In today’s information society, image encryption technology is crucial to protecting Internet security. However, traditional image encryption algorithms have problems such as insufficient chaotic characteristics, insufficient randomness of keys, and insecure Ribonucleic Acid (RNA) encoding. To address these issues, a chaos-RNA encryption scheme that combines chaotic maps and RNA encoding was proposed in this research. The initial values and parameters of the chaotic system are first generated using the Secure Hash Algorithm 384 (SHA-384) function and the plaintext image. Next, the Lü hyperchaotic system sequence was introduced to change the image’s pixel values to realize block scrambling, and further disturbance is achieved through spiral index sequence to enhance encryption effectiveness. Subsequently, to obtain the final encrypted image, the diffusion is accomplished through different RNA encoding rules and operation rules corresponding to the chaotic sequence generated by an improved one-dimensional chaotic map (1DCM). Here innovatively propose four new RNA operation rules, increasing the difficulty of decryption. Simulation results demonstrate that the normalized pixel change rate (NPCR) and the unified average changed intensity (UACI) values of the tested encrypted images were 99.61% and 33.46%, respectively. The average ciphertext entropy value in the Red Green Blue (RGB) channels were 7.9986, 7.991, and 7.991. Furthermore, this algorithm exhibits a low correlation coefficient and enhanced robustness. This encryption method effectively improves the security and reliability of image encryption compared to other similar techniques.

With the continuous popularization of big data and artificial intelligence technology, the importance of image transmission and encryption technology is becoming increasingly prominent. Image encryption finds diverse applications across various domains, encompassing scientific research, finance, healthcare, military safeguarding of confidential information, and scenarios like network communication and video surveillance. In the context of image transmission, ensuring the protection of the information contained within is paramount to prevent unauthorized access. But traditional encryption algorithms like Data Encryption Standard (DES), Rivest Cipher 4 (RC4), Blowfish, and Advanced Encryption Standard (AES) [

Chaotic systems are dynamic systems whose behavior is characterized by unpredictability and disorder. These systems exhibit desirable properties such as pseudo-aperiodicity, initial conditions sensitivity, ergodicity, and randomness, which make them well-suited for high-strength encryption protection [

Scrambling is a conventional encryption technique that has been used in early image encryption methods. The technique involves rearranging the position of pixels in plaintext images to achieve encryption. Examples of scrambling methods include Zigzag, Arnold, and spiral transformations, among others [

Diffusion is commonly employed to modify the values of regular image pixels, enhancing the encryption process. Several techniques have been utilized for diffusions, such as block diffusion, Boolean network, and fractal sorting matrix [

DNA possesses excellent characteristics, such as a large storage capacity, fast calculation speed, and low energy consumption. Consequently, several methods utilizing DNA base sequences have been proposed for image encryption [

In recent years, there are relatively few studies on RNA encryption algorithms, and most of the literature [

Based on the above discussion, the importance of image encryption is self-evident. Chaotic systems have shown promise in providing robust encryption foundations due to their unpredictable nature. However, existing algorithms face challenges such as inadequate chaotic characteristics, insufficient key randomness, and vulnerabilities in RNA coding. To address these issues, this study presents a novel chaos-RNA encryption scheme. The article presents the following contributions:

(1) An improved 1DCM system with better randomness and chaotic characteristics is obtained by improving the one-dimensional chaotic system.

(2) Four new RNA operation rules are proposed, improving the complexity and security of RNA encryption.

(3) A method for image-filling pixel blocks of images is proposed. The pixel filling is performed first, then the plaintext image is split into multiple block matrices.

(4) A new RNA diffusion method is proposed, using 1DCM to generate chaotic sequences as the basis for randomly selecting encoding rules, decoding rules, and participating in RNA encoding operations.

The rest of the paper is structured as follows:

According to the description in literature [

In the 1DCM, this research uses the following iterative formula:

Here

The histogram of sequence statistics in literature [

0 <

0.313 <

Statistical test | Statistical test | ||||
---|---|---|---|---|---|

Result | Result | ||||

1. Approximate entropy | 0.396048 | Pass | 9. Overlapping template matching | 0.69238 | Pass |

2. Block frequency | 0.815434 | Pass | 10. Random excursions | 0.14567 | Pass |

3. Cumulative sums | 0.125986 | Pass | 11. Random excursions variant | 0.16690 | Pass |

4. FFT | 0.406496 | Pass | 12. Rank | 0.43319 | Pass |

5. Frequency | 0.087931 | Pass | 13. Runs | 0.64816 | Pass |

6. Linear complexity | 0.197588 | Pass | 14. Serial | 0.57127 | Pass |

7. Longest run of ones | 0.589388 | Pass | 15. Spectral | 0.48525 | Pass |

8. Non-overlapping template matching | 0.477882 | Pass |

The Lü chaotic system is a three-dimensional (3D) chaotic map proposed by Lü et al. in 2001 [

12.7 <

17.0 <

23.0 <

In this study, the parameters

The Lü chaos system has three Lyapunov exponents. As illustrated in

RNA consists of four bases: adenine (A), cytosine (C), guanine (G), and uracil (U). Unlike DNA, RNA uses uracil instead of thymine. RNA bases pair with each other through hydrogen bonds, with A-U and G-C pairings being the most stable. By using the properties of RNA coding, it is possible to convert numbers or characters into RNA sequences, allowing for encryption. According to

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

A | 00 | 00 | 11 | 11 | 01 | 01 | 10 | 10 |

G | 01 | 10 | 01 | 10 | 00 | 11 | 00 | 11 |

C | 10 | 01 | 10 | 01 | 11 | 00 | 11 | 00 |

U | 11 | 11 | 00 | 00 | 10 | 10 | 01 | 01 |

Based on the RNA complementary pairing rules, and operation rules, eight RNA operators have been designed: addition (+), subtraction (−), XOR

+~ | A | G | C | U | −~ | A | G | C | U | ~+ | A | G | C | U | ~− | A | G | C | U |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A | U | C | G | A | A | U | A | G | C | A | C | G | A | U | A | A | G | C | U |

G | C | G | A | U | G | C | U | A | G | G | G | A | U | C | G | U | A | G | C |

C | G | A | U | C | C | G | C | U | A | C | A | U | C | G | C | C | U | A | G |

U | A | U | C | G | U | A | G | C | U | U | U | C | G | A | U | G | C | U | A |

It is important to note that four of these operators are user-defined: addition and inversion operation (bitwise inversion operation after addition), subtraction and inversion (bitwise inversion operation after subtraction), reverse addition (addition after bitwise inversion operation) and reverse subtraction (bitwise inversion operation followed by subtraction).

This section presents a novel image encryption method for RNA coding, utilizing a chaotic system consisting of four key components. Firstly, the SHA-384 hash function produces the initial value, parameter, and block size. Secondly, the original image is divided into blocks based on the block size determined by the Lü chaotic map and the hash value and then subjected to Fisher-Yates permutation and sort permutation. Thirdly, introduces an improved 1DCM, which generates a chaotic sequence for encoding, decoding, and operation rules in the RNA diffusion process. Finally, the RNA encoding, decoding, and computing operations are executed. This encryption technique is designed for plaintext image encryption with

To prevent potential compromise of the encryption algorithm through pixel manipulation, the SHA-384 hash function is employed to generate 384-bit hash values. Subsequently, each 32-bit binary number is partitioned into twelve groups, ordered from the front to the back. This expression can be formulated as: _{1}, _{2},...,_{12}. _{i} = {_{i,0}, _{i,1},...,_{i,31}}, and

The initial values _{1}(_{1}, _{2}, _{3}) of the 1DCM chaotic system and the system parameter

The calculation of initial value _{2}(_{4}, _{5}, _{6}) and system parameter

The sub-block size of the image to be split is determined by calculating rows’ number (

To increase the security of the encryption algorithm, the study explores a novel diffusion and permutation model.

The encryption scheme involves the following specific steps:

Step 1: The sub-block size of the image after block partitioning needs to be calculated from the above equation and results in an _{b} rows and _{b} columns to the original image. Additionally, these pixels are assigned a value of 260 using

Step 2: Initialize the Lü hyperchaotic system with the initial values _{4}, _{5}, _{6}, and the value of the parameter c, and iterate it for 1024 + (_{b}) × (_{b}) times. To eliminate the transient effects, remove the first 1024 iterations and obtain three chaotic sequences,

Step 3:

Step 4: To perform an effective intra-block and inter-block scrambling, rearrange each

In this case, the 3 × 3 sub-block is taken as an example,

Step 5: Perform a scrambling operation on _{1}.

Step 6: For the 1DCM chaotic system, r is used as a parameter, and the system initial values _{1}, _{2}, and _{3} are respectively substituted into the 1DCM system for 3_{1}, _{2}, and _{3}.

Step 7: To diffuse the pixel value of _{1}, two addition modulo operations are performed, resulting in the diffused pseudo-random image _{2} through

Step 8: The RNA codec rules

Step 9: Applying the RNA encoding process to diffuse images _{2} and chaotic sequences _{d}. Furthermore, the chaotic sequences _{1} and _{1}.

Step 10: The ciphertext matrix _{d} and further scrambling the image. The specific ciphertext matrix is generated using

Here,

Step 11: After the operations above, the encrypted image _{P} is obtained by decoding the ciphertext image

The decryption process, which is the reverse of the previously described process, is not described here.

The experimental simulations were performed using MATLAB R2022A on a laptop equipped with an Intel i5-12500H processor, 16 GB of memory, and running the Windows 11 system.

A secure encryption algorithm should produce a significant difference between the plaintext image and ciphertext images when a pixel value in a normal image is changed [

_{1} and _{2} represent the encrypted images before and after a pixel value in the plaintext image is modified. The parameters

Image | NPCR (%) | Average (%) | UACI (%) | Average (%) | ||||
---|---|---|---|---|---|---|---|---|

R/Gray | G | B | R/Gray | G | B | |||

Lena (512 × 512) | 99.6075 | 99.6304 | 99.5926 | 99.6102 | 33.4849 | 33.4441 | 33.4921 | 33.4737 |

Plane (512 × 512) | 99.6223 | 99.6117 | 99.6078 | 99.6139 | 33.4644 | 33.4359 | 33.4902 | 33.4635 |

Football (320 × 256) | 99.6118 | 99.6082 | 99.6155 | 99.6118 | 33.4188 | 33.4837 | 33.5107 | 33.4711 |

Couple (256 × 256) | 99.6201 | 99.6429 | 99.6414 | 99.6348 | 33.5094 | 33.3426 | 33.4038 | 33.4186 |

Airport (1024 × 1024) | 99.6146 | / | / | 99.6146 | 33.4792 | / | / | 33.4792 |

Proposed scheme | Literature [ |
Literature [ |
Literature [ |
Literature [ |
Theoretical value | |
---|---|---|---|---|---|---|

NPCR Average (%) | 99.61 | 95.59 | 99.62 | 99.61 | 99.61 | |

UACI Average (%) | 33.5 | 33.4 | 33.51 | 33.5 | 33.46 |

An image’s pixel value distribution is often represented through histograms, a statistical feature. The consistency of the pixel values can be assessed by graphing the frequency of pixels for each color intensity level.

An effective image encryption algorithm requires a sufficiently large key space to withstand brute force attacks. The key consists of 384 binary arrays generated via the SHA-384 algorithm. Therefore, the size of the encryption algorithm proposed in this paper is 2^{384}. Clearly, the proposed encryption algorithm has a key space much larger than the encryption requirement of 2^{100}. This is far beyond the processing capability of current computing technology, indicating that the key space is difficult to crack with traditional methods.

A high-quality encryption algorithm should be highly sensitive to changes in the keys, where a small alteration can result in a significant change in the output. In this paper, the algorithm's sensitivity to modifying one bit of the hash value of the key’s SHA-384 is analyzed. The specific changes are as follows:

_{1} =

Decrypting the ciphertext image encrypted with _{1} does not yield the correct plaintext image (as _{1} demonstrates average values of NPCR (99.60%) and UACI (32.23%) that closely resemble the ideal values of the ciphertext. This observation highlights the high sensitivity of the encryption key.

In addition to histogram analysis, pixel correlation analysis is also significant. Four thousand adjacent pixels were chosen from the plaintext and encrypted images in different directions. The results of correlations in different directions on the R channel, G channel, and B channel are presented in

Plain image | Horizontal | Vertical | Diagonal | Cipher image | Horizontal | Vertical | Diagonal |
---|---|---|---|---|---|---|---|

Lena (512 × 512) | Lena (512 × 512) | ||||||

R | 0.9903 | 0.9818 | 0.9724 | R | −0.0182 | −0.0044 | 0.0018 |

G | 0.9809 | 0.9695 | 0.9565 | G | −0.0057 | 0.0313 | 0.0449 |

B | 0.9585 | 0.9309 | 0.9176 | B | −0.0036 | −0.0056 | 0.0122 |

Football (320 × 256) | Football (320 × 256) | ||||||

R | 0.9719 | 0.9764 | 0.9700 | R | −0.0060 | −0.0031 | −0.0094 |

G | 0.9174 | 0.9122 | 0.9039 | G | 0.0036 | −0.0321 | 0.0120 |

B | 0.9353 | 0.9383 | 0.9151 | B | 0.0014 | −0.0120 | 0.0101 |

Airport (1024 × 1024) | 0.9070 | 0.9064 | 0.8432 | Airport (1024 × 1024) | −0.0036 | −0.0037 | 0.0092 |

Black_white (512 × 512) | 0.9935 | 0.9960 | 0.9895 | Black_white (512 × 512) | −0.0113 | −0.0131 | 0.0154 |

The randomness of a system and the uncertainty of image information are assessed using information entropy. A higher entropy value usually indicates more uncertainty and less visual information. The entropy formula is

_{i}) denotes the possibility of pixel _{i}.

Plaintext image | R/Gray | G | B | Ciphertext image | R/Gray | G | B |
---|---|---|---|---|---|---|---|

Lena (512 × 512) | 7.2351 | 7.5940 | 6.9684 | Lena (512 × 512) | 7.9993 | 7.9993 | 7.9994 |

Baboon (512 × 512) | 7.7067 | 7.4744 | 7.7522 | Baboon (512 × 512) | 7.9992 | 7.9992 | 7.9993 |

Lake (512 × 512) | 7.3124 | 7.6429 | 7.2136 | Lake (512 × 512) | 7.9992 | 7.9993 | 7.9992 |

Peppers (512 × 512) | 7.3388 | 7.5184 | 7.0584 | Peppers (512 × 512) | 7.9993 | 7.9993 | 7.9992 |

Football (320 × 256) | 6.6198 | 6.6644 | 6.9961 | Football (320 × 256) | 7.9979 | 7.9980 | 7.9979 |

Couple (256 × 256) | 6.2501 | 6.0640 | 5.9313 | Couple (256 × 256) | 7.9993 | 7.9993 | 7.9992 |

Airport (1024 × 1024) | 6.8303 | / | / | Airport (1024 × 1024) | 7.9980 | / | / |

Black_white (512 × 512) | 0.0000 | / | / | White (256 × 256) | 7.9972 | / | / |

Average | 7.0014 | 7.1091 | 6.8763 | Average |

Majority logic criteria (MLC) is a metric used to assess the properties of Boolean functions and is a commonly employed texture feature in fingerprint image processing. In addition to correlation coefficients and information entropy, which have been previously analyzed, it also includes contrast, energy, and homogeneity. As shown in

Encryption Algorithms | Correlation | Entropy | Homogeneity | Contrast | Energy |
---|---|---|---|---|---|

Original Lena image | 0.962 | 7.2658 | 0.7472 | 0.3223 | 0.0832 |

Propose algorithms | 0.0023 | ||||

Literature [ |
−0.0015 | 7.9992 | 0.3124 | 12.1567 | 0.0116 |

Literature [ |
0.0749 | 7.7959 | 0.4601 | 5.2671 | 0.0259 |

The transmission of images may result in data loss or information changes. Therefore, a robust encryption algorithm should be capable of recovering most of the valuable information even in these situations. This section tests the algorithms against clipping and noise attacks. A clipping attack refers to setting some pixel values of the ciphertext image to black, simulating an image being cropped.

Noise attack refers to the interference of ciphertext images with different degrees and types of noise. A reliable encryption system must have some degree of resistance to noise during transmission. In the following experiment, this study added dual noise to the encrypted image shown in

“Complexity and Speed Analysis” is regarded as one of the crucial criteria for assessing the efficiency of an algorithm. This analysis entails the evaluation of the algorithm’s time complexity and execution speed. The proposed image encryption algorithm consists of three methods: block scrambling, RNA dynamic encoding and decoding, and RNA diffusion. The block scrambling method has a time complexity of O(_{b} × _{b} ×

Parameter | Proposed scheme | Literature [ |
Literature [ |
Literature [ |
---|---|---|---|---|

Encryption time (s) | 19.14 | 3.888769 | 4.212 | |

Speed test (Mbps) | 0.328599 | 1.61906 | 1.492241 |

This paper presents a novel image encryption scheme that combines chaos and RNA techniques. This paper introduces a novel 1DCM, which demonstrates excellent diffusion characteristics assessed through bifurcation analysis, LE, NIST test, and chaos sequence analysis. The 1DCM algorithm is utilized to modify the pixel values of images, and it establishes RNA encoding, decoding, and operation rules. Additionally, 3D Lü chaos serves as a pseudo-random matrix, generating inter-block sorting scrambling and intra-block Fisher-Yates scrambling, thus enhancing the encryption intensity. Moreover, this study proposes four new RNA operation rules to enhance the security of the ciphertext.

The experimental results on grayscale and color images illustrate that the encryption scheme offers several advantages, including a significant key space, heightened sensitivity, high entropy, and adaptability for various image applications. Furthermore, it exhibits high resistance to noise, cropping, and known plaintext attacks. Therefore, the proposed encryption scheme is secure and reliable for image encryption and can be applied to secure communication. In future research, we aim to extend this method to multi-image encryption while enhancing the key space.

We would like to take this opportunity to express our heartfelt gratitude to all those who made a contribution to the completion of this article.

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 62105004, and in part by the Open Fund of the State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mine under the Grant (SKLMRDPC19KF10).

The authors confirm their contributions to the paper as follows: study conception and design: Y. Hong, J. Su; data collection: W. Xu, Y. Wei, J. Wu; draft manuscript preparation: S. Fang, Z. Yang. All authors reviewed the results and approved the final version of the manuscript.

The data and materials used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest to report regarding the present study.