High confidence bessel map based bit-level image encryption method

Abstract

The invention relates to a computer-based image encryption method using a Bessel map with high chaotic performance, which is developed to fill the gaps between a high performance chaotic map and a simple encryption scheme.

Description

[0001]DESCRIPTION HIGH CONFIDENCE BESSEL MAP BASED BIT-LEVEL IMAGE ENCRYPTION METHOD Technical Field The invention relates to a computer-based image encryption method using a Bessel map with high chaotic performance, which is developed to fill the gaps between a high performance chaotic map and a simple encryption scheme. Prior Art With the development of information technologies and the increasing possibility of unauthorized access to data published on the internet, the need for data protection has become an important issue. This issue has necessitated studies on image encryption methods. The patent document numbered JP5277660B2 discloses an image encryption device that encrypts an image of a random document, an image decryption device that decrypts an encrypted image, an image encryption method and an image decryption method. The document also discloses an image encryption program. The innovation describes a comprehensive image encryption system used to protect the image of any document. The patent document numbered US10467427B2 discloses novel methods for decrypting an image. The first method captures a portion of an encrypted image and processes it by decrypting that portion using a decryption key. Then, in addition to displaying the decrypted portion on the screen, it displays the image of the portion next to it using the partial information obtained from the decrypted portion. The second method works by capturing the first part of an image encrypted with the first key and the second key, decrypting it with the first key and projecting it on the screen. The paper includes these methods for efficiently decrypting encrypted images, which can be useful in applications that require secure image transmission and display. The patent document numbered CN113259089A describes an image encryption method based on a combination of a chaos principle and a genetic algorithm. The method includes the following steps: image processing, initial key generation, image row and column encryption, chaotic array generation, chaotic mapping, and image storage and output. This invention can improve image security and ensure pixel connectivity in the transmission process of the image. The image pixels generated after encryption have low correlation and present high difficulty in key breaking, which ensures the security of image information transmission. It avoids economic losses and technical leakage caused by image leakage, and ensures the secure and efficient transmission of image information. The patent document numbered CN103489151B discloses a color image encryption method based on a chaos sequence and hyper-chaos system. The color image encryption method mainly includes the following steps, an original color image is subjected to a bit-level composite mixing process to obtain a scrambled image; the scrambled image is divided into three basic color components, namely R, G and B, and the hyper-chaos system is used to generate an encryption matrix which is used to encrypt the scrambled image; all pixel values of the three basic color components of the scrambled image are replaced by combining the encryption matrix with the plaintext information and the information of the three basic color components, and the three basic color components of the image are obtained after combined diffusion by combined diffusion, thus obtaining a final encrypted image. The color image encryption method greatly expands the secret key space, the security, encryption effect and sensitivity of the secret key are higher, the attack resistance is stronger, and the hardware implementation is easier. The patent document numbered CN113225449B describes an image encryption method based on a chaotic sequence and DNA encoding. This method includes the following steps, is to perform g compute the complexity value of an image matrix transformed from an image with ri levels and update the initial value for the chaotic system; Generating an array as a random value according to the Knuth-Durstenfeld mixing method according to the control parameters of the Bernoulli shear mapping and the updated initial valueiterate the Lorenz chaotic system and obtain the 3 sequences; separate the elements used to perform bit-level shuffling for use in cyclic shifting; use the elements in the sequence for DNA coding rules and select and encode them as DNA sequences; To obtain a new DNA sequence by performing state transformation using the Mealy state machine; DNA decoding using a DNA coding rule to select elements within the sequence and obtain an encoded image. This invention makes full use of chaos randomization and the linearity of DNA encoding, effectively eliminating the correlation of adjacent pixels in the image and enhancing the security of the encrypted image. When the works in the known state of the art are examined, there is a need to develop a computer-based image encryption method using the Bessel map with high chaotic performance, which is developed to fill the shortcomings of high performance chaotic map and simple encryption scheme. The Objects of the Invention The object of the present invention is to develop a computer-based image encryption method using the Bessel map with high chaotic performance, which is developed to fill the shortcomings of high performance chaotic map and simple encryption scheme. Another object of the present invention is the development of a computer-based image encryption method with increased security, which allows the method to greatly expand the key space thanks to the high complexity of the Bessel map. Another object of the present invention is the development of a computer-based image encryption method that offers a robust defense mechanism against potential crypto-analysis and attacks in terms of bit-level resistance. Detailed Description of the Invention The invention relates to a computer-based image encryption method utilizing a Bessel map with high chaotic performance, which is developed to fill the shortcomings of a high performance chaotic map and a simple encryption scheme, comprising these following steps; - Generating key vector B with hash functions (SHA-512 / MD5) using the FP image, - Creating vector C by repeating vector B(1:480)in ceil(m / 2)+ceil((m / 2) / 80), - Summing the 1st to 480th bit elements of B to obtain the value of T, - Generating the control parameters and initial values for the number 3m forming the vector R for the diffusion process, - Creating vectors L1, L2and L3by repeating bit elements 481 to 496 of B and bit elements 497 to 512 of B, - Generating control parameters u1, v1and initial value x1using algorithm 2 for the permutation process, - Generating of chaotic sequence X1with the help of Bessel map, - Ordering the chaotic sequence from smallest to largest and indexing its order as vector P, - Then transferring the kth input of A1((â1k)1) to the ith input of A2((â1i)2), generating chaotic sequences for each row of the permuted image of length column number, - Combining these chaotic sequences by successively adding Y to form vector X2, - Converting the corresponding pixel value to W2with calculation of Vector X2, floor(256X2), - Obtaining vector A3by XOR operation between vectors A2and W2, - Obtaining the encrypted image. Bessel functions were first introduced by Daniel Bernoulli and later defined by Friedrich Bessel. These functions are solutions of the following Bessel differential equation: ^^^^2^^^^ ^^^^^^^^ ^^^^2^^^^^^^^2+ ^^^^^^^^^^^^+ (^^^^2 − ^^^^2)^^^^ = 0Here v represents the degree of the Bessel function. The Bessel functions of the first and second kind, denoted as Jv(x) and Yv(x), can be expressed as solutions of theBessel differential equation, respectively:^^^^ = ^^^^^^^^^^^^(^^^^) + ^^^^^^^^^^^^(^^^^)Here A and B are any chosen constants. Although Bessel functions are usually presented in integer-degree forms, they can in fact be defined for all real values in the range -∞ < v < +∞. The behavior of the Bessel function is similar to that of the Sine and Cosine functions, which decay with x. After various analyses, the chaotic map obtained based on the first type Bessel function Jv(x) is as follows: Here t, u, and v are assigned as control parameters in the range [0, +∞). Throughout this study, the control parameter was set to t = 3. The "mode 1" operation is used to keep xi+1in the range [0,1]. The Bessel map exhibits a structure that varies with t and u as well as the degree v, providing a higher sensitivity than the Sine map. Therefore, it offers higher security and reliability compared to the Sine map. The method of the invention, Bessel map-based bit-level image encryption (Bessel IMage Encryption - BIME), is realized through a two-step process of permutation and propagation. During the permutation and propagation processes, bit positions and values are shuffled and manipulated respectively. Before these procedures, the key is used to obtain the control parameters and initial values of the Bessel map. The control parameters and initial values are generated through Algorithm 1 using the key obtained using the fingerprint (FP), specifically called the Control Parameter Calculator (CPC). The fingerprint is used as input and the vector R with control parameters u1, v1and initial value x1is generated as output. u1,v1and x1are used in the permutation, while R is used in the diffusion process. First, the key vector B in Line 1 is generated with hash functions (SHA-512 / MD5) using the FP image. In row 2, vector C is formed by repeating vector B(1:480)with the number ceil(m / 2)+ceil((m / 2) / 80). Here the ceil function rounds the number to the nearest upper integer. For example, if the image is 40×5 pixels, C(1×10080)=RepMat(B(1:480),1, 21). Here the RepMap function is used to replicate the matrix. The reason for this repetition is to use different chaotic sequences to manipulate each line of the image, which increases diversity. In Row 3, the 1st to 480th bit elements of B are summed to get the value T. From Line 4 to Line 9, 3m numbers of control parameters and initial values are generated, forming the vector R for the diffusion process. Here, a fraction generator (Fraction Generator - FrGn) specified in Algorithm 2 is used to generate a floating-point number containing the 16-digit fractional part to the right of the point. In Line 10, bit elements 481 to 496 of B and bit elements 497 to 512 of B are repeated to create three vectors L1, L2and L3. Finally, in Line 11, Algorithm 2 is used for the permutation process to generate the control parameters u1, v1and the initial value x1. Algorithm 1: CBC of the Bessel map using the key obtained from the FP Output: x1, u1, v1, R 1 Build a key B via hash functions (SHA-512 / MD5) using the FP image 2 C = RepMat (B1:480, 1, ceil((m / 2) / 80)) 3 T = sum(B1:480) 4 for i = 1 to 3m 5 D = C80(i-1)+1+k:80i+k6 ri= FrGn(D, T) / / Algorithm 2 7 If ((i-1) mod 6 == 0) k++ 8 If (mod(i, 3) == 0 ^ mod (i,3) == 2) ri= 10ri 9 end 10 L1= RepMat(B481:496, 1, 5), L2= RepMat(B497:512, 1, 5), L3= B433:51211 x1= FrGn(L1, T), u1= FrGn(L2,T), v1= 10 * FrGn(L3, T) / / Algorithm 2 Algorithm 2: Fractional Generator (FrGn) Output: H 1 for j = 1 to 16 3 G = mod(T + (E)10, 10) 4 H = H +^^^^10^^^^5 end Algorithm 3 is the main block containing all the Encryption Processes (EP) of the inventive method. (The line numbers indicated here refer to the line numbers in Algorithm 3.) First, the control parameters and initial values of the Bessel generator in Line 1 are generated as described in Algorithm 1. Then, in Line 2, the Bessel map is used to generate a chaotic sequence X1 as described in Algorithm 4. In row 3, the chaotic sequence is sorted from smallest to largest and its order is indexed in vector P. Then the kth input ((â1k)1) of A1is transferred to the ith input ((â1i)2) of A2. This transfer is performed at bit level. In Line 9, for each row of the permuted image, chaotic sequences are generated for the length of the number of columns. In Line 10, these chaotic sequences are multiplexed together consecutively with Y using the MerMat function to form vector X2. On line 12, vector X2is converted to the corresponding pixel value W2by calculating floor(256X2). On line 13, vector A3is obtained by the XOR operation between vectors A2and W2, the result of the permutation. Finally, in row 14, the spread matrix A3is obtained as an encrypted image by reshaping the vector A2. Algorithm 3: Encyption Processes (EP) of the BIME scheme EP (A1, FP) Output: A2 1 [x1, u1, v1, R] = CPC(FP) / / Algorithm 1 2 X1= CSG(x1, u1, v1, 8m) / / Algorithm 4 3 [W1P] = sort (X1) 4 for i = 1 to 8mn 5 k = p1i6 (â1i)2= (â1k)17 end 8 for i = 1 to 3m by 3 9 Y(i+2) / 3 = CSG (ri, ri+1, ri+2, n) 10 X2 = MerMat(X2, Y(i+2) / 3) 11 end 12 W2:= floor (256X2) 13 A3:= A2⊕ W214 Reshape A3to m x n Algorithm 4: Chaotic sequence generator (CSG) via Bessel map CSG (x1, u, v, s) Output: X 1 for i = 1 to s 2 xi+1= 10tuJv(10t(1-uxi)) mod 1 3 end 4 X = [xij] 1xs

Claims

CLAIMS 1. A computer-based image encryption method using a Bessel map with high chaotic performance, which is developed to fill the shortcomings of a high performance chaotic map and a simple encryption scheme, characterized in that the method comprises the following steps; - Generating key vector B with hash functions (SHA-512 / MD5) using the FP image, - Creating vector C by repeating vector B(1:480)in ceil(m / 2)+ceil((m / 2) / 80), - Summing the 1st to 480th bit elements of B to obtain the value of T, - Generating the control parameters and initial values for the number 3m forming the vector R for the diffusion process, - Creating vectors L1, L2 and L3by repeating bit elements 481 to 496 of B and bit elements 497 to 512 of B, - Generating control parameters u1, v1and initial value x1using algorithm 2 for the permutation process, - Generating of chaotic sequence X1with the help of Bessel map, - Ordering the chaotic sequence from smallest to largest and indexing its order as vector P, - Then transferring the kth input of A1((â1k)1) to the ith input of A2((â1i)2), generating chaotic sequences for each row of the permuted image of length column number, - Combining these chaotic sequences by successively adding Y to form vector X2, - Converting the corresponding pixel value to W2with calculation of Vector X2, floor(256X2), - Obtaining vector A3by XOR operation between vectors A2and W2, - Obtaining the encrypted image.

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