DNA-based Algorithms Research Articles

Encryption with DNA: The Manipulation of DNA to Deal with the Cyber Security Attacks

The witnessed technological developments in wireless communications have made an individual’s dependency on online transactions. As is the nature of wireless, the wireless networks are more prone to man-in-middle attacks, which are intended for crucial information theft, modification called active and passive attacks. Recent investigations of the application of biology DNA (deoxribonucleic acid) to encrypt the data have shown improved security results. The proposed technique is an advanced version of DNA-based cryptography, is a hybrid technique of Improved Pig-Pen Cipher and DNA encryption techniques, uses a 256-bit length key to encrypt the message with prescribed shapes. This algorithm takes less processing time and it will work faster for encryption and decryption with minimum throughput. The DNA-based cryptographic algorithms were defined by using the biological properties of DNA strands.

A Review of Modern DNA-based Steganography Approaches

In the last two decades, the field of DNA-based steganography has emerged as a promising domain to provide security for sensitive information transmitted over an untrusted channel. DNA is strongly nominated by researchers in this field to exceed other data covering mediums like video, image, and text due to its structural characteristics. Features like enormous hiding capacity, high computational power, and the randomness of its building contents, all sustained to prove DNA supremacy. There are mainly three types of DNA-based algorithms. These are insertion, substitution, and complementary rule-based algorithms. In the last few years, a new generation of DNA-based steganography approaches has been proposed by researchers. These modern algorithms overpass the performance of the old ones either by exploiting a biological factor that exists in the DNA itself or by using a suitable technique available in another field of computer science like artificial intelligence, data structure, networking, etc. The main goal of this paper is to thoroughly analyze these modern DNA-based steganography approaches. This will be achieved by explaining their working mechanisms, stating their pros and cons, and proposing suggestions to improve these methods. Additionally, a biological background about DNA structure, the main security parameters, and classical concealing approaches will be illustrated to give a comprehensive picture of the field.

The DNA-Based Algorithms of Implementing Arithmetical Operations of Complex Vectors on a Biological Computer.

Here we show that arithmetical operations of complex vectors can be implemented by means of the proposed DNA-based algorithms.

Molecular solutions of the RSA public-key cryptosystem on a DNA-based computer

The RSA public-key cryptosystem is an algorithm that converts a plain-text to its corresponding cipher-text, and then converts the cipher-text back into its corresponding plain-text. In this article, we propose five DNA-based algorithms—parallel adder, parallel subtractor, parallel multiplier, parallel comparator, and parallel modular arithmetic—that construct molecular solutions for any (plain-text, cipher-text) pair for the RSA public-key cryptosystem. Furthermore, we demonstrate that an eavesdropper can decode an encrypted message overheard with the linear steps in the size of the encrypted message overheard.

Fast parallel DNA-based algorithms for molecular computation: discrete logarithm

Diffie and Hellman (IEEE Trans. Inf. Theory 22(6):644---654, 1976) wrote the paper in which the concept of a trapdoor one-way function was first proposed. The Diffie---Hellman public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption, and converts the unrecognizable data back into its original decryption form. The security of the Diffie---Hellman public-key cryptosystem is based on the difficulty of solving the problem of discrete logarithms. In this paper, we demonstrate that basic biological operations can be applied to solve the problem of discrete logarithms. In order to achieve this, we propose DNA-based algorithms that formally verify our designed molecular solutions for solving the problem of discrete logarithms. Furthermore, this work indicates that public-key cryptosystems based on the difficulty of solving the problem of discrete logarithms are perhaps insecure.

Fast Parallel Molecular Algorithms for DNA‐Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over GF(2n)

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.

Fast Parallel DNA-Based Algorithms for Molecular Computation: The Set-Partition Problem

This paper demonstrates that basic biological operations can be used to solve the set-partition problem. In order to achieve this, we propose three DNA-based algorithms, a signed parallel adder, a signed parallel subtractor and a signed parallel comparator, that formally verify our designed molecular solutions for solving the set-partition problem.

A DNA-based solution to the graph isomorphism problem using Adleman–Lipton model with stickers

Since the experimental demonstration of its feasibility, DNA-based computing has been applied to a number of decision or combinatorial optimization problems. The graph isomorphism problem belongs to the class of NP problems, and has been conjectured intractable, although probably not NP-complete. In this paper, we demonstrate the power of DNA-based computing by showing the graph isomorphism problem can be efficiently solved under this computation model. By generating the solution space using stickers, we present DNA-based algorithms to solve the problem using polynomial number of basic biological operations.

Fast Parallel Molecular Algorithms for DNA-Based Computation: Factoring Integers

The RSA public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption and converts the unrecognizable data back into its original decryption form. The security of the RSA public-key cryptosystem is based on the difficulty of factoring the product of two large prime numbers. This paper demonstrates to factor the product of two large prime numbers, and is a breakthrough in basic biological operations using a molecular computer. In order to achieve this, we propose three DNA-based algorithms for parallel subtractor, parallel comparator, and parallel modular arithmetic that formally verify our designed molecular solutions for factoring the product of two large prime numbers. Furthermore, this work indicates that the cryptosystems using public-key are perhaps insecure and also presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.

Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem

In this paper our main purpose is to give molecular solutions for the subset-product problem. In order to achieve this, we propose three DNA-based algorithms – parallel adder, parallel multiplier and parallel comparator – that formally verify our designed molecular solutions for the subset-product problem. We also show that Boolean circuits are not needed to perform mathematical operations on a molecular computer. Furthermore, this work indicates that the subset-product problem is solved and also presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.

DNA-based algorithms for learning Boolean formulae

We apply a DNA-based massively parallel exhaustive search to solving the computational learning problems of DNF (disjunctive normal form) Boolean formulae. Learning DNF formulae from examples is one of the most important open problems in computational learning theory and the problem of learning 3-term DNF formulae is known as intractable if RP ≠ NP. We propose new methods to encode any k-term DNF formula to a DNA strand, evaluate the encoded DNF formula for a truth-value assignment by using hybridization and primer extension with DNA polymerase, and find a consistent DNF formula with the given examples. By employing these methods, we show that the class of k-term DNF formulae (for any constant k) and the class of general DNF formulae are efficiently learnable on DNA computer. Second, in order for the DNA-based learning algorithm to be robust for errors in the data, we implement the weighted majority algorithm on DNA computers, called DNA-based majority algorithm via amplification (DNAMA), which take a strategy of ``amplifying'' the consistent (correct) DNA strands. We show a theoretical analysis for the mistake bound of the DNA-based majority algorithm via amplification, and imply that the amplification to ``double the volumes'' of the correct DNA strands in the test tube works well.

The bounded complexity of DNA computing

This paper proposes a new approach to analyzing DNA-based algorithms in molecular computation. Such protocols are characterized abstractly by: encoding, tube operations and extraction. Implementation of these approaches involves encoding in a multiset of molecules that are assembled in a tube having a number of physical attributes. The physico–chemical state of a tube can be changed by a prescribed number of elementary operations. Based on realistic definitions of these elementary operations, we define complexity of a DNA-based algorithm using the physico–chemical property of each operation. We show that new algorithms for Hamiltonian path are about twice as efficient as Adleman’s original one and that a recent algorithm for Max-Clique provides a similar increase in efficiency. Consequences of this approach to tube complexity and DNA computing are discussed.