A new DNA-based model for finite field arithmetic

Abstract

A B S T R A C TA Galois field GFðp n Þ with p ! 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 over GFðp n Þ. 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 for p ! 2, while the tile assembly and the sticker models are limited to p ¼ 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 order Oð1Þ and OðnÞ, for the addition and multiplication over GFðp n Þ, 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 GFðp n Þ.

A New COVID-19 Detection Method Based on CSK/QAM Visible Light Communication and Machine Learning

“…A few studies have employed Galois fields to numerically represent DNA [29,31]. Representation through Galois Fields GF(p) is based on gel electrophoresis, a standard method for separating double-stranded DNA (dsDNA) fragments of different sizes previously obtained by the Polymerisation Chain Reaction.…”

“…It is defined as the maximum width of the region parallel to the hyperplane that has no interior data points. Equation (29) shows how a linear SVM predicts the class of a new x instance by calculating the decision function w T x + b = w 1 x 1 + +w n x n + b: if the result is positive, the predicted class f (x) is the positive class (1); otherwise, it is the negative class (0) [75]. b is the bias and w is the feature weight.…”

“…In relation to this paper, our team has published original models of underground channels [24][25][26][27][28]. Additionally, before the pandemic, we produced papers on DNA [29][30][31] and work on MIMO [32][33][34]. Pathogens will always be around humans, so it is crucial to conduct channel studies that allow us to transfer information under any circumstance in a secure and fast manner.…”

A DNA Cryptographic Solution for Secured Image and Text Encryption

“…The following content shows the operations that are taken place during the decryption of encrypted text. <reshape>4<reshape><crossover><type>both<type><rotate><rot ation_offset>2<rotation_offset><rotation_types>right|left|right|ri ght|right|<rotation_types><rotate><single_point>2|3|<single_poi nt><crossover><mutation><mutation_table>{'A':'C','C':'A','T':'G', 'G':'T'}<mutation_table><chromosome><complement_mutation> (0,5)<complement_mutation><alter_mutation>(1,3)<alter_mutati on><chromosome><chromosome><complement_mutation> (5,6) <complement_mutation><alter_mutation> (3,3)<alter_mutation> <chromosome><chromosome><complement_mutation>(2,5)<co mplement_mutation><alter_mutation>(3,3)<alter_mutation><chr omosome><chromosome><complement_mutation> (3,6)<comple ment_mutation><alter_mutation>(0,1)<alter_mutation><chromos ome><chromosome><complement_mutation> (1,4)<complement _mutation><alter_mutation>(2,3)<alter_mutation><chromosome ><mutation><round><round><reshape>2<reshape><crossover> <type>rotate_crossover<type><rotate><rotation_offset>2<rotatio n_offset><rotation_types>right|left|right|right|left|left|right|left|rig ht|left|<rotation_types><rotate><crossover><mutation><mutatio n_table>{'A':'T','T':'A','C':'G','G':'C'}<mutation_table><chromoso me><complement_mutation>(0,3)<complement_mutation><alter _mutation>(0,0)<alter_mutation><chromosome><chromosome> <complement_mutation> (3,3)<complement_mutation><alter_mu tation>(1,1)<alter_mutation><chromosome><chromosome><co mplement_mutation>(1,1)<complement_mutation><alter_mutati on>(0,0)<alter_mutation><chromosome><chromosome><compl ement_mutation>(2,3)<complement_mutation><alter_mutation>( 0,1)<alter_mutation><chromosome><chromosome><complemen t_mutation>(2,)<complement_mutation><alter_mutation>(0,1)<a lter_mutation><chromosome><chromosome><complement_mut ation> (3,3)<complement_mutation><alter_mutation>(1,1)<alter_ mutation><chromosome><chromosome><complement_mutation >(0,0)<complement_mutation><alter_mutation>(1,1)<alter_muta tion><chromosome><chromosome><complement_mutation>(0,0 )<complement_mutation><alter_mutation>(1,1)<alter_mutation> <chromosome><chromosome><complement_mutation>(1,2)<co mplement_mutation><alter_mutation>(0,0)<alter_mutation><chr omosome><chromosome><complement_mutation>(1,3)<comple ment_mutation><alter_mutation>(0,0)<alter_mutation><chromos ome><mutation><round><round><reshape>4<reshape><crossov er><type>single_point_crossover<type&...…”

“…To bring dynamicity, better storage, and time complexity, high parallelism, and low power consumption Adleman introduced DNA computing in 1994, which makes DNA cryptography the right choice for today's Internet applications [5]. DNA computing is still an area of interest for many researchers for its massively parallel processing capabilities and high resistance to brute force attacks [6]. The existing image encryption standards and mathematical models combined with DNA cryptography show defects in terms of CPU time, memory consumption, and battery usage [11].…”