A graph invariant is a number that can be easily and uniquely calculated through a graph.Recently,part of mathematical graph invariants has been portrayed and utilized for relationship examination.Nevertheless,no reli...A graph invariant is a number that can be easily and uniquely calculated through a graph.Recently,part of mathematical graph invariants has been portrayed and utilized for relationship examination.Nevertheless,no reliable appraisal has been embraced to pick,how much these invariants are associated with a network graph in interconnection networks of various fields of computer science,physics,and chemistry.In this paper,the study talks about sudoku networks will be networks of fractal nature having some applications in computer science like sudoku puzzle game,intelligent systems,Local area network(LAN)development and parallel processors interconnections,music composition creation,physics like power generation interconnections,Photovoltaic(PV)cells and chemistry,synthesis of chemical compounds.These networks are generally utilized in disorder,fractals,recursive groupings,and complex frameworks.Our outcomes are the normal speculations of currently accessible outcomes for specific classes of such kinds of networks of two unmistakable sorts with two invariants K-banhatti sombor(KBSO)invariants,Irregularity sombor(ISO)index,Contraharmonic-quadratic invariants(CQIs)and dharwad invariants with their reduced forms.The study solved the Sudoku network used in mentioned systems to improve the performance and find irregularities present in them.The calculated outcomes can be utilized for the modeling,scalability,introduction of new architectures of sudoku puzzle games,intelligent systems,PV cells,interconnection networks,chemical compounds,and extremely huge scope in very large-scale integrated circuits(VLSI)of processors.展开更多
This paper proposes a cryptographic technique on images based on the Sudoku solution.Sudoku is a number puzzle,which needs applying defined protocols and filling the empty boxes with numbers.Given a small size of numb...This paper proposes a cryptographic technique on images based on the Sudoku solution.Sudoku is a number puzzle,which needs applying defined protocols and filling the empty boxes with numbers.Given a small size of numbers as input,solving the sudoku puzzle yields an expanded big size of numbers,which can be used as a key for the Encryption/Decryption of images.In this way,the given small size of numbers can be stored as the prime key,which means the key is compact.A prime key clue in the sudoku puzzle always leads to only one solution,which means the key is always stable.This feature is the background for the paper,where the Sudoku puzzle output can be innovatively introduced in image cryptography.Sudoku solution is expanded to any size image using a sequence of expansion techniques that involve filling of the number matrix,Linear X-Y rotational shifting,and reverse shifting based on a standard zig-zag pattern.The crypto key for an image dictates the details of positions,where the image pixels have to be shuffled.Shuffling is made at two levels,namely pixel and sub-pixel(RGB)levels for an image,with the latter having more effective Encryption.The brought-out technique falls under the Image scrambling method with partial diffusion.Performance metrics are impressive and are given by a Histogram deviation of 0.997,a Correlation coefficient of 10−2 and an NPCR of 99.98%.Hence,it is evident that the image cryptography with the sudoku kept in place is more efficient against Plaintext and Differential attacks.展开更多
Sudoku风靡全球的智力游戏蕴藏着丰富的数学知识。本文对如何依据难度系数生成sudoku的算法进行了探究。首先通过自反性、对称性、传递性等等价关系生成一个正确完整的sudoku,并对其完备性进行了讨论。其次,通过一个二维数组分别代表候...Sudoku风靡全球的智力游戏蕴藏着丰富的数学知识。本文对如何依据难度系数生成sudoku的算法进行了探究。首先通过自反性、对称性、传递性等等价关系生成一个正确完整的sudoku,并对其完备性进行了讨论。其次,通过一个二维数组分别代表候补sudoku的两个自由度子空格数目和空格的自由度表征难度系数。再次,应用ILP(integer linear programming)模型和ASP(another solution problem)模型来确保sudoku解得唯一性。最后,利用MATLAB软件对实上诉算法,算法复杂度较低。展开更多
Division arithmetic and generalized exploiting modification direction （DA-GEMD） method has perfect efficiency in data-hiding. However, there exist some weaknesses in DA-GEMD. Because the benchmarks are their median ...Division arithmetic and generalized exploiting modification direction （DA-GEMD） method has perfect efficiency in data-hiding. However, there exist some weaknesses in DA-GEMD. Because the benchmarks are their median of nine pixels in each block of cover-image, it will give a hint for the attacker to hack the stego-image. In the paper, we utilize the Sudoku table to randomize the benchmark for each 3×3 block of cover-image. It will mix up the pixels in each image block and prevent the secret information from being extracted. The proposed method still keeps the original efficiency as DA-GEMD while promoting the security for data-hiding.展开更多
Recently, Chang et al. proposed a Sudoku-based secret image sharing scheme. They utilized the Sudoku grid to generate meaningful shadow images, and their scheme satisfied all essential requirements. Based on Chang et ...Recently, Chang et al. proposed a Sudoku-based secret image sharing scheme. They utilized the Sudoku grid to generate meaningful shadow images, and their scheme satisfied all essential requirements. Based on Chang et al.＇s scheme, we propose a novel （n, n） secret image sharing scheme based on Sudoku. In the proposed scheme, a secret image can be shared among n different cover images by generating n shadow images, and the secret image can be reconstructed without distortion using only these n shadow images. Also, the proposed scheme can solve the overflow and underflow problems. The experimental results show that the visual quality of the shadow images is satisfactory. Furthermore, the proposed scheme allows for a large embedding capacity.展开更多
This paper proposes a dynamic load balancing with learning model for a Sudoku problem solving system that has multiple workers and multiple solvers.The objective is to minimise the total processing time of problem sol...This paper proposes a dynamic load balancing with learning model for a Sudoku problem solving system that has multiple workers and multiple solvers.The objective is to minimise the total processing time of problem solving.Our load balancing with learning model distributes each Sudoku problem to an appropriate pair of worker and solver when it is received by the system.The information of the estimated solution time for a specific number of given input values,the estimated finishing time of each worker,and the idle status of each worker is used to determine the worker-solver pairs.In addition,the proposed system can estimate the waiting period for each problem.Test results show that the system has shorter processing time than conventional alternatives.展开更多
基金King Saud University through Researchers Supporting Project number(RSP2022R426),King Saud University,Riyadh,Saudi Arabia.
文摘A graph invariant is a number that can be easily and uniquely calculated through a graph.Recently,part of mathematical graph invariants has been portrayed and utilized for relationship examination.Nevertheless,no reliable appraisal has been embraced to pick,how much these invariants are associated with a network graph in interconnection networks of various fields of computer science,physics,and chemistry.In this paper,the study talks about sudoku networks will be networks of fractal nature having some applications in computer science like sudoku puzzle game,intelligent systems,Local area network(LAN)development and parallel processors interconnections,music composition creation,physics like power generation interconnections,Photovoltaic(PV)cells and chemistry,synthesis of chemical compounds.These networks are generally utilized in disorder,fractals,recursive groupings,and complex frameworks.Our outcomes are the normal speculations of currently accessible outcomes for specific classes of such kinds of networks of two unmistakable sorts with two invariants K-banhatti sombor(KBSO)invariants,Irregularity sombor(ISO)index,Contraharmonic-quadratic invariants(CQIs)and dharwad invariants with their reduced forms.The study solved the Sudoku network used in mentioned systems to improve the performance and find irregularities present in them.The calculated outcomes can be utilized for the modeling,scalability,introduction of new architectures of sudoku puzzle games,intelligent systems,PV cells,interconnection networks,chemical compounds,and extremely huge scope in very large-scale integrated circuits(VLSI)of processors.
基金supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 Research Programs,respectively。
文摘This paper proposes a cryptographic technique on images based on the Sudoku solution.Sudoku is a number puzzle,which needs applying defined protocols and filling the empty boxes with numbers.Given a small size of numbers as input,solving the sudoku puzzle yields an expanded big size of numbers,which can be used as a key for the Encryption/Decryption of images.In this way,the given small size of numbers can be stored as the prime key,which means the key is compact.A prime key clue in the sudoku puzzle always leads to only one solution,which means the key is always stable.This feature is the background for the paper,where the Sudoku puzzle output can be innovatively introduced in image cryptography.Sudoku solution is expanded to any size image using a sequence of expansion techniques that involve filling of the number matrix,Linear X-Y rotational shifting,and reverse shifting based on a standard zig-zag pattern.The crypto key for an image dictates the details of positions,where the image pixels have to be shuffled.Shuffling is made at two levels,namely pixel and sub-pixel(RGB)levels for an image,with the latter having more effective Encryption.The brought-out technique falls under the Image scrambling method with partial diffusion.Performance metrics are impressive and are given by a Histogram deviation of 0.997,a Correlation coefficient of 10−2 and an NPCR of 99.98%.Hence,it is evident that the image cryptography with the sudoku kept in place is more efficient against Plaintext and Differential attacks.
文摘Sudoku风靡全球的智力游戏蕴藏着丰富的数学知识。本文对如何依据难度系数生成sudoku的算法进行了探究。首先通过自反性、对称性、传递性等等价关系生成一个正确完整的sudoku,并对其完备性进行了讨论。其次,通过一个二维数组分别代表候补sudoku的两个自由度子空格数目和空格的自由度表征难度系数。再次,应用ILP(integer linear programming)模型和ASP(another solution problem)模型来确保sudoku解得唯一性。最后,利用MATLAB软件对实上诉算法,算法复杂度较低。
文摘Division arithmetic and generalized exploiting modification direction （DA-GEMD） method has perfect efficiency in data-hiding. However, there exist some weaknesses in DA-GEMD. Because the benchmarks are their median of nine pixels in each block of cover-image, it will give a hint for the attacker to hack the stego-image. In the paper, we utilize the Sudoku table to randomize the benchmark for each 3×3 block of cover-image. It will mix up the pixels in each image block and prevent the secret information from being extracted. The proposed method still keeps the original efficiency as DA-GEMD while promoting the security for data-hiding.
基金supported by the National Natural Science Foundation of China Under Grant No.61272374 and No.61272371
文摘Recently, Chang et al. proposed a Sudoku-based secret image sharing scheme. They utilized the Sudoku grid to generate meaningful shadow images, and their scheme satisfied all essential requirements. Based on Chang et al.＇s scheme, we propose a novel （n, n） secret image sharing scheme based on Sudoku. In the proposed scheme, a secret image can be shared among n different cover images by generating n shadow images, and the secret image can be reconstructed without distortion using only these n shadow images. Also, the proposed scheme can solve the overflow and underflow problems. The experimental results show that the visual quality of the shadow images is satisfactory. Furthermore, the proposed scheme allows for a large embedding capacity.
文摘This paper proposes a dynamic load balancing with learning model for a Sudoku problem solving system that has multiple workers and multiple solvers.The objective is to minimise the total processing time of problem solving.Our load balancing with learning model distributes each Sudoku problem to an appropriate pair of worker and solver when it is received by the system.The information of the estimated solution time for a specific number of given input values,the estimated finishing time of each worker,and the idle status of each worker is used to determine the worker-solver pairs.In addition,the proposed system can estimate the waiting period for each problem.Test results show that the system has shorter processing time than conventional alternatives.
