseudo random numbers as being cryptographically
strong then only a sub-space of the ECA rule space ℜ can be considered useful for this
application. The ECA under test is designed to run uniformly on one local transition rule in a
periodic boundary configuration. The ECA was run for a wide range of span lengths 27 ≤ ≤
1503. A random seed was used for each span length and the same seed was used by all the 16
rules in the sub-space . In the case that the ECA fails any of the 230 p-values by the Diehard
test suite, 9 more random seeds are generated and the ECA is re-run on all these seeds to create a
new average of the p-values passed and then recorded. The results evidently show that cluster
outperforms all the other rules followed by cluster ∅ . Although the linear rules sub-space
can pass all the Diehard 230 p-values, it is clear that in addition to the fact that the
passing rate is visibly lower than the results obtained from the rules of the non-linear sub-space
the dependencies of these rules on the linear primitives operations makes them
inherently amenable to cracking and render them weak in cryptographic applications. The results
also show that all the rules exhibit some periodic patterns of seed length differences of 32, 16, 8
and 4, or in terms of powers of two. {2} . Since the common denominator is a power of two up to
power of 5, it has little to do with the span lengths since the failures take place at odd numbers of
the span length as well as even numbers in addition to prime numbers. One of the possible
causes of this trend may be attributed to the tests in the Diehard test suite itself. The Diehard
deals with numbers of 32-bit wide and therefore some sensitivity to this number may propagate to
the results and possible inclusion of divisible numbers as well. In conclusion it can be deduced
for recommendation that when the ECA is intended for use to generate pseudo random numbers
of high or cryptographic quality based on the criterion stated above, namely that the whole data
output is used as key number generator for the synchronous stream and that the output must pass
all the 230 p-values generated by the Diehard test suite, then the best choice would be cluster rule
30, i.e. any one of the four rules , , , , running with a repertoire of seeds collected
as discussed in the body of this paper. Any seed used outside this carefully compiled repertoire
would leave the output data to the probabilistic failure. A recommendation for future work would
be to construct an efficient algorithm that allows the computation in polynomial time of the state
diagrams of the useful rules for the range of span lengths . The results will facilitate the
compilation of a reliable repertoire of a set of seeds to be used for the applications in question.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Menezes, J. Alfred, van Oorschot, C. Paul, & Vanstone A. Scott (1996), “Handbook of Applied
Cryptography”, Editors: Kenneth H. Rosen, CRC Press, ISBN: 0-8493-8523-7, Fifth Printing Edition,
816 pages.
Berlekamp, E.R. (1968), "Algebraic Coding Theory", McGraw-Hill, New York, chapter 7.
Wolfram, Stephen (1986), "Random Sequence Generation by Cellular Automata", Advances In
Applied Mathematics 7, pp 123-169.
Wolfram, S. (2002), “A New Kind of Science”, Champaign, IL: Wolfram Media, ISBN: 1579550088.
Langton, Chris G. (1990), “Computation at the edge of chaos: Phase transitions and emergent
computation”, Physica D, 42:12-37.
Wuensche Andrew, and Mike Lesser (1992), “The Global Dynamics of Cellular Automata”,
Reference Volume I, Addison Wesley Publishing Company, ISBN: 0-201-55740-1.
21
22. International Journal of Security, Privacy and Trust Management (IJSPTM) Vol 2, No 6, December 2013
[7]
K. Salman (2013), “Elementary Cellular Automata (ECA) Research platform”, Cyber Journals:
Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Software
Engineering (JSSE), Volume 3, Issue 6, June Edition, 2013, pp 1-15.
[8] K. Salman (2013), “Feedback Shift Registers As Cellular Automata Boundary Conditions”, First
International Conference on Computational Science and Engineering (CSE-2013), pp 11-21,
http://airccj.org/CSCP/vol3/csit3302.pdf
[9] K. Salman (August 2013), “Analysis Of Elementary Cellular Automata Boundary Conditions”,
International Journal of Computer Science & Information Technology (IJCSIT) Vol. 5, No 4, pp. 3551
[10] S.W. Golomb (1986), “Shift Register Sequences”, Aegean Park Press; Revised edition, ISBN-10:
0894120484.
[11] Edward Jack Powley, (2009), “Global Properties of Cellular Automata”, Ph.D., Department of
Computer Science, University of York.
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