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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.

With the rapid development of multimedia technology and network technology, digital image processing has been widely applied to all aspects of human life, such as remote sensing, industrial inspection, medical field, meteorology, communications, reconnaissance, and intelligent robots. As a result, increasing attention has been paid to image information. Additionally, it is more important to protect the security of image data, especially in military, commercial, and medical fields. Image encryption technology has become an effective way to protect the transmission of digital images [

As a type of complex nonlinear system, chaotic systems have initial value sensitivity, pseudorandomness, and nonperiodicity, which are consistent with the characteristics required for cryptography. A chaotic sequence can be used as a random key, which can achieve the same encryption effect as the first time, and it is not capable of being broken, in theory. Thus, chaotic encryption technology has been widely used in the field of information security, especially in the field of image encryption [

At present, most of the confusion and diffusion structure of image encryption algorithms is based on chaotic systems for the use of chaotic sequences, and it is restricted by the computer word length, which can cause degradation in the chaotic dynamics, especially for a low-dimensional chaotic system [

DNA is an important carrier of the biological genetic information that is stored in the body, and genetic metabolism plays an important role in the organism. It has a very large scale of parallelism, ultrahigh storage density, and low energy consumption as well as a unique molecular structure and molecular recognition mechanism, which determines its outstanding information storage and information processing ability [

In recent years, combined with the dual advantage of the DNA molecule and chaotic systems, an image encryption algorithm based on DNA molecules and chaotic systems is presented. In 2012, Liu et al. proposed an image encryption algorithm based on DNA encoding and chaotic map [

Therefore, in this paper, a new image encryption algorithm based on chaotic systems and dynamic DNA encoding is proposed. The algorithm uses Keccak to compute the hash value of the given DNA sequence as the initial value of the chaotic map, generating a chaotic index of the image position that performs scrambling, which is coupled with a butterfly network to achieve a level of scrambling. Finally, through the study of the dynamic DNA encoding of images and the operations of a given DNA sequence, the additional use of ciphertext feedback can help to achieve the replacement and diffusion of the pixels, which has further improved the security of the encryption.

As a type of special nonlinear phenomenon, chaos has good pseudorandomness and unpredictability of the orbit and has extreme sensitivity to initial conditions and structure parameters; in addition, it is iterative and not repetitive and has a series of excellent features, which are widely used toward the secrecy of communication. Compared with a low-dimensional chaotic system, high-dimensional chaotic systems have a more positive Lyapunov exponent and are more complex, and it is more difficult to predict the dynamic characteristics, which can effectively solve the degradation problem of the low-dimensional chaotic system with dynamics characteristics. It also has strong confidentiality, a simple algorithm, and large key space characteristics. In 2005, Lee and others constructed a hyperchaos Chen system via state feedback control, and its equation is

Keccak is a standard one-way hash function algorithm. The hash functions are designed to take a string of any length as input and produce a fixed-length hash value. When the hash value is attached to the message or stored with the message, the message can be prevented from being modified in the process of storage for transmission. Messages are different; the resulting hash value is also different, and even if there is only one bit of change in the message, the hash value will be completely useless. By using this feature, we can change the pixel value of the image by selecting the appropriate message and using the hash value generated by the Keccak hash function and the operation of the image. At the same time, the hash value is modified to set the initial value and system parameters of the chaotic system, to further improve the security of the encryption. Keccak has no length limit on the upper limit of the input data length, and it can generate arbitrary hash values.

The DNA molecule is composed of four DNA nucleotides, which are adenine (A), cytosine (C), guanine (G), and thymine (T). For two single-stranded DNA molecules, a stable DNA molecule can be formed by hydrogen bonds between nucleotides. The chemical structure of the base determines the principle of complementary base pairing, and it is also known as the Watson-Crick base pairing principle. In other words, A and T are paired by two hydrogen bonds, and G and C are paired by three hydrogen bonds. The natural combination is quaternary, similar to the binary semiconductor formed by on and off [

8 encoding rules.

Rule | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

00 | A | A | C | G | C | G | T | T |

01 | C | G | A | A | T | T | C | G |

10 | G | C | T | T | A | A | G | C |

11 | T | T | G | C | G | C | A | A |

For a gray image, the gray value of each pixel can be represented by an 8-bit binary number. If we use the DNA encoding, then each pixel needs four base sequence encodings. By converting the image matrix to a sequence of DNA, the operators for the sequence of the DNA can be applied to the image processing. To reach the goal of pixel value disturbance, the following base operations and transformation rules are defined at the same time.

The XOR operation for DNA sequences.

XOR | A | C | G | T |
---|---|---|---|---|

A | A | C | G | T |

C | C | A | T | G |

G | G | T | A | C |

T | T | G | C | A |

The addition operation for DNA sequences.

ADD | A | C | G | T |
---|---|---|---|---|

A | A | C | G | T |

C | C | G | T | A |

G | G | T | A | C |

T | T | A | C | G |

The subtraction operation for DNA sequences.

Sub | A | C | G | T |
---|---|---|---|---|

A | A | T | G | C |

C | C | A | T | G |

G | G | C | A | T |

T | T | G | C | A |

The digital image encryption is realized by using the hyperchaos Chen system, the Keccak algorithm, bit permutation, a dynamic DNA encoding technique, and its pixel gray value transformation and operation to achieve the purpose of confusion and diffusion, to realize the digital image encryption.

The nucleic acid database is a database of all known nucleic acid information sets. It contains nucleotide sequences, single nucleotide polymorphisms, structure, properties, and related descriptions. The ID number of a sequence in a database is called the sequence code, which is unique and permanent. With the rapid development of sequencing technology, the size of the nucleic acid database is growing exponentially; thus far, public access to DNA sequences includes more than 163 million sequences. This enormous database is equivalent to a natural password. It provides a new idea and solution for image encryption.

The DNA sequence is mainly used for ciphertext diffusion as well as the generation of hash values. Using the Keccak algorithm to generate the hash value

Scrambling is an important means to hide plaintext information with an encryption algorithm. The diffusion of text can be achieved through position displacement. The bits permutation provides the functionality of the confusion and diffusion that byte operations cannot achieve.

Butterfly is a common network of communication exchanges [

Bit replacement elements.

Element without control bit

Element with control bit

Bit permutation network.

After the image has been dislocated, the pixels have changed, and the pixel values have been changed to further enhance the security.

The given initial state values for

Here,

We are given a two-dimensional matrix

According to the sequence

For the grayscale image

According to the sequence

After the scrambling of each of the submatrices Sub_I and Sub_II, the two submatrices are restored to an image matrix

Pixel scrambling quickly disrupts the position of the image through the initial change in the matrix, destroying the correlation between adjacent pixels, but it is unable to effectively resist partial cryptography attacks, and further, through pixel substitution and ciphertext diffusion, it can thoroughly confuse the relationship between the plaintext image and the ciphertext image.

It is possible to achieve a better confusing effect by using complex nonlinear alternative transformations. Alternative encryption means to include modulo arithmetic and addition operations, which can cause the pixel values to be associated with other values and, thus, make the distribution of the pixel values more uniform and eliminate the texture feature of the replacement image.

Since each pixel value can be represented by an 8-bit binary, each pixel is encoded as 4 bases. Then, the encoded DNA sequence length is

The sequence DNA_S is algebraically manipulated with the given DNA sequence SQ. Algebraic operations can be one of the operations in Tables

subject to

Finally, we use DNA encoding rule

The digital image encryption algorithm proposed in this paper includes the following: first, bit permutation, the use of the butterfly network to achieve each pixel bit position permutation; second, pixel location scrambling transforms. The image pixel location will be changed through the displacement index created by the hyperchaotic Chen system to constitute the necessary permutation indices. Third, there are pixel substitution and ciphertext diffusion. The value of each pixel of the original image is converted into a DNA sequence, and the sequence of the DNA coding sequence library is calculated; then, it iterates through the ciphertext feedback. The encrypted flowchart is shown in Figure

Description of the encryption process.

Convert the grayscale image

Download the DNA sequence SQ whose ID number is NZ_LOZQ01000068 from the GenBank database, using the Keccak algorithm to calculate the hash value

According to sequence

According to the bit permutation principle described in Section

According to the subgraph scrambling and diffusion technique described in Section

Using the dynamic DNA encoding technique, the image matrix

According to the ciphertext diffusion technique described in Section

The decryption algorithm is the inverse process of the above process. This process is no longer elaborated.

This algorithm can also be applied to color image encryption, by processing only the values of the pixel RGB decomposition.

Aiming at the algorithm proposed in this paper, the feasibility of the algorithm is verified by MATLAB software programming. This paper adopts a Lena grayscale image with the size

Lena image and ciphered Lena.

Plain Lena image

Ciphered Lena image

Decrypted image with the modified key

Ciphered Lena image with the modified key

The key used in this paper is mainly used for the scrambling and diffusion of the pixels, namely, the following: the Chen system initial parameter

If the computation precision is 10^{–14}, then the key space can reach 10^{100}, which shows that the algorithm has sufficient space to resist an exhaustive attack.

To test the sensitivity of the key, the initial value of the

The statistical information of the image can reveal the distribution of the gray value of the original image to a certain extent, and whether it can change the statistical distribution of the original image is also an important indicator of the image encryption. The purpose of this algorithm is to strike the attack side against a grayscale statistical attack. As shown in Figure

Histogram of the plain Lena image and ciphered Lena image.

Histogram of the plain Lena image

Histograms of the ciphered Lena image

The correlation between the pixels in the original image is relatively large, and to prevent the statistical analysis, we must reduce the correlation of adjacent pixels. We randomly select from the original image and encrypted image each pixel to 2500-pixel correlation, observing the horizontal and vertical and diagonal directions, as shown in Table

Correlation coefficients of the proposed algorithm compared with that of Ye’s algorithm, X. Wang and Q. Wang’s algorithm, and Liu et al.’s algorithm.

Original image | Encryption image (the proposed algorithm) | Encryption image (Ye’s algorithm) | Encryption image (X. Wang and Q. Wang’s algorithm) | Encryption image | |
---|---|---|---|---|---|

Horizontal direction | 0.9646 | 0.0082 | 0.0163 | 0.0097 | −0.0152 |

Vertical direction | 0.9304 | 0.0032 | −0.0029 | 0.0136 | 0.0140 |

Diagonal direction | 0.9030 | 0.0150 | 0.0309 | 0.0178 | 0.0218 |

Correlation Analysis of Lena as a ciphered image in three directions.

Horizontal correlation of the plain image

Horizontal correlation of the ciphered image

Vertical correlation of the plain image

Vertical correlation of the ciphered image

Diagonal correlation of the plain image

Diagonal correlation of the ciphered image

The performance for ciphered image of Lena is compared with that of Ye’s algorithm [

Information entropy is a measure of uncertainty. The formula is as follows:

Here,

This paper presents a hyperchaos digital image encryption technique that is based on bit permutation and dynamic DNA encoding. By using bit permutation, chaos mapping, and the dynamic DNA encoding technique, the scrambling transformation of the pixel locations and the diffusion of pixel values are achieved. The security analysis shows that the algorithm can effectively resist plaintext attacks, differential attacks, and statistical attacks because the algorithm is based on bit permutations and dynamic DNA encoding, and the key space is large; thus, the security is high. Comparisons between this proposed scheme and other researches are just to give us an intuitive and quantitative measures, from which we can infer that the performance of the proposed algorithm has reached the expectation.

The authors declare that they have no conflicts of interest.

The work for this paper was supported by the National Natural Science Foundation of China (Grant nos. 61602424, 61472371, 61572446, and 61472372), Plan for Scientific Innovation Talent of Henan Province (Grant no. 174100510009), Program for Science and Technology Innovation Talents in Universities of Henan Province (Grant no. 15HASTIT019), and Key Scientific Research Projects of Henan High Educational Institution (18A510020).