“…Currently, DNA computing algorithms for different complex problems are being proposed, for example, Wu et al [ 48 ] and Tian et al [ 31 ] used DNA computing to solve the family traveling salesperson problem and job shop scheduling problem respectively, achieving great efficiency gains in terms of algorithmic computational complexity. In addition, DNA computing has been increasingly applied to different scenarios, such as image recognition [ 53 ], artificial neural network design [ 54 ] and quantum computing [ 55 ]. It is foreseen that pioneering research in the cross-fertilisation of DNA computing with disciplinary needs will drive significant developments in many aspects of science and technology.…”
Section: Discussionmentioning
confidence: 99%
“…Proof. Set l � (i, j) and the length of the different strands is: 41,8,5,53,58,24,35,11,48,38,1,39,28,33,20,37,26,55,43,10,56,22,18,23,54,44,3,50,27,42,6,34,19,14,25,51,36,59,49,45, 0] 60 [0, 34,3,26,23,58,53,5,18,1,9,16,8,…”
The quota traveling salesman problem (QTSP) is a variant of the traveling salesman problem (TSP), which is a classical optimization problem. In the QTSP, the salesman visits some of the
n
cities to meet a given sales quota
Q
while having minimized travel costs. In this paper, we develop a DNA algorithm based on Adleman-Lipton model to solve the quota traveling salesman problem. Its time complexity is
O
n
2
+
Q
, which is a significant improvement over previous algorithms with exponential complexity. A coding scheme of element information is pointed out, and a reasonable biological algorithm is raised by using limited conditions, whose feasibility is verified by simulation experiments. The innovation of this study is to propose a polynomial time complexity algorithm to solve the QTSP. This advantage will become more obvious as the problem scale increases compared with the algorithm of exponential computational complexity. The proposed DNA algorithm also has the significant advantages of having a large storage capacity and consuming less energy during the operation. With the maturity of DNA manipulation technology, DNA computing, as one of the parallel biological computing methods, has the potential to solve more complex NP-hard problems.
“…Currently, DNA computing algorithms for different complex problems are being proposed, for example, Wu et al [ 48 ] and Tian et al [ 31 ] used DNA computing to solve the family traveling salesperson problem and job shop scheduling problem respectively, achieving great efficiency gains in terms of algorithmic computational complexity. In addition, DNA computing has been increasingly applied to different scenarios, such as image recognition [ 53 ], artificial neural network design [ 54 ] and quantum computing [ 55 ]. It is foreseen that pioneering research in the cross-fertilisation of DNA computing with disciplinary needs will drive significant developments in many aspects of science and technology.…”
Section: Discussionmentioning
confidence: 99%
“…Proof. Set l � (i, j) and the length of the different strands is: 41,8,5,53,58,24,35,11,48,38,1,39,28,33,20,37,26,55,43,10,56,22,18,23,54,44,3,50,27,42,6,34,19,14,25,51,36,59,49,45, 0] 60 [0, 34,3,26,23,58,53,5,18,1,9,16,8,…”
The quota traveling salesman problem (QTSP) is a variant of the traveling salesman problem (TSP), which is a classical optimization problem. In the QTSP, the salesman visits some of the
n
cities to meet a given sales quota
Q
while having minimized travel costs. In this paper, we develop a DNA algorithm based on Adleman-Lipton model to solve the quota traveling salesman problem. Its time complexity is
O
n
2
+
Q
, which is a significant improvement over previous algorithms with exponential complexity. A coding scheme of element information is pointed out, and a reasonable biological algorithm is raised by using limited conditions, whose feasibility is verified by simulation experiments. The innovation of this study is to propose a polynomial time complexity algorithm to solve the QTSP. This advantage will become more obvious as the problem scale increases compared with the algorithm of exponential computational complexity. The proposed DNA algorithm also has the significant advantages of having a large storage capacity and consuming less energy during the operation. With the maturity of DNA manipulation technology, DNA computing, as one of the parallel biological computing methods, has the potential to solve more complex NP-hard problems.
“…DNA Algebraic Operations. Since the development of DNA computing, researchers have proposed using the algebraic operation of DNA sequence to replace the traditional computational algebraic operation [12,32,33]. In this article, different operations for DNA sequences have been used like addition, subtraction, multiplication, Xor, Xnor, and right circular shift, which moves the final entry to the first position and left circular shift, which moves the initial entry to the final position, as shown in Fig.…”
Modern cryptography is a key element of data security, ensuring the confidentiality and integrity of information. In an increasingly digital world, cryptography remains crucial for the protection of sensitive data. In this context, we propose a novel hybrid security system for encrypted color images using a DNA model, chaotic systems, and SHA256-MD5 hash functions as a basis. The proposed hybrid system includes DNA permutation and diffusion. In DNA permutation, we unpredictably rearrange the location of DNA image elements by using the logistic map of low computational complexity. In DNA diffusion, we diffuse the permuted image of DNA with the DNA image key generated by a 5D hyper-chaotic system, using a variety of algebraic operators such as the circular offset in both directions. Considering the experimental outcomes and security evaluation, we can infer that the proposed hybrid security system demonstrates a high level of security, resistance to existing attacks, and practical application suitability while maintaining speed.
“…There are other algorithms that can help improve the proposed encryption system [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. For example, RGB DNA image encryption technology was designed in [46].…”
In this paper, a novel image encryption algorithm based on a new permutation scheme and DNA operations are introduced. In our algorithm, SHA 256 and DNA hamming distance participate in the generation of the initial conditions of the 4D chaotic system, which can associate the encryption system with the original image. In the permutation process, based on the adjustment process of the IAVL (improved balanced binary tree), a new scrambling algorithm is constructed. Then the dynamic block coding rules are designed, in which different image blocks have different coding rules. In the diffusion process, a new diffusion algorithm with intra-block and inter-block is proposed to perform DNA operations on the intermediate encryption result and the key matrix. In the security analysis, the key space of the encryption system is 2 933 and the information entropy is about 7.9973. In addition, the NPCR and UACI in the differential attack test are close to the ideal values of 99.6094% and 33.4653%. To further prove the security of the encryption algorithm, the Irregular deviation, Maximum deviation, Energy, Contrast, and Homogeneity tests are introduced into the analysis. Experimental results illustrate that the encryption scheme can against multiple illegal attacks like statistical, brute-force and differential attacks.
INDEX TERMSImage encryption; 4D chaotic system; DNA operations
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