Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to...Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to scrambling blocks in this paper. At first, the original image is scrambled by using logistic mapping to obtain the encrypted image, and then the encrypted image is divided into many blocks. Finally, the position of the blocked image is scrambled by using the improved Josephus ring to get the encrypted image. According to the experiments, the information entropy of the encrypted image reaches 7.99 and the adjacent correlations in three directions are within ±0.1. The experimental results show that the proposed algorithm has advantages of large key space, high key sensitivity and can effectively resist the attacks of statistical analysis and gray value analysis. It has good encryption effect on digital image encryption.展开更多
We define and study the Extended Feline Josephus Game, a game in which n players, each with ℓlives, stand in a circle. The game proceeds by alternating between hitting k consecutive players—each of whom wil...We define and study the Extended Feline Josephus Game, a game in which n players, each with ℓlives, stand in a circle. The game proceeds by alternating between hitting k consecutive players—each of whom will consequently lose a life—and skipping s consecutive players. This cycle continues until every player except one loses all of their lives. Given the nonnegative integer parameters n, k, s and ℓ, the goal of the game is to identify the surviving player. In this paper, we show how the defining parameters n, k, s, and ℓaffect the survivor of games with specific constraints on those parameters and our main results provide new closed formulas to determine the survivor of these Extended Feline Josephus Games. Moreover, for cases where these formulas do not apply, we provide recursive formulas for reducing the initial game to other games with smaller parameter values. For the interested reader, we present a variety of directions for future work in this area, including an extension which considers players lying on a general graph, rather than on a circle.展开更多
The Australian Shuffle consists of placing a deck of cards onto a table according to this rule: put the top card on the table, the next card on the bottom of the deck, and repeat until all the cards have been placed o...The Australian Shuffle consists of placing a deck of cards onto a table according to this rule: put the top card on the table, the next card on the bottom of the deck, and repeat until all the cards have been placed on the table. A natural question is “Where was the very last card placed located in the original deck?” Card trick magicians have known empirically for years that the fortieth card from the top of a standard fifty-two card deck is the final card placed by this shuffle. The moniker “Australian” comes from putting every other card “Down Under”. We develop a formula for the general case of N cards, and then extend that generalization further to cases involving the discard of k cards before or after putting one on the bottom of the deck. Finally, we discuss the connection of the Australian Shuffle and its generalizations to the famous Josephus problem.展开更多
This study proposes a new medical image encryption scheme based on Josephus traversing and hyper-chaotic Lorenz system.First,a chaotic sequence is generated through hyperchaotic system.This hyperchaotic sequence is us...This study proposes a new medical image encryption scheme based on Josephus traversing and hyper-chaotic Lorenz system.First,a chaotic sequence is generated through hyperchaotic system.This hyperchaotic sequence is used in the scrambling and diffusion stages of the algorithm.Second,in the scrambling process,the image is initially confused by Josephus scrambling,and then the image is further confused by Arnold map.Finally,generated hyperchaos sequence and exclusive OR operation is used for the image to carry on the positive and reverse diffusion to change the pixel value of the image and further hide the effective information of the image.In addition,the information of the plaintext image is used to generate keys used in the algorithm,which increases the ability of resisting plaintext attack.Experimental results and security analysis show that the scheme can effectively hide plaintext image information according to the characteristics of medical images,and is resistant to common types of attacks.In addition,this scheme performs well in the experiments of robustness,which shows that the scheme can solve the problem of image damage in telemedicine.It has a positive significance for the future research.展开更多
文摘Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to scrambling blocks in this paper. At first, the original image is scrambled by using logistic mapping to obtain the encrypted image, and then the encrypted image is divided into many blocks. Finally, the position of the blocked image is scrambled by using the improved Josephus ring to get the encrypted image. According to the experiments, the information entropy of the encrypted image reaches 7.99 and the adjacent correlations in three directions are within ±0.1. The experimental results show that the proposed algorithm has advantages of large key space, high key sensitivity and can effectively resist the attacks of statistical analysis and gray value analysis. It has good encryption effect on digital image encryption.
文摘We define and study the Extended Feline Josephus Game, a game in which n players, each with ℓlives, stand in a circle. The game proceeds by alternating between hitting k consecutive players—each of whom will consequently lose a life—and skipping s consecutive players. This cycle continues until every player except one loses all of their lives. Given the nonnegative integer parameters n, k, s and ℓ, the goal of the game is to identify the surviving player. In this paper, we show how the defining parameters n, k, s, and ℓaffect the survivor of games with specific constraints on those parameters and our main results provide new closed formulas to determine the survivor of these Extended Feline Josephus Games. Moreover, for cases where these formulas do not apply, we provide recursive formulas for reducing the initial game to other games with smaller parameter values. For the interested reader, we present a variety of directions for future work in this area, including an extension which considers players lying on a general graph, rather than on a circle.
文摘The Australian Shuffle consists of placing a deck of cards onto a table according to this rule: put the top card on the table, the next card on the bottom of the deck, and repeat until all the cards have been placed on the table. A natural question is “Where was the very last card placed located in the original deck?” Card trick magicians have known empirically for years that the fortieth card from the top of a standard fifty-two card deck is the final card placed by this shuffle. The moniker “Australian” comes from putting every other card “Down Under”. We develop a formula for the general case of N cards, and then extend that generalization further to cases involving the discard of k cards before or after putting one on the bottom of the deck. Finally, we discuss the connection of the Australian Shuffle and its generalizations to the famous Josephus problem.
基金the National Natural Science Foundation of China(No.61402051)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2016JM6076)。
文摘This study proposes a new medical image encryption scheme based on Josephus traversing and hyper-chaotic Lorenz system.First,a chaotic sequence is generated through hyperchaotic system.This hyperchaotic sequence is used in the scrambling and diffusion stages of the algorithm.Second,in the scrambling process,the image is initially confused by Josephus scrambling,and then the image is further confused by Arnold map.Finally,generated hyperchaos sequence and exclusive OR operation is used for the image to carry on the positive and reverse diffusion to change the pixel value of the image and further hide the effective information of the image.In addition,the information of the plaintext image is used to generate keys used in the algorithm,which increases the ability of resisting plaintext attack.Experimental results and security analysis show that the scheme can effectively hide plaintext image information according to the characteristics of medical images,and is resistant to common types of attacks.In addition,this scheme performs well in the experiments of robustness,which shows that the scheme can solve the problem of image damage in telemedicine.It has a positive significance for the future research.
