• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6C
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• pp.361-367
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• 2011

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.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.5
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• pp.873-880
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• 2020

The proposed encryption algorithm strengthens its security by converting pixel-specific values and changing pixel positions. The state transition matrix created by Wolfram's rule creates a complemented CA sequence with the maximum length. Then, we convert the sequence into a 2D basis image and go through a XOR operation with the original image. The final encrypted image is created by shear stressing and rearranging. The image stability analysis verified that the proposed encryption method has high security.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.10
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• pp.2171-2179
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• 2009

In this paper, we propose a novel Image Encryption using MLCA (Maximum Length Cellular Automata) and CAT (Cellular Automata Transform). Firstly, we use the Wolfram rule matrix to generate MLCA state transition matrix T. Then the state transition matrix T changes pixel value of original image according to pixel position. Next, we obtain Gateway Values to generate 2D CAT basis function. Lastly, the basis function encrypts the MLCA encrypted image into cellular automata space. The experimental results and security analysis show that the proposed method guarantees better security and non-lossy encryption.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.2
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• pp.439-446
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• 2019

In this paper, we propose a encryption method using C-MLCA and 1D CAT to secure medical image for efficiently. First, we generate a state transition matrix using a Wolfram rule and create a sequence of maximum length. By operating the complemented vector, it converts an existing sequence to a more complex sequence. Then, we multiply the two sequences by rows and columns to generate C-MLCA basis images of the original image size and go through a XOR operation. Finally, we will get the encrypted image to operate the 1D CAT basis function created by setting the gateway values and the image which is calculated by transform coefficients. By comparing the encrypted image with the original image, we evaluate to analyze the histogram and PSNR. Also, by analyzing NPCR and key space, we confirmed that the proposed encryption method has a high level of stability and security.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.545-567
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• 2023

This study investigates effective ChatGPT prompts for solving mathematical problems, focusing on the chapters of quadratic equations and quadratic functions. A structured prompt was designed, following a sequence of 'Role-Rule-Example Solution-Problem-Process'. In this study, an artificial intelligence model combining GPT-4, Wolfram plugin, and Advanced Data Analysis was utilized. Wolfram was used as the primary tool for calculations to reduce computational errors. When using the structured prompt, the accuracy rate for problems from nine high school mathematics textbooks on quadratic equations and quadratic functions was 91%, showing higher performance compared to zero-shot prompts. This confirmed the effectiveness of the structured prompts in solving mathematical problems. The structured prompts designed in this study can contribute to the development of intelligent information systems for personalized and customized education.

• Proceedings of the Korea Multimedia Society Conference
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• 2012.05a
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• pp.336-339
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• 2012

본 논문에서는 비선형 MLCA(Maximum Length Cellular Automata)와 1D CAT(One-Dimensional Cellular Automata Transform)를 이용하여 의료 영상 암호화 방법을 제안한다. 암호화 방법은 먼저, Wolfram Rule 행렬에 의해 전이행렬 T를 생성한다. 그 후, 암호화하려는 원 영상에 생성된 전이 행렬 T를 곱하여 원 영상의 픽셀 값을 변환한다. 또한 변환된 원 영상을 여원 벡터 F와 XOR 연산하여 비선형 MLCA가 적용된 영상으로 변환한다. 다음, 게이트웨이 값을 설정하여 1D CAT 기저함수를 생성한다. 그리고, 비선형 MLCA가 적용된 영상에 생성된 1D CAT 기저함수를 곱하여 암호화를 한다. 마지막으로 키 공간 분석을 통하여 제안한 방법이 높은 암호화 수준의 성질을 가졌음을 검증한다.