Based on the robust chaos theorem of S-unimodal maps, this paper studies a kind of cubic polynomial discrete maps (CPDMs) and sets up a novel theorem. This theorem gives general conditions for the occurrence of robust chaos in the CPDMs. By using the theorem, we construct a CPDM. The parameter regions of chaotic robustness of the CPDM are larger than these of Logistic map. By using a fixed point arithmetic, we investigate the cycle lengths of the CPDM and a Logistic map. The results show that the maximum cycle lengths of 1000 chaotic sequences with length 3×107 generated by different initial value conditions exponentially increase with the resolutions. When the resolutions reach 10-7~10-13, the maximum cycle lengths of the cubic polynomial chaotic sequences are significantly greater than these of the Logistic map. When the resolution reaches 10-14, there is the situation without cycle for 1000 cubic polynomial chaotic sequences with length 3×107. By using the CPDM and Logistic map, we design four chaos-based pseudorandom number generators (CPRNGs): CPRNGI, CPRNGII, CPRNGIII, and CPRNGIV. The randomness of two 1000 key streams consisting of 20000 bits is tested, respectively, generated by the four CPRNGs. The result suggests that CPRNGIII based on the cubic polynomial chaotic generalized synchronic system has better performance.

In this paper, we deal with the mean-square stability of nonlinear stochastic pantograph equations. An equivalent form of stochastic delay differential equations with constant delay is introduced by the transformation approach. An optimal stability condition is presented, since it is independent of the proportion and coincides with the necessary condition for linear pantograph equations with real coefficients.

This study proposes a chaos robustness criterion for a kind of 2D piecewise smooth maps (2DPSMs). Using the chaos robustness criterion, one can easily determine the robust chaos parameter regions for some 2DPSMs. Combining 2DPSM with a generalized synchronization (GS) theorem, this study introduces a novel 6-dimensional discrete GS chaotic system. Based on the system, a 216-word chaotic pseudorandom number generator (CPRNG) is designed. The key space of the CPRNG is larger than 2996. Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of the 1000 key streams consists of 20,000 bits generated by the CPRNG, the RC4 algorithm, and the ZUC algorithm, respectively. The numerical results show that the three algorithms do not have significant differences. The CPRNG and a stream encryption scheme with avalanche effect (SESAE) are used to encrypt an image. The results demonstrate that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. The SESAE with one-time-pad scheme makes any attackers have to use brute attacks to break our cryptographic system.

该文提出一类4维离散系统.利用系统平衡点处Jacobi矩阵的特征值来分析系统在平衡点处的稳定性,建立了一个判别这类系统为周期或混沌的定理.依据该定理构造了一个新的4维离散系统.该系统具有正的Lyapunov指数,数值模拟显示该系统的动力学行为具有混沌特性.结合该系统和系统广义同步定理构造了一个8维广义同步混沌系统.利用该系统构造了一个16 bit混沌伪随机数发生器(CPRNG),其密钥空间大于21245.利用FIPS 140-2检测/广义FIPS 140-2检测判别标准分别检测由CPRNG,Narendra RBG,RC4 PRNG和ZUCPRNG生成的1000个长度为20000 bit的密钥流的随机性.检测结果表明,分别有100％/99％,100％/82.9％,99.9％/98.8％和100％/97.9％密钥流通过FIPS 140-2检测/广义FIPS 140-2检测标准.数值仿真显示不同密钥流之间有平均50.004％不同码.结果说明设计的伪随机数发生器有好的随机性,可以抵抗穷尽攻击.该文提出的CPRNG为密码安全的研究与发展提供了新的工具.

Based on a stream encryption scheme with avalanche effect (SESAE), a stream encryption scheme with both key avalanche effect and plaintext avalanche effect (SESKPAE) is introduced. Using this scheme and an ideal [Formula: see text]-word ([Formula: see text]-segment) pseudorandom number generator (PRNG), a plaintext can be encrypted such that each bit of the ciphertext block has a change with the probable probability of [Formula: see text] when any word of the key is changed or any bit of the plaintext is changed. To that end, a novel four-dimensional discrete chaotic system (4DDCS) is proposed. Combining the 4DDCS with a generalized synchronization (GS) theorem, a novel eight-dimensional discrete GS chaotic system (8DDGSCS) is constructed. Using the 8DDGSCS, a [Formula: see text]-word chaotic pseudorandom number generator (CPRNG) is designed. The keyspace of the [Formula: see text]-word CPRNG is larger than [Formula: see text]. Then, the FIPS 140-2 test suit/generalized FIPS 140-2 test suit is used to test the randomness of the 1000-key streams consisting of 20[Formula: see text]000 bits generated by the [Formula: see text]-word CPRNG, the RC4 algorithm PRNG and the ZUC algorithm PRNG, respectively. The test results show that for the three PRNGs, there are 100%/98.9%, 99.9%/98.8%, 100%/97.9% key streams passing the tests, respectively. Furthermore, the SP800-22 test suite is used to test the randomness of four 100-key streams consisting of 1000[Formula: see text]000 bits generated by four PRNGs, respectively. The numerical results show that the randomness performances of the [Formula: see text]-word CPRNG is promising, showing that there are no significant correlations between the key streams and the perturbed key streams generated via the [Formula: see text]-word CPRNG. Finally, using the [Formula: see text]-word CPRNG and the SESKPAE to encrypt two gray-scale images, test results demonstrate that the [Formula: see text]-word CPRNG is able to generate both key avalanche effect and plaintext avalanche effect, which are similar to those generated via an ideal CPRNG, and performs better than other comparable schemes.

Focusing on the design of a good pseudorandom number generator, a novel four-dimensional discrete chaotic system was proposed. Using the theorem of discrete chaotic generalized synchronization, an eight-dimensional chaotic generalized synchronization system ( 8D-CGS) was constructed. Based on the 8D-CGS and by transforming the real number set to the integer set, a novel chaotic pseudorandom number generator ( CPRNG) was designed. The undisturbed key stream was compared with the key streams produced by different key disturbation and Matlab commands respectively. The two groups of average correlation and different rate are 0. 005 585 7 and 49. 988 5% , and 0. 005 877 3 and 49. 982 8%. It shows that the key streams produced by the CPRNG almost independent absolutely and the different rate very close to the ideal value 50%. FIPS 140-2 and G FIPS 140-2 test criterions were used to test the randomness of three 1 000 sequences of {0, 1} generated respectively by the CPRNG, the RC4 algorithm and the ZUC algorithm. The results show that three{0, 1} sequences all pass the FIPS 140-2 test criterion and there are 10, 19 and 22 sequences fail to pass the G FIPS 140-2 test criterion respectively, so the pass rate of the CPRNG is the highest. The means and variances of the tested results show that the CPRNG designed by this paper has promising randomness performance.

Using the judgment theorem of Li-York chaos,this paper generates a class of piecewise linear chaotic maps.Based on the chaotic maps,a constructing theorem of piecewise nonlinear robust chaotic map is proposed.As an application,this theorem is used to construct a piecewise nonlinear robust chaotic map with a polynomial function and a trigonometric function.This study com-putes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseu-do-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis,the generation algo-rithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography perfor-mance is tested and the tested results show that generated S-boxes have good cryptographic properties,and can not only better resist the linear and differential attacks,but also provide the foundation and conditions for the research and development of cryptography.

Streetlight control system has a well-designed function that ensures a good condition of urban lighting and effectively saves energy. It can do an important job for resident traveling. The entire streetlight control system is made up of system control module, clock module, display module, etc, and each module is an integrated design of hardware and software. The program is designed by embedded C language, loaded into SCT89C51 MCU and debugged by STC_ISP.Observation results show that streetlight control system can collect information of moving objects and the change of light and shade in the environment.Based on sentenced object and display module, it can automatically turn on or off the lights, change the light status, and send audio and visual alarm of streetlight breakdown using the information collected by photosensitive elements.

To design sound S-boxes,the generation algorithm based on the chaotic synchronization system is proposed.Based on the theorem of generalized synchronization for discrete chaos systems and 3-dimensional Lorenz chaos system,a new chaos synchronization system(GCS)is designed.In the new system,a novel S-box generation approach is put forward,and the cryptographic properties of the novel 8×8S-box are tested.The results show that S-box generated by the algorithm has sound cryptographic performance.The sensitivity property is dependent on initial condition,which makes dynamically designed S-boxes has sound properties.This approach is easy to implement,and the nonlinear resource is provided for block cipher.

基于修正版的 Marotto定理提出了一种新的2维离散混沌映射。通过一个实数域到整数域的变换将该映射产生的混沌流转换成二进制伪随机序列。在此基础上结合二维非等长 Arnold 变换设计了数字图像加密算法，该算法具有类似一次一密的功能。对该算法的密钥空间、密钥敏感性、统计特性和抗干扰能力进行仿真分析。研究结果表明：该加密算法可以达到较好的加解密效果，可以满足商业网络安全通讯的需求。

Edge detection is one of the most important steps in image processing and pattern recognition, it is also a critical technology of hand bone identification. Canny edge detection algorithm is simple, easy to implement and fast execution advantage, therefore, it still maintain a certain degree of competitiveness in the practical application. Firstly, the principles and the existing problems of Canny algorithm are studied in this paper, against threshold problem, improved method of an adaptive threshold is proposed, using Otsu method selected threshold, the split results would be better. Finally, the experimental results show that the proposed method can effectively extract the edge of the images.

This paper introduce a novel 3-dimensional discrete chaotic map. The calculated Lyapunov exponents of the map are 1.1638, 0.8946 and -0.2177. Numerical simulations show that the dynamic behaviors of the map have chaotic attractor characteristics. Based on the chaotic map and a chaos generalized synchronization (GS) theorem, a 6-dimensional chaotic GS system is constructed. Using the chaotic GS system and a transformation T form R to an integer set {0, 1} designs a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2 test suit tests the randomness of two 1000 key streams consisting of 20000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/97.7% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that for the perturbations of the keys of the CPRNG, the keystreams have an average 49.995% codes which are different from the codes generated by the unperturbed key. The results imply that CPRNG has sound pseudo randomness, the key space of the CPRNG is larger than 2747. As an application, an image encryption example via the CPRNG is given. Experimental results show that the correlation parameters between the plaintext and the ciphertext and the decrypted cipher texts via the 100 key streams with perturbed keys is less than 0.00414. The results suggest that the plaintext can be well hidden in the ciphertext, and brute attacks are needed to break the cryptographic system.

Ant colony optimization (ACO) is a swarm intelligence algorithm and it has been successfully applied to several NP-hard combinatorial problems such as traveling salesman, quadratic assignment problem (QAP), job-shop scheduling, vehicle routing and telecommunication networks. Howere, the ants' solutions are not guaranteed to be optimal with respect to local changes. In this paper, an improved ACO algorithm is proposed. Particle swarm optimization (PSO) has been applied to improve the performances of ACO. ACO is firstly used to find optimal solutions. Then PSO is used to optimize local optimal solutions searched by ACO. In order to check the performance of the proposed method, the proposed algorithm is utilized to solve QAP. The improved ACO algorithm and ACO algorithm are respectively implemented on some instances extracted from QAPLIB. The experimental results demonstrate that the improved ACO algorithm has better performance in terms of the quality of the returned solution than the original ones.

Based on a stream encryption scheme with avalanche effect, this paper introduces a block encryption scheme with avalanche effect (BESAE), gives the definition of ideal block pseudo random number generators (BPRNG). Using any key stream generated by an ideal 2d word BPRNG with different seed to decrypt the ciphertext encrypted via the ideal BPRNG and the BESAE will generate an avalanche-liked text whose number of “1” codes appear in a probability (2d-1)/2d. This paper proposes an 8-dimensional discrete chaotic generalized synchronization system. Based on this system, an 8-word long 210 word BPRNG is designed. The key space and the seed space of the BPRNG are larger than 21036. Using FIPS 140-2/gneralized FIPS 140-2 test suite tests 100 key streams generated from the 8-word long 210 word BPRNG with different keys (randomly perturbed system parameters and initial condition). The results showed that over 99%/96.9% 210 word streams passed the tests. Using the BPRNG and the BE-SAE encrypts an RGB Tower image. The results suggest that the BPRNG is able to generate the avalanche effects which are similar to those generated via ideal BPRNGs.

To improve pseudorandom number generators, on the basis of a modified version Marotto′theorem, a novel three-dimensional discrete-time chaotic system was introduced. A chaos-based pseudo-random number generator (CPNG) was designed by transforming a real set to an integer set. The auto-correlation, cross-correlation and linear complexity of the binary codes generated by CPNG were analyzed. The randomness of 1 000 binary number sequences generated via CPNG was verified respectively by SP800-22 standard tests. The results show that the CPNG is able to generate sound random sequences and be easily realized, thus, CPNG can be used in the information security field.

Based on the theorem of generalized synchronization for discrete chaos systems, a new discrete chaos synchronization system was designed. Using the new system and the properties of sensitive dependent on initial condition, a novel S-box generation approach was proposed. An affine transformation was used to shuffle S-box. Testing the cryptographic properties shows that the S-box generated in the proposed algorithm has sound cryptographic performance.

For nodes’ mobility in mobile P2P networks and the consistency of overlay network, an unstructured Modified Gnutella-like P2P protocol (M-GIA) is proposed in this paper. The advantage of GIA protocol is presented fully, while the physical location information of nodes and the distance between nodes as parameters are added into the GIA protocol. The distance between two nodes can decide logical relation between these two nodes in M-GIA protocol, in order to improve the consistency in the overlay network and the physical network, which can improve GIA’s performance in mobile network. Finally, through the simulation, the results show that M-GIA protocol is more efficient than the traditional Gnutella-like P2P protocols in terms of query success rate, query delay and path expansion rate varying with network scale and nodes’ moving speed.

In the design of cryptographic algorithms, S-boxes provide the cryptosystems with the information confusion function. The traditional cryptography indexes of the S-boxes generally include linear deviation, differential characteristics, algebraic immunity, fixed point mumber, snowslide effect, and so on. In 2006, Kocarev et al. (Kocarev L, Szczepanski J, Amigo J M and Tomovski I 2006 IEEE Transactions on Circuits and Systems-I: regular papers 53 6 1300) set up a discrete chaos theory based on the finite set. In light of the theory in this paper, we introduce the definition of the Lyapunov exponent with Hamming distance, calculate and compare the Lyapunov exponent values of the S-boxes in several cryptographic algorithms. In this paper we prove that a map defined on the Euclidean distance has a maximal Lyapunov exponent value of 0. In this paper it is shown that the relationship between the Lyapunov exponent and the snowslide effect of the S-box is the relationship between the butterfly effect in chaos theory and the snowslide effect in cryptography. The definition of the Lyapunov exponent of the proposed S-boxes may be complementary to the traditional cryptography indexes of the S-box.