Fast parallel molecular algorithms for DNA-based computation: factoring integers

Quantum Image Encryption Based on Quantum DNA Codec and Pixel-Level Scrambling

In order to increase the security and robustness of quantum images, this study combined the quantum DNA codec with quantum Hilbert scrambling to offer an enhanced quantum image encryption technique. Initially, to accomplish pixel-level diffusion and create enough key space for the picture, a quantum DNA codec was created to encode and decode the pixel color information of the quantum image using its special biological properties. Second, we used quantum Hilbert scrambling to muddle the image position data in order to double the encryption effect. In order to enhance the encryption effect, the altered picture was then employed as a key matrix in a quantum XOR operation with the original image. The inverse transformation of the encryption procedure may be used to decrypt the picture since all the quantum operations employed in this research are reversible. The two-dimensional optical image encryption technique presented in this study may significantly strengthen the anti-attack of quantum picture, according to experimental simulation and result analysis. The correlation chart demonstrates that the average information entropy of the RGB three channels is more than 7.999, the average NPCR and UACI are respectively 99.61% and 33.42%, and the peak value of the ciphertext picture histogram is uniform. It offers more security and robustness than earlier algorithms and can withstand statistical analysis and differential assaults.

Comparison of Monkeypox and Wart DNA Sequences with Deep Learning Model

After the COVID-19 disease, monkeypox disease has emerged today and has started to be seen almost everywhere in the world in a short time. Monkeypox causes symptoms such as fever, chills, and headache in people. In addition, rashes are seen on the skin and lumps are formed. Early diagnosis and treatment of monkeypox, which is a contagious disease, are of great importance. An expert interpretation and clinical examination are usually needed to detect monkeypox. This may cause the treatment process to be slow. Furthermore, monkeypox is sometimes confused with warts. This leads to incorrect diagnosis and treatment. Because of these disadvantages, in this study, the DNA sequences of HPV causing warts and MPV causing monkeypox were analyzed and the classification of these sequences was performed with a deep learning algorithm. The study consisted of four stages. In the first stage, DNA sequences of viruses that cause warts and monkeypox were obtained. In the second stage, these sequences were mapped using various DNA-mapping methods. In the third stage, the mapped sequences were classified using a deep learning algorithm. At the last stage, the performances of DNA-mapping methods were compared by calculating accuracy and F1-score. At the end of the study, an average accuracy of 96.08% and an F1-score of 99.83% were obtained. These results showed that these two diseases can be effectively classified according to their DNA sequences.

Quantum Speedup and Mathematical Solutions of Implementing Bio-Molecular Solutions for the Independent Set Problem on IBM Quantum Computers

In this paper, we propose a bio-molecular algorithm with O( n² + m ) biological operations, O( 2ⁿ ) DNA strands, O( n ) tubes and the longest DNA strand, O( n ), for solving the independent-set problem for any graph G with m edges and n vertices. Next, we show that a new kind of the straightforward Boolean circuit yielded from the bio-molecular solutions with m NAND gates, ( m +n × ( n + 1 )) AND gates and (( n × ( n + 1 ))/2) NOT gates can find the maximal independent-set(s) to the independent-set problem for any graph G with m edges and n vertices. We show that a new kind of the proposed quantum-molecular algorithm can find the maximal independent set(s) with the lower bound Ω ( 2^n/2 ) queries and the upper bound O( 2^n/2 ) queries. This work offers an obvious evidence for that to solve the independent-set problem in any graph G with m edges and n vertices, bio-molecular computers are able to generate a new kind of the straightforward Boolean circuit such that by means of implementing it quantum computers can give a quadratic speed-up. This work also offers one obvious evidence that quantum computers can significantly accelerate the speed and enhance the scalability of bio-molecular computers. Next, the element distinctness problem with input of n bits is to determine whether the given 2ⁿ real numbers are distinct or not. The quantum lower bound of solving the element distinctness problem is Ω ( 2^n×(2/3) ) queries in the case of a quantum walk algorithm. We further show that the proposed quantum-molecular algorithm reduces the quantum lower bound to Ω (( 2^n/2 )/( [Formula: see text]) queries. Furthermore, to justify the feasibility of the proposed quantum-molecular algorithm, we successfully solve a typical independent set problem for a graph G with two vertices and one edge by carrying out experiments on the backend ibmqx4 with five quantum bits and the backend simulator with 32 quantum bits on IBM's quantum computer.

Complex dynamical behaviors of a novel exponential hyper-chaotic system and its application in fast synchronization and color image encryption

This paper proposes a novel exponential hyper-chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan-Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper-chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high-order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper-chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper-chaotic system to increase the security of image encryption.

A new DNA-based model for finite field arithmetic

A Galois fieldG F ( p n ) withp ≥ 2 a prime number and n ≥ 1 is a mathematical structure widely used in Cryptography and Error Correcting Codes Theory. In this paper, we propose a novel DNA-based model for arithmetic overG F ( p n ) . Our model has three main advantages over other previously described models. First, it has a flexible implementation in the laboratory that allows the realization arithmetic calculations in parallel forp ≥ 2 , while the tile assembly and the sticker models are limited to p = 2 . Second, the proposed model is less prone to error, because it is grounded on conventional Polymerase Chain Reaction (PCR) amplification and gel electrophoresis techniques. Hence, the problems associated to models such as tile-assembly and stickers, that arise when using more complex molecular techniques, such as hybridization and denaturation, are avoided. Third, it is simple to implement and requires 50 ng/μL per DNA double fragment used to develop the calculations, since the only feature of interest is the size of the DNA double strand fragments. The efficiency of our model has execution times of orderO ( 1 ) andO ( n ) , for the addition and multiplication overG F ( p n ) , respectively. Furthermore, this paper provides one of the few experimental evidences of arithmetic calculations for molecular computing and validates the technical applicability of the proposed model to perform arithmetic operations over G F ( p n ) .

Correcting Errors in Image Encryption Based on DNA Coding

As a primary method, image encryption is widely used to protect the security of image information. In recent years, image encryption pays attention to the combination with DNA computing. In this work, we propose a novel method to correct errors in image encryption, which results from the uncertainty of DNA computing. DNA coding is the key step for DNA computing that could decrease the similarity of DNA sequences in DNA computing as well as correct errors from the process of image encryption and decryption. The experimental results show our method could be used to correct errors in image encryption based on DNA coding.

Chaotic Image Encryption Algorithm Based on Bit Permutation and Dynamic DNA Encoding

With the help of the fact that chaos is sensitive to initial conditions and pseudorandomness, combined with the spatial configurations in the DNA molecule's inherent and unique information processing ability, a novel image encryption algorithm based on bit permutation and dynamic DNA encoding is proposed here. The algorithm first uses Keccak to calculate the hash value for a given DNA sequence as the initial value of a chaotic map; second, it uses a chaotic sequence to scramble the image pixel locations, and the butterfly network is used to implement the bit permutation. Then, the image is coded into a DNA matrix dynamic, and an algebraic operation is performed with the DNA sequence to realize the substitution of the pixels, which further improves the security of the encryption. Finally, the confusion and diffusion properties of the algorithm are further enhanced by the operation of the DNA sequence and the ciphertext feedback. The results of the experiment and security analysis show that the algorithm not only has a large key space and strong sensitivity to the key but can also effectively resist attack operations such as statistical analysis and exhaustive analysis.

Image Encryption Algorithm Based on Hyperchaotic Maps and Nucleotide Sequences Database

Image encryption technology is one of the main means to ensure the safety of image information. Using the characteristics of chaos, such as randomness, regularity, ergodicity, and initial value sensitiveness, combined with the unique space conformation of DNA molecules and their unique information storage and processing ability, an efficient method for image encryption based on the chaos theory and a DNA sequence database is proposed. In this paper, digital image encryption employs a process of transforming the image pixel gray value by using chaotic sequence scrambling image pixel location and establishing superchaotic mapping, which maps quaternary sequences and DNA sequences, and by combining with the logic of the transformation between DNA sequences. The bases are replaced under the displaced rules by using DNA coding in a certain number of iterations that are based on the enhanced quaternary hyperchaotic sequence; the sequence is generated by Chen chaos. The cipher feedback mode and chaos iteration are employed in the encryption process to enhance the confusion and diffusion properties of the algorithm. Theoretical analysis and experimental results show that the proposed scheme not only demonstrates excellent encryption but also effectively resists chosen-plaintext attack, statistical attack, and differential attack.

Reversible Data Hiding Based on DNA Computing

Biocomputing, especially DNA, computing has got great development. It is widely used in information security. In this paper, a novel algorithm of reversible data hiding based on DNA computing is proposed. Inspired by the algorithm of histogram modification, which is a classical algorithm for reversible data hiding, we combine it with DNA computing to realize this algorithm based on biological technology. Compared with previous results, our experimental results have significantly improved the ER (Embedding Rate). Furthermore, some PSNR (peak signal-to-noise ratios) of test images are also improved. Experimental results show that it is suitable for protecting the copyright of cover image in DNA-based information security.

A general resolution of intractable problems in polynomial time through DNA Computing

Based on a set of known biological operations, a general resolution of intractable problems in polynomial time through DNA Computing is presented. This scheme has been applied to solve two NP-Hard problems (Minimization of Open Stacks Problem and Matrix Bandwidth Minimization Problem) and three co-NP-Complete problems (associated with Hamiltonian Path, Traveling Salesman and Hamiltonian Circuit), which have not been solved with this model. Conclusions and open questions concerning the computational capacity of this model are presented, and research topics are suggested.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation.

Molecular Sticker Model Stimulation on Silicon for a Maximum Clique Problem

Molecular computers (also called DNA computers), as an alternative to traditional electronic computers, are smaller in size but more energy efficient, and have massive parallel processing capacity. However, DNA computers may not outperform electronic computers owing to their higher error rates and some limitations of the biological laboratory. The stickers model, as a typical DNA-based computer, is computationally complete and universal, and can be viewed as a bit-vertically operating machine. This makes it attractive for silicon implementation. Inspired by the information processing method on the stickers computer, we propose a novel parallel computing model called DEM (DNA Electronic Computing Model) on System-on-a-Programmable-Chip (SOPC) architecture. Except for the significant difference in the computing medium—transistor chips rather than bio-molecules—the DEM works similarly to DNA computers in immense parallel information processing. Additionally, a plasma display panel (PDP) is used to show the change of solutions, and helps us directly see the distribution of assignments. The feasibility of the DEM is tested by applying it to compute a maximum clique problem (MCP) with eight vertices. Owing to the limited computing sources on SOPC architecture, the DEM could solve moderate-size problems in polynomial time.

Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers

Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

Quantum algorithms for biomolecular solutions of the satisfiability problem on a quantum machine

In this paper, we demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented more efficiently by our proposed quantum algorithm on the quantum machine proposed by Deutsch. To test our theory, we carry out a three-quantum bit nuclear magnetic resonance experiment for solving the simplest satisfiability problem.

Fast parallel molecular algorithms for DNA-based computation: solving the elliptic curve discrete logarithm problem over GF2

Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP), especially over GF(2ⁿ), n ∈ Z⁺. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2ⁿ) are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.