Maximum Length Cellular Automata Research Articles

Light-field 3D image parallel encryption based on the state transition diagram of Maximum Length Cellular Automata

In our work, we proposed a parallel encryption scheme based on the state transition diagram of Maximum Length Cellular Automata (MLCA) to protect 3D images. Compared with the previous random mode decomposition (RMD) encryption scheme and DNA sequences and chaotic systems scheme, our scheme effectively reduces the time consumption, especially for the RME scheme, by up to 5 times. Meanwhile, leveraging MLCA’s abundant rules, high parallelism, and straightforward hardware implementation, our encryption scheme exhibits flexible key selection, parallel processing capabilities, and easy hardware implementation. The results of key space analysis, differential attack analysis, and statistical analysis verify the high-security level achieved by our proposed parallel encryption scheme.

3D image steganography using cellular automata transform and depth estimation network

Traditional 3D image steganography is cumbersome and difficult owing to the special structure of 3D image, imposing a practical limit for its applications. Herein, we propose a 3D image steganography scheme utilizing cellular automata transformation (CAT). By using CAT with various rule numbers to hide images, the weakness of previous algorithms with only one transformation plane is overcome, and the hidden image quality can be improved by reducing energy loss. In the 3D reconstruction process, we apply a depth estimation algorithm based on a convolutional network to obtain corresponding depth maps from a single RGB image, simplifying the elemental image array (EIA) pickup process and even overcoming the phase difference problem caused by the traditional optical pickup process using lens arrays. Before hiding, we use the maximum length cellular automata (MLCA) to encrypt a single RGB image instead of encrypting EIA images with huge data, which greatly reduces the complexity of the encryption algorithm and improves efficiency. Finally, we reconstruct the decrypted image optically and obtain a full color and full parallax 3D image through the display device.

Encryption and display of multiple-image information using computer-generated holography with modified GS iterative algorithm

In this paper, a new scheme of multiple-image encryption and display based on computer-generated holography (CGH) and maximum length cellular automata (MLCA) is presented. With the scheme, the computer-generated hologram, which has the information of the three primitive images, is generated by modified Gerchberg–Saxton (GS) iterative algorithm using three different fractional orders in fractional Fourier domain firstly. Then the hologram is encrypted using MLCA mask. The ciphertext can be decrypted combined with the fractional orders and the rules of MLCA. Numerical simulations and experimental display results have been carried out to verify the validity and feasibility of the proposed scheme.

Double color image encryption scheme based on off-axis holography and maximum length cellular automata

A double color image encryption scheme based on off-axis holography and maximum length cellular automata (MLCA) is proposed. The original image is separated into three channels: red, green, and blue, and each channel is independently encrypted by using MLCA mask to make the intensity values change in the spatial domain. Then the reference waves with different incident angles are introduced into the off-axis Fourier transform hologram to accomplish double color image encryption. The system parameters of the off-axis Fourier transform in each channel are also keys in image encryption and decryption. When we want to decrypt one of the original images, the reference wave with certain incident angle and corresponding MLCA mask are used. Some numerical simulations have demonstrated to show the effectiveness of the proposed scheme, and we present the results of our preliminary experiments.

Nonlinear Cryptosystem Based on QC-LDPC Codes for Enhanced Security and Reliability with Low Hardware Complexity and Reduced Key Size

The main issues to be addressed in resource limited devices are security, reliability and hardware complexity. Cryptosystems that combine encryption and error correction in a single step can offer a good solution to meet these issues. In this work, a nonlinear cryptosystem based on structured Low-Density Parity-Check code that offers small key size, low hardware complexity and high security against differential type of attack is proposed. The method adopted to introduce nonlinearity in a cryptosystem plays a key role in deciding the hardware complexity and security of the overall system. The work adopts a method for generating nonlinear function using maximum length Cellular Automata, so that enhanced security can be attained without going for a complex hardware structure. Also a light weight stream cipher is adopted for generating random error vectors for encryption and addition of intentional noise in such a way that the security is increased by a large margin at a low hardware cost. Different permutation matrices are generated for different message blocks for achieving good degrees of freedom with reasonable key size. Analysis shows that the proposed system provides high security with smaller key size and lower hardware complexity when compared with a nonlinear cryptosystem called Error Correction Based Cipher.

비디오 암호화를 위한 여원 최대길이 셀룰라 오토마타

비디오 암호화를 위한 여원 최대길이 셀룰라 오토마타

Video Image Encryption Technique Using Maximum-Length Cellular Automata and Arnold’s Cat Map

In this paper, we propose a video image encryption approach by using maximum length cellular automata (MLCA) methods. First, the plane images of video of the encryption method are obtained by dividing frame units. Then the XOR operation and Arnold transform are applied to each of RGB plane images. Lastly, the encryption image is encrypted by the basis image of MLCA. To demonstrate the usefulness of the proposed method, we carry out preliminary experiments and present the experimental results. The experimental results show that the proposed method provides high security.

Novel 3-D Image Encryption Using Computational Integral Imaging and Linear-Complemented MLCA

Three dimensional (3-D) images encryption schemes can provide feasible and secure for images encryption due to the 3-D properties of images. In this paper, we present a novel 3-D images encryption algorithm by combining use of integral imaging (II) and maximum-length cellular automata (MLCA) as the secret key ciphering for 3D image encryption technique. In this proposed algorithm, a lenslet array first decomposes the 3-D object into 2-D elemental images (EIs) via the pick-up process of II. We encrypt the 2-D EIs with an encryption method based on linear and complemented MLCA. Decryption process is the opposite of operation encryption process: The 2-D EIs is recovered by the MLCA key, 3-D object is reconstructed by the recovered EIs via computational integral imaging (CII) reconstruction. To verify the usefulness of the proposed algorithm, we carry out the computational experiments and present the experimental results for various attacks. Experimental results show that the proposed algorithm can improve the performance of encryption against various attacks due to large key space in MLCA and 3-D characteristic of data redundancy.

3D Image Encryption Using Integral Imaging Scheme and MLCA Technology

A new 3D image encryption method using integral imaging technology and maximum length cellular automata (MLCA) is proposed in this paper. First, an elemental image (EI) is generated by the integral imaging pickup process. The Wolfram rule is then selected and the state transition matrix, T, is created by MLCA. A random number matrix (RNM) is generated according to the MLCA rule. The generated EI and RNM are compared and pixel values are transitioned. Finally, a basis image is generated by another MLCA rule. The basis image is applied by performing a logic bit exclusive-OR (XOR) operation on the final encrypted image. This method changes the basic image information. Using pixel values to visualize image data gives better encryption results than the previous method. The robustness of the encryption method for lost data, including added noise or cropping attacks, was analyzed and the results of encryption method safety test experiments are presented using histograms.

Computational integral imaging-based 3D digital watermarking scheme using cellular automata transform and maximum length cellular automata

A novel 3D watermarking algorithm by combining use of computational integral imaging (CII) and cellular automata transform (CAT) is proposed in this paper. In this proposed scheme, first, the original image signal is decomposed into three resolution levels by using the level-3 2D CAT, and meanwhile, the middle-frequency domains are obtained. Then, an elemental images (EIs) array is generated by recording the information of rays of light coming from an object through a pinhole array in the CII system. The EIs array is encrypted by linear maximum-length cellular automata as the encrypted watermark embedded into the CAT middle-frequency domains. Finally, the watermarked image is obtained by using the level-3 2D inverse CAT. To verify the usefulness of the proposed algorithm, we carry out the computational experiments and present the experimental results for various attacks. Experimental results show that this proposed watermarking system provides excellent results in unobtrusiveness and robustness.

Cost Optimized Design Technique for Pseudo-Random Numbers in Cellular Automata

In this research work, we have put an emphasis on the cost effective design approach for high quality pseudo-random numbers using one dimensional Cellular Automata (CA) over Maximum LengthCA. This work focuses on different complexities e.g ., space complexity, time complexity, design complexity and searching complexity for the generation of pseudo -random numbers in CA. The optimization procedure for these associated complexities is commonly referred as the cost effective generation approach for pseudorandom numbers. The mathematical approach for proposed methodology over the existing maximum length CA emphasizes on better flexibility to fault coverage. The randomness quality of the generated patterns for the proposed methodology has been ve rified using Diehard Tests which reflects that the randomness quality achieved for proposed methodology is equal to the quality of randomness of the patterns generated by the maximum length cellular automata. The cost effectiveness results a cheap hardware implementation for the concerned pseudo-random pattern generator. Short version of this paper has been published in [1].

NBCA 에 기초한 여원 MLCA와 2D CAT를 이용한 새로운 영상 암호화

본 논문에서는 효율적인 영상 암호화를 위해 NBCA(Null Boundary CA)에 기초한 여원 MLCA(Maximum Length Cellular Automata)와 2D CAT(Two-Dimensional Cellular Automata Transform)를 이용한 암호화 방법을 제안한다. 암호화 방법은 먼저, Wolfram Rule 행렬에 의해 전이행렬 T를 생성한다. 그 후, 암호화하려는 원영상에 생성된 전이 행렬 T를 곱하여 원 영상의 픽셀 값을 변환한다. 또한 변환된 원 영상을 여원 벡터 F와 XOR 연산하여 여원 MLCA가 적용된 영상으로 변환한다. 다음, 게이트웨이 값을 설정하여 2D CAT 기저함수를 생성한다. 그리고, 여원 MLCA가 적용된 영상에 생성된 기저함수를 곱하여 2D CAT 암호화를 한다. 마지막으로 안정성 분석을 통하여 제안한 방법이 높은 암호화 수준의 성질을 가졌음을 검증한다. In this paper, we propose encryption method to using complemented MLCA(Maximum Length Cellular Automata) based on NBCA(Null Boundary CA) and 2D CAT (Two-Dimensional Cellular Automata Transform) for efficient image encryption. The encryption method is processed in the following order. First, a transition matrix T is created using the Wolfram Rule matrix. Then, the transition matrix T is multiplied to the original image that is intended to be encrypted, which transfers the pixel values of the original image. Furthermore, the converted original image goes through a XOR operation with complemented vector F to convert into a complemented MLCA applied image. Then, the gateway value is set and 2D CAT basis function is created. Also, the 2D CAT is encrypted by multiplying the created basis function to the complemented MLCA applied image. Lastly, the stability analysis verifies that proposed method holds a high encryption quality status.

Watermarking Based on Complemented MLCA and 2D CAT

Digital watermarking has gained importance in recent years in copyright protection and multimedia. This paper proposes a secure and novel watermarking system based on complemented Maximum Length Cellular Automata (MLCA) and Two-Dimension Cellular Automata Transform (2D CAT). In this watermarking scheme, the original watermark is first encrypted by complemented MLCA with the private keys, and then the encrypted watermark is embedded into the CAT domain of the cover image, at last use the inverse CAT for the transformed image, the watermarked image is obtained. Experiment results show that this new method is more secure and provides robust performance against watermarking attacks.

셀룰라 오토마타 기반의 수축-삽입 수열의 분석

The shrinking generator which is one of clock-controlled generator is a very simple generator with good cryptographic properties. A nonlinear sequence generator based on two 90/150 maximum length cellular automata can generate pseudorandom sequences at each cell of cellular automata whose characteristic polynomials are same. The nonlinear sequence generated by cellular automata has a larger period and a higher linear complexity than shrunken sequence generated by LFSRs. In this paper we analyze shrunken-interleaved sequence based on 90/150 maximum length cellular automata. We show that the sequence generated by nonlinear sequence generator based on cellular automata belongs to the class of interleaved sequence. And we give an effective algorithm for reconstructing unknown bits of output sequence based on intercepted keystream bits.

두 개의 최대 주기를 갖는 셀룰라 오토마타 수열을 이용한 영상 암호화

본 논문에서는 두 개의 선형 MLCA(Maximum Length Cellular Automata)을 이용한 영상 암호화 방법을 제안한다. 암호화 방법은 먼저 8 비트 초기 값을 임의로 설정한다. 그 다음, 설정된 초기 값을 이용하여 행과 열을 단계적으로 변화시켜 고품질의 PN(pseudo noise) 수열을 생성한다. 생성된 수열을 이용하여 기저영상을 생성한다. 마지막으로 기저영상을 원 영상과 XOR 연산함으로서 암호화 수준이 높은 결과 영상을 얻는다. 히스토그램 및 안정성 분석을 통하여 제안한 방법이 높은 암호화 수준의 성질을 가졌음을 검증한다. In this paper, we propose an image encryption method using two linear MLCA(Maximum Length Cellular Automata). The encryption method first sets arbitrary 8 bit initial values. Next, we create high quality PN(pseudo noise) sequences by converting rows and columns with the set initial values. hen we generate a basis image using the set PN sequences. Lastly, the final image with high encryption level is produced by XOR operation of the basis image and the original image. In order to verify that the proposed method has the high encryption level, we performed histogram and stability analysis.

LAYERED CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set {Af | f = 1, 2, …, 2n -1} formed by the transformation matrix A of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L = 1, 2, 3, 4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions f30 and f45 in place of the linear function f204 used in the L-LCA. Linear complexity is significantly increased when f30 or f45 is used.

Permutation and sampling with maximum length CA or pseudorandom number generation

In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested – weighted permutation vector sampling with controlled multiplexing, weighted permutation vector sampling with irregular decimation and permutation programmed CA sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA.