A Survey and Analysis of the Image Encryption Methods

Home , FISH (cipher), ISAAC (cipher), Salsa20, SEAL (cipher), Triple DES

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 23 (2017) pp. 13265-13280 © Research India Publications. http://www.ripublication.com

Omar Farook Mohammad1, Mohd Shafry Mohd Rahim1,2, Subhi Rafeeq Mohammed Zeebaree3 and Falah Y.H. Ahmed4, 1 Faculty of Computing, Universiti Teknologi Malaysia (UTM), Johor, Malaysia. 2 IRDA Digital Media Center, Universiti Teknologi Malaysia (UTM), Johor, Malaysia. 3 Computer and Communications Engineering Department, College of Engineering, Nawroz University, Duhok, Iraq. 4 Faculty of Information Sciences & Engineering, Management and Science University (MSU), 40100 Shah Alam, Selangor, Malaysia.

1Orcid: 0000-0001-7347-5283

Abstract Being a good source to provide users with security and privacy needed, the digital imaging can play a significant role in At the present time, the protection of multimedia data has multimedia technology field. Image encryption is a significant become a very important process which can be achieved by process to deny any unauthorized user access [2,3]. Sometime encryption. Basically, so many different techniques have been encryption used to increase the ambiguity of the data inside the used to protect private image data from those who illegally try image when it used with steganography at the same time and to have access. An efficient cryptographic scheme is one that watermarking as well [4,5]. In addition to images many has a space of a large key that resists brute force search time, algorithms applied on text for recognize scripts which is done less execution time complexity/ Highspeed and should be able by the segmentation where is play a vital role in script to provide high confusion and diffusion for good security. In recognition process, as well as some algorithms employed on this paper, we survey an existing work which uses classic and voice with multi-speaker by vocal tract length normalization to modern techniques for image encryption, as the classic automatic speech recognition [6,7]. techniques used for text based on alphabets as basic elements while the modern techniques overcome this limitation by used The two terms cryptography and cryptanalysis need to be mathematical algorithms for coding the information due to their clearly defined to give wide comprehension for the work in digital system. A comparison has been conducted between progress. Cryptography mathematically encrypts and decrypts several ciphers techniques (classic and modern) for images information so that the user becomes capable of storing and based on various parameters such as: Histogram, Correlation, transmitting information that is sensitive within insecure Number of Pixels Change Rate (NPCR), Unified Average networks. This information is viable to the public except the Changing Intensity (UACI), Peak Signal to Noise Ratio specified recipients. As for cryptanalysis, it be defined as a (PSNR), Entropy and Time complexity. An analysis of process to analyze and break down secure communication. simulation result shows that chaotic encryption technique Encryption is a process in which an algorithm is used to make especially hyper-chaotic is the most efficient among the all. the transformed information is un-readable by unauthorized users. Therefore, cryptographic method is simply based on Keywords: Classical and Modern cryptography, Chaotic, encoding and transforming information into unreadable cipher Correlation, Histogram, Key Sensitivity, Entropy. text to protect a sensitive data such as credit card number. The encoded data may only be decrypted or turned readable by a INTRODUCTION key. Both of symmetric-key and asymmetric-key encryptions are considered as primary types of encryption [8]. Many Recently, additional security and privacy problems have been evaluation methods used in this regard such as histogram, emerged from the rapid development that occurred in the chaotic which is most popular issue to generate key in communication networks field. The need to secure and reliable encryption and other methods such as simulation [9-11]. means of communication containing images and videos have Decryption is a reverse process in which unreadable become extremely necessary, not to mention other related transformed data that has been subjected to encryption is turned issues that should be taken into consideration. Accordingly, back to unencrypted form. In a decryption process, the system network security and data encryption issues are considered as a extracts and converts the garbled data and then transform it into significant subject. Currently, images are considered as the texts and images that are easily to be understood by both reader most important source of information. The applications of and system. Generally, decryption process can be accomplished image and video encryption can be used in various fields like either manually, automatically or by using set of keys or wireless communication, multimedia systems, medical passwords [12]. Image encryption techniques give challenging imaging, telemedicine, and military communication [1]. due to used widely in many fields such as pattern recognition, face detection, image restoration and matching, etc. [13].

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Figure 1: Classification of Cryptography [16]

Image encryption techniques are different from data encryption  Polyalphabetic cipher: techniques. There are several security problems associated with The Polyalphabetic Cipher is simply referred to a substitute digital image processing and transmission, so that it is cipher whereas a cipher alphabet of a plain alphabet may appear necessary to maintain both the integrity and the confidentiality dissimilar from a place to another during encryption process. of the image [14]. For example, Vigenere Cipher.

(a) Vigenere Cipher CLASSIFICATION OF CRYPTOGRAPHY Vigenere cipher is specifically used to encode an alphabetic The use of cryptography technique is urgently needed to ensure text by implementing several Caesar ciphers of different shift security when parties exchange confidential messages among values. Generally, each character of key and plain text will be themselves via a communication line. illustrated by its index during the encryption process. A table known as Vigenere table or Vigenere square is used in Cryptography technique can be classified according to its Vigenere cipher to make substitution in accordance with the diverse standard methods as a classical and modern techniques key. Basically, the table is a 26*26 matrix which means that the as shown in Fig. 1, those techniques will be described with give English alphabets are written 26 times in different rows example for each method [15]. reflecting diverse possible shifts. Obviously, both of table and substitution are used and arranged according to the various shift Classical cryptography values that derived from the key. These clusters behave same as image segmentation that divided homogenously [21-23]. There are two main types of classical cryptography: Substitution and Transposition[17,18]: The vigenere table proposed in this technique is used further to implement many different algorithms. According to this table, the plaintext CALLMEATNINE will be replaced by cipher text Substitution cipher CTELOOAMGIPO using Key ATTACKATTACK. Substitution itself is divided into two main types [19,20]: Moreover, Vigenere Cipher can also be viewed from algebraic aspect. For instance, If the letters A–Z are taken to represent  Monoalphabetic cipher: numbers 0–25 then Vigenere encryption of E using key K will The monoalphabetic cipher is a term referred to a simple be written as [24]: substitute cipher for used key in which a cipher alphabet for Ci = EK(Pi) = (Pi + Ki) mod 26 (1) each plain alphabet is constant throughout the encryption and decryption D using the key K, process. For example, if ‘A’ is encrypted as ‘D’, any number occurs in that plaintext, ‘A’ will remains encrypted as ‘D’. Pi = DK(Ci) = (Ci – Ki) mod 26 (2) Caesar cipher is example of Monoalphabetic cipher. where

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Pi = P0…Pn is the message, Symmetric key cryptography Ci = C0….Cn is the ciphertext and Privacy plays main role in symmetric algorithms, therefore, both parties who share same key of encryption and decryption K= K0.....Km is the used key. must kept it in secrecy. Accordingly, no third party is allowed to know the key, otherwise the safety is lost. Obviously, Transposition cipher symmetric algorithm is characterized by not consuming too much computing power. DES, triple DES (3DES), IDEA, Transposition cipher is simply referred to a mechanism of CAST5, BLOWFISH, TWOFISH, are examples for symmetric encryption process where the positions are occupied by units of algorithm [28,29]. Generally, it's categorized as one of two: plaintext (commonly characters or groups of characters) that stream ciphers or block ciphers. are able to shift according to a regular system in which a permutation of the plaintext is constituted accordingly. Thus, the order of units is clearly changed (the plaintext is reordered). Stream cipher : Mathematically, a bijective function is used on the characters' A stream cipher can be operated on a single bit (byte or positions for encrypting and decrypting respectively. Generally, computer word) and encrypted bits individually at a time. Rail Fence cipher, Detection and cryptanalysis, Route cipher, Basically, this process can be achieved when a bit from a key Columnar transposition, Double transposition, Combinations stream is added to a plaintext bit. It's worth mentioning that and Fractionation, Myszkowski transposition, Disrupted there are two types of stream ciphers known as synchronous transposition and Grilles are all considered as some of stream ciphers where a key stream depends mainly on the key transposition cipher techniques[25]. and asynchronous stream ciphers in which a key stream They are two types of transposition cipher: depends on the ciphertext, for example: ISAAC, Quad, Fish, RC4 and SEAL[30].  Keyless transposition: (a) RC4 Cipher Keyless ciphers are a method in which characters are permuted by implementing writing plaintext in a specific way that differs RC4 is officially known as ''Rivest Cipher 4" which's named form a way of reading. Essentially, the whole ciphertext can't after Ron Rivest who designed a stream cipher in 1987, as both be produced unless the permutation is carried out on the entire encryption and decryption process use the same algorithm. plaintext. The rail fence cipher is example of keyless Basically, the algorithm bases are operating on the use of transposition. random permutation. The encryption and decryption procedures include two main processes, the first process is key  Keyed transposition: scheduling algorithm (KSA) a changeable length key from 1 to The key is a method where the plaintext is divided into groups 256 bytes is used for initializing a 256-byte state table, the of predetermined size called blocks, and then characters are second process is the pseudorandom generation algorithm permuted by using a key in each block separately. The (PRGA), data stream is simply composed of XORed and series Columnar is considered as an example of keyed transposition. of generated keys, while key stream doesn’t rely on plaintext in general. Due to its simplicity, vernam stream cipher is widely

used as it's depends on variable key-size[31]. The schematic Modern cryptography representation of RC4 is shown in Fig. 2. Modern cryptography is based on strongly scientific approach in which cryptographic algorithms around computational are designed in a way that supposedly to be difficult for an adversary to break. Theoretically, such systems are not unbreakable, even so they are infeasible in terms of resisting practical adversary attempts. Generally, information is considered to be theoretically secure schemes that provably cannot be broken, even though they are less practical than computationally-secure mechanisms. One-time pad is an example of such systems. Below are two main types of modern cryptography [26,27]:  Symmetric key cryptography.  Asymmetric key cryptography. Figure 2: Schematic representation of RC4[31]

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It is frequently used in file encryption and communications forward the notion of Salsa20; it is considered one candidates security such as SSL. The RC4 algorithm is also used in the of the stream, a new synchronous stream cipher. He found it WEP (wireless equivalent privacy) protocol to serve reasonable if utilizing uncomplicated operations like addition, confidentiality purpose. Moreover, it was used by many other XOR, constant distance rotation, and non-multiplication of S- email encryption products. Expectedly, the cipher can operate boxes. This step shows development of a quite fast primitive too fast in software. The algorithm can be effectively used in which is immune to timing attacks, by construction. There was both software and hardware due to its simplicity, speed, and transmission of Salsa20 to phase 3 without significant attacks easiness. Basically, it was believed to be secure until it was recognized. Moreover, a Hash function of 64-byte input and 64- unprotected to the BEAST attack [32]. byte output is considered as a core of Salsa20. A stream cipher is manifested in counter mode by employing the Hash function. (b) Salsa20 The encryption of a plain text of 64-byte block is achieved by Stream ciphers are short of proficiency and safety; therefore, hashing the key, block number, and XOR-ing outcome of a ECRYPT is employed to manage and coordinate the plaintext, a function done by Salsa20. Below is the definition eSTREAM of multiyear effort for the identification of novel of Salsa20/r algorithm [33]: stream ciphers for common implementation. Brenstein put

푧 푦 z1 = y1 ⊕ ((y0 + y3) <<< 7) 0 0 푧1 푦1 z2 = y2 ⊕ ((z1 + y0) <<< 9) [ 푧 ] = 푞푢푎푟푡푒푟푟표푢푛푑 [ 푦 ] → (3) 2 2 z3 = y3 ⊕ ((z2 + z1) <<< 13) 푧3 푦3 { z0 = y0 ⊕ ((z3 + z2) <<< 18)

Rowround Operations______푦 푦 푦 푦 ( z , ,. z , z ) = 푞푢푎푟푡푒푟푟표푢푛푑(푦 , 푦 , 푦 , 푦 ) 0 1 2 3 0 2 3 0 1 2 3 푦4 푦5 푦6 푦7 ( z5, z6, z7, z4) = 푞푢푎푟푡푒푟푟표푢푛푑(푦5, 푦6, 푦7, 푦4) [ 푦 푦 푦 푦 ] → (4) 8 9 10 11 ( z10, , z11, z8, z9) = 푞푢푎푟푡푒푟푟표푢푛푑(푦10, 푦11, 푦8, 푦9) 푦 푦 푦 푦 12 13 14 15 {( z15, z12, z13, z14) = 푞푢푎푟푡푒푟푟표푢푛푑(푦15, 푦12, 푦13, 푦14)

Columnround Operations______푦 푦 푦 푦 ( z , z , z , z ) = 푞푢푎푟푡푒푟푟표푢푛푑(푦 , 푦 , 푦 , 푦 ) 0 1 2 3 0 4 8 12 0 4 8 12 푦4 푦5 푦6 푦7 ( z5, z9, z13, z1) = 푞푢푎푟푡푒푟푟표푢푛푑(푦5, 푦9, 푦13, 푦1) [ 푦 푦 푦 푦 ] → (5) 8 9 10 11 ( z10, z14, z2, z6) = 푞푢푎푟푡푒푟푟표푢푛푑(푦10, 푦14, 푦2, 푦6) 푦 푦 푦 푦 12 13 14 15 {( z15, z3, z7, z11) = 푞푢푎푟푡푒푟푟표푢푛푑(푦15, 푦3, 푦7, 푦11)

Salsa20(x) = x + (rowround (columnround (x)))R

The R and r stand for both, double rounds and number of brought into play for two dissimilar messages. The Salsa20 ciphering rounds respectively; that means, (r = 2Rs). Three quarter-round diagram is shown in Fig. 3. variants of rounds are manifested by Salsa20 stream cipher: Salsa20/20, having 20 ciphering rounds; Salsa20/12, a reduction of Salsa20 from 20 rounds to 12 rounds; and Salsa20/8, a diminution of Salsa20 from 20 rounds to 8 rounds. Image matrix is a binary sequence of 8×R×C length, where R stands for the number of rows and C for the number of columns. Salsa algorithm generates a keystream- a set of pseudo-random 64-byte stream which is equal to image matrix size. To obtain the cipher image below, each 64-byte block of keystream is XOR-ed with its equivalent 64-byte block in the plain-image as follows: Cipher_image (i) = Keystream(i) ⊕ Plain_image (i) (6) where, i ={0,1, 2,...,264-1}. The Salsa20 key is a uniform haphazard sequence of bytes, and the same nonce is never Figure 3: Salsa20 quarter-round diagram [34]

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Block cipher : The Block cipher is characterized by its ability to encrypt both single and entire block of plaintext bits at a time using the same key. Obviously, all plaintext bits in the same given block will depend on each other during the encryption process. Practically, the vast majority of block ciphers are either have a block length of 128 bits (16 bytes) such as the advanced encryption standard (AES), or a block length of 64 bits (8 bytes) such as the data encryption standard (DES) or triple DES (3DES) algorithm.

Moreover, there are other block cipher methods such as Blowfish, Serpent, Twofish, Camellia, CAST-128, IDEA, RC2, Figure 4: Flowchart of 3DES encryption and decryption RC5, SEED, ARIA, Skipjack, TEA, XTEA [35]. algorithm [40]. (a) Data Encryption Standard(DES) DES was evolved in 1974 by an IBM team and was adopted as (c) Advanced Encryption Standard (AES) a national standard in 1997. Therefore, it was approved by Joan and Vincent Rijmen were the two scientists who NIST (National Institute of Standards and Technology) as the developed AES in 2000 by using Rijndael block cipher. Both first encryption standard. of Rijndael key and block length are128, 192 or 256 bits. DES is simply a 64– bit block cipher under 56– bit key. Generally, Rijndael will implement 9 processing rounds in case Basically, algorithm and primary alteration are operated both the key length as well as the block key is 128 bit, but if together as sixteen rounds block cipher and a final alteration. It either the block or the key is 192 bit, Rijndael will implement has been discovered that there is a proportional correlation 11 processing rounds, while Rijndael implements 13 between the number of rounds and the amount of time required processing rounds if it's 256 bit [39]. Basically, algorithm for finding a key through the usage of brute- force attack. When would act rather different as a result to each encryption key size, there is an increase to the number of rounds, there is an accordingly, when the key size increases, it will have a double- automatic increase to the safety of algorithm. In the recent facet function: the number of the bits increases for rushing data, decades, DES applications have been widely implemented in and the complication of the cipher algorithm increases [42]. many fields such as commercial, Military, and so on[36]. Round 10 slightly different from others where the Mix Column Although the DES standard was publicly revealed, its design step is not performed in this round. criteria has been remained classified. As result, the design has  Byte Substitution (SubBytes): A four rows and four caused considerable controversy especially when it comes to columns matrix is the upshot of the independent operation selection of a 56-bit key [37]. of the nonlinear byte substitution on each byte of the State (b) Triple DES (TDES) using the SBox table known as SubByte transformation. Due to the development of key searching, a triple DES (3DES)  Shiftrows: There is a left- shift movement of the four rows algorithm has become crucially required as a substitute for a of the matrix. The last three rows of the State witness a DES. Basically, TDES is considered as the strongest encryption cyclical shift over 1, 2 and 3 bytes, respectively; there is algorithm due to the use of three round message which simply no shift in the first row. Shifting with respect to each other, stretches the main size of DES when the algorithm is a new matrix with the same 16 bytes is the consequence. implemented three times respectively using three diverse keys.  MixColumns: A specific mathematical task is used for the Noticeably, a joint key size of 168 bits(three times size 56), is transformation of each column of four bytes. The input of far enough away from a brute–force [36]. Furthermore, the use four bytes and four novel bytes in one column and are of two different keys for the encryption algorithm is another taken by the task, there is substitution of the former by the option to reduce the memory requisite of keys in TDES as it is later. The process is not implemented as a final step and available today and used in internet protocol. Although, TDES the outcome is another matrix of 16 new bytes. is very secure (used in most banks to keep valuable business deals safe), but it is very slow and consuming too much time  Addroundkey: The matrix has 16 bytes and they are seen [39]. Fig.4 is a Flowchart of 3DES encryption and decryption as 128 bits XORed to 128 bits of the round key. As the algorithm. process continues, a new another analogous round takes place, but if it is the step, the output is the ciphertext.

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Asymmetric Key Cryptography In the above Fig. 5., P is chosen on the curve and is used as an element of public key while any random of integer K is taken The technique that uses different keys in a process of as the private key. K is a scalar and Q is also point on an elliptic encrypting and decrypting data is called Public Key curve can be calculated Q = K*P, where P, Q ∈ E(K) and P+Q Cryptography (PKC). Essentially, a public key is used for ∈ E(K). Finally, the sum of points P and Q is an equal to the R encrypting data, while a private key is used for decrypting data. is a reflection in the x-axis of the third point at which this line Public Key Cryptography rely on mathematical one–way intersects the curve. E, P, n and Q together makes the entire functions which are easily calculate but it is hard to calculate public key. their inverse function. Generally, PKC disadvantage is that it's slower than symmetric key cryptography [43]. This method some time used in color filtering array of real images taken CHAOTIC TECHNIQUES from camera [44, 45]. The following are the diverse algorithm within asymmetric key cryptography: RSA, DSA, YAK, Diffie Chaos in dynamical systems has got its share of investigation Hellman, El Gamal, Merkle's Puzzles, ECC. for a long-time span. With the advent of fast computers, the last two decades witnessed a dramatic increase in the numerical (a) Elliptic Curve Cryptography (ECC) investigations on chaos. Two examples are to be taken into Elliptic curve cryptography [46,47], based on elliptic curves account: Chaotic map and Hyper-chaotic map. over limited domains, is the public key device. Neal Koblitz and Victor Miller were the ones who individually put forward the technique in 1985. It provides many facilities in over other Chaotic map public cryptosystems one main of which is that it provides a The logistic map [49,50] is considered as the simplest chaotic smaller, faster public key cryptosystem. A 160-bit key in ECC map and the most transparent systems in which order to chaos is considered as safe as 1024-bit key in RSA. It is based on the transition is obvious. Being a discrete dynamical system, the Elliptic Curve Discrete Logarithm issue, recognized as NP- logistic map is defined by, Hard problem. The definition of an elliptic curve is revealed by the equation, xi+1 =  xi (1−xi) (8) 2 3 푌 = 푥 + 푎푥 + 푏 (7) where 0 ≤ xi ≤ 1 and 0 ≤  ≤ 4. The chaotic behavior is achieved In the equation, a finite field is represented by a , b and Pn when 3.57< ≤4 as shown in Fig. 6. elements, P is a prime larger than 3, and 4a3 + 27b2 ≠ 0. The overall points on the curve are the group of ordered pairs (x, y) and selected items in the field and such as x and finite field (P ≠ 2 or 3), two affine points and distinct x-coordinates are added, and the result of addition or subtraction in the field is ignored. The elliptic curves graph as shown as in Fig. 5.

Figure 6: The bifurcation diagram of the 1D logistic map [50]. Logistic map used by [51] for encrypting image, the encryption scheme is consisting of two steps: permutation and diffusion process as shown as in Fig.7.

Addition: P + Q = R.

Figure 5: An elliptic curve graph [46]. Figure 7: Encryption Structure [51].

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Encryption process logistic map with same initial value that was used in encryption process. Then, the permutation and diffusion will be used to The image encryption process includes permutation and retrieval the original image. diffusion process. The chaotic logistic maps are used to generate random sequence to scramble and diffuse the original image pixels. In permutation process, pixels of the original Hyper-chaotic map image will be scrambled in spatial domain. While in diffusion process, the randomly generated binary sequence will be Hyper-chaotic map is a high-dimensional chaotic system and masked with bits of pixel in the original image. Encryption considered safer than the low-dimensional chaotic maps when process is explained in details as follow: used in encryption algorithms because the high-dimensional chaotic systems have a better sensitivity, larger key space, more (a) Permutation process: pixels of original image will be randomness and complex dynamic characteristics such as 5-D scrambled based on the random sequence generated from multi-wing hyper-chaotic system [52] is defined as follow, logistic map. 푋 = −푎푋 + 푌푍 (b) Diffusion process: based on the random integer sequence is generated by (9) the scrambled image pixel bits are 푌 = −푏푌 + 푓푊 shifted either right side (if odd) or left side (if even). 푍 = −푐푍 + 푔푈 + 푋푌 (10) 푟푛푑_푠푞 = 푚표푑(푥 × 232. 256) (9) 푖 푖 푈 = 푑푈 − ℎ푋 The random binary sequence will be generated by sine map 푊 = 푒푊 − 푌푋2 and cubic map, the scrambled image pixel bits is changed according to generated sequence. Finally, the cipher image is produced by convert the random binary sequence to inter Where X, Y, Z, U, W represent state variables, a, b, c, d, e, f, g, sequence and this process will be repeated two rounds. h represent real parameters of system (10). Fig. 8 Phase portraits of the system (10) attractor with parameters a=10, b=60, c=20, d=15, e=40, f =1, g =50, h =10. Decryption process

A decryption process is deemed to be an inverse method for an encryption process. First, the random sequence is generated by

Figure 8: Phase portraits of system (10) (a) 3D viewed in X–Y–Z space; (b) projection on X–Y plane; (c) projection on X–Z plane; (d) projection on Y–Z plane; (e) projection on X–W plane; (f) projection on Z–U plane [52].

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5-D multi-wing hyper-chaotic system is used by [52] for (b) Bit-level permutation process: it is responsible to change encryption image, this encryption scheme has one round bits of the pixel by recreate four new bytes and combining consisting of three steps: pixel-level permutation, bit-level them to change bits of each byte. The sequence A will be permutation and diffusion process as shown as in Fig.9. divided into MN/16 which are 4x4, then multiplying 4x4 matrix and constant matrix to get a new 4x4 matrix, the

multiplication is repeated until executed all MN/16 Initial keys matrices. MN/16 matrices will be combined to obtain a matrix Dm×n. (c) Diffusion process: can enhance the robustness encryption

Chaotic system system against differential attack and statistical attack by using a key stream strongly related to plain image. The key stream created by using chaotic sequence L according to (12):

Chaotic sequence Chaotic sequence 퐾푖 = 푚표푑(푎푏푠(퐿푖) − 푓푙표표푟(푎푏푠(퐿푖))) × 10, 256) (12)

The pixel values of the image matrix Dm×n will be encrypted by (13) and (14):

Plain image Pixel-level Bit-level Diffusion Cipher image permutation permutation 퐶1 = 푚표푑(퐷1 + 퐶0 , 256) ⨁ 푚표푑(푄1 + 퐾1 , 256) (13)

퐶푖 = 푚표푑(퐷푖 + 퐶푖−1 , 256) ⨁ 푚표푑(푄푖 + 퐾푖 , 256) (14) Figure 9: The encryption process [52] where C0 is a constant, in addition to can be used as the

encryption key Encryption process The ciphered image will be obtained by repeating the (13) and The encryption process includes generating chaotic sequence (14) until i=MN. keys by 5-D multi-wing hyper-chaotic system which related to

characteristics of plain image, according to these sequence keys the plain image pixel will be shuffled by implementing pixel- Decryption process level permutation, to increase the security of the cryptosystem A decryption process is considered as an inverse method for the bit-level permutation is used. Finally, a diffusion operation encryption process. First, generating a chaotic sequence from is used to get cipher image. Encryption process is explained in chaotic system. Then, inverse the diffusion process by (15) to details as follow: restore the shuffled image D' and divided it into MN/16 (a) Pixel-level permutation process: A process in which the matrices and inversion matrix to implement inverse operation correlation of adjacent pixels of a plain image is of bit-level permutation. Finally, carry out inverse operation of disintegrated, done by covert a plain image matrix IMxN to pixel-level permutation to obtain the plain image P`.

one dimensional vector P={p1,p2,p3,···,pm×n}, then ′ ′ 퐷푖 = 푚표푑((퐶푖 ⊕ 푚표푑(푄푖 + 퐾푖 , 256) + 256) − 퐶푖−1, 256) calculating the summation of all pixels of the plain image i = 2, 3, …. mxn (15) and calculating the initial keys X,Y,Z,U,Z of chaotic system(10) according to (11) : (11) 푠푢푚 + 푆푧 PERFORMANCE METRICS 푥 = 푘 1 223 + 푆푧 To have a thorough scrutiny of the techniques, diverse 6 푥푖 = 푚표푑(푥푖−1 × 10 , 1) 푖 = 2, 3, 4, 5 parameters have been put into work. The current section tackles all the parameters in detail. The chaotic system (10) will be created by make iterations for T0+MN times and to avoid any harmful effects the former T0 values will be discarded. The chaotic sequence Visual Assessment has MN elements, L={L1,L2,L3,···,Lm×n}, sorting the chaotic sequence in ascending order according to the vector For an efficient encryption method, the encrypted images must position in the initial chaotic sequence. The image pixel not have any visual information. They should be arbitrary and positions P will be permuted by applying the sorted highly disordered so that there will impossible for any intruder sequence of L to get shuffled image to guess even a part of the encrypted image. Q={Q1,Q2,Q3,···,Qm×n}.

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Key-Space Analysis Differential analysis Sensitivity to keys and initial parameters used in encryption Sensitivity to minor changes in key and plain image is should be a basic feature of image encrypted schemes. prerequisite to encrypt any image. Generally, numbers of pixel Reduction of brute force attacks is due to large key space. Large change (henceforth NPCR) and unified changing intensity stands for the key space while stands for the time taken to (henceforth UACI) are calculated in encryption scheme for decode the key. evaluating the changes in a single bit of key or in any pixel value in the plain-image. NPCR is utilized for measuring the

changes in the rate of pixels number in cipher image if there is Statistical Analysis modification on only one bit of key or pixel. The symmetrical plain images of the two ciphered images are assumed to be only It is a method in which confusion and diffusion properties of an one- pixel disparity. The grayscale level values of ciphered encrypted image are analyzed. Evaluation of correlation images C1, C2 at row i, and column j are all labeled as C1(i,j) coefficients signifies how strongly the pixels are related to each and C2(i,j), respectively. NPCR is calculated by using other and histograms demonstrate pixel relation in frequency equation(13). domain. Correlation analysis and histogram analysis can specify which technique has better features of confusion and ∑푖,푗 퐷(푖, 푗) 푁푃퐶푅 = × 100% (13) diffusion that show a great resistance to statistical attacks. 푀 × 푁 where M and N are the width and height of two random images and D(i, j) is defined as in equation (14). Histogram Analysis 1, 푖푓 퐶 (푖, 푗) ≠ 퐶 (푖, 푗) Frequency of pixel value shows the histograms of images. 퐷(푖, 푗) = 푓(푥) = { 1 2 (14) 0, 표푡ℎ푒푟푤푖푠푒 There is a thorough statistical discrepancy between the histograms of encrypted images and the original images. Moreover, UACI can be used to measure the average of Uniformity of the histograms in encrypted images is an integral intensity for contrast in color component between the two part for resisting statistical histogram's attacks. cipher images C1(i, j) and C2(i, j), are calculated using equation (15).

1 퐶1 (푖, 푗) − 퐶2(푖, 푗) Correlation Analysis 푈퐴퐶퐼 = [∑ ] × 100% (15) 푀 × 푁 푖,푗 255 This parameter calculates the correlation among the adjacent pixels of an image. A good encryption technique should result into an encrypted image with no or zero correlation between Key Sensitivity pixels close to each other. This term is used when even a little distinct key is created, the A correlation between pairs of plain and cipher image channels result will be a completely dissimilar cipher image. Two has been analyzed in order to test a correlation between two divergent cipher images are measured by the computation of adjacent pixels in two plain and cipher images. Equations NPCR and UACI; the original key is normally used to encrypt below (9-12) illustrate how the correlation coefficients in one whereas one bit change in the key is used to encrypt the horizontal, vertical and diagonal directions are calculated. other. 푐표푣푎푟푖푎푛푐푒 (푥,푦) NPCR > 99% and UACI around 33% illustrates the possibility 푅푥푦 = (9) √퐷(푥) √퐷(푦) of the scheme to resist differential attack. 푁 1 퐸(푥) = ∑ 푥 (10) 푁 푖 푖=1 Pixel/Plain image sensitivity 푁 1 It means that an entire individual encrypted image is the result 퐷(푥) = ∑(푥 − 퐸(푥))2 (11) of even tiny change in a plain image. The two encrypted images 푁 푖 푖=1 are differentiated by calculating NPCR and UACI. A plain 푁 image shows one bit change then encryption employing the 1 푐표푣푎푟푖푎푛푐푒 (푥, 푦) = ∑(푥 − 퐸(푥))(푦 − 퐸(푦)) (12) same key and initial parameters for the formation of the second 푁 푖 푖 푖=1 cipher image and the first constituted from the original image. The scheme showing NPCR over 99% and UACI over 33% is In above formulae, x and y stand for adjacent pixels, while N considered to be secure against differential attack and to be represents the overall number of duplets (x, y) that obtained highly sensitive to pixel change. from the image.

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Information Entropy Analysis is 255 when having pixel of 8 bits per sample, Formula used for calculation of PSNR are given based on equation (17,18): The degree of arbitrariness in image content is referred to as information entropy. The calculation of entropy H(S) of 1 푚−1 푛−1 푀푆퐸 = ∑ ∑ [퐼(푖, 푗) − 퐾(푖, 푗)]2 (17) message m is illustrated in equation(16). 푚푛 푖=0 푗=0 푁−1 1 퐻(푚) = ∑ 푃(푚 ) log (16) 푖 2 푃(푚 ) 2 푖 푀퐴푋퐼 푖=0 푃푆푁푅 = 10 푙표푔 (18) ⋅ 10 푀푆퐸 Where P(mi) refers to probability of symbol mi occurrence and log denotes base 2 logarithm. The notion of randomness is proposed as a result of the occurrence of 256 likely results of Computational Speed Analysis the message m with the same probability. In this case, H(m) = 8 which is deemed an ideal value. The security of the The process of encryption should be fast and not time- encryption algorithm against entropy attack is highlighted consuming even for bulky images. The types of processor, when the entropy value is close to 8. programming language and encryption techniques are decisive for computational speed.

Peak Signal to Noise Ratio (PSNR) analysis Results In this analysis, both of image and encrypted image are referred to signal and noise respectively. Basically, MSE represents a Visual Assessment collective squared error between stego and original image. Results of various techniques for have been given in Table 1, There is proportional relation between MSE and error in which in this paper all techniques used Lena image size (256*256) for lower value of MSE is the lower error. Below is the relation encryption processes. between m x n monochrome image. Thus, MAX indicates the maximum value of image pixel. Generally, the value of image

Table 1: Plain, encrypted and decrypted images

Encryption Type of Technique Plain image Encrypted image Decrypted image Technique

Polyalphabetical Vigenère Cipher

Substitution

RC4

Steam Cipher Symmetric Salsa20

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DES

Block Cipher 3DES

AES

ECC

Asymmetric

Chaotic

map[49]

Techniques

Hyper-chaotic

Chaotic map[50]

Key Space Analysis Table 2 gives the comparison of key space of all the techniques Throughout the application of all the diverse schemes in the implemented. current research, it becomes very obvious that the scheme that the hyper-chaotic has large key space but the Salsa20 map has Table 2: Key Space Analysis largest one. Cipher Key length Key space Vigenère 128 2128 Statistical Analysis RC4 256 2256 Salsa20 256 2320 To avoid statistical attacks histogram analysis and correlation DES 56 256 analysis should be done. The results of these both analysis have been shown in sections below. 3DES 168 2168 AES 128 2128 ECC 2*64 2128 Chaotic map[49] 3*50 2150 Hyper-chaotic map[50] 273 2273

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Histogram analysis Table 3: Histogram analysis Encryption Type of Technique Plain image Encrypted image Decrypted image Technique

Polyalphabetical Vigenère Cipher

Substitution

RC4

Steam Cipher

Salsa20

DES Symmetric

Block Cipher 3DES

AES

ECC

Asymmetric

Chaotic map[49]

Hyper-chaotic Chaotic Techniques map[50]

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In table 3, one can intuitively see the discrepancies in the At one bit change in the original image, NPCR and UACI are histograms of the images encrypted that were the product of the compared. The results show the efficiency of RC4 and chaotic application of the many different ways of cryptography. It is to map for NPCR but the best is hyper-chaotic map as it is clear be noted that RC4 and Slasa20 cryptography, provide a in Table 6. Along with the efficiency of the aforementioned satisfying histogram yet the chaotic map and the hyper-chaotic techniques the RC4 and logistic map have comparable results map was to be the pre-eminent among all as it is the most for UACI result, but hyper-chaotic map proves to be the best. standardized one and prevents revealing any data when the intruder tries to do some synthesis on the histogram of the encrypted image. Entropy Analysis This section includes results for key and pixel sensitivity on three different size of images. Correlation analysis Table 7: Entropy Analysis

Table 4: Correlation analysis Plain image sensitivity Entropy Vigenère 7.7943 Cipher Horizontal Vertical Diagonal RC4 7.9968 Vigenère 0.0892 −0.0907 −0.0758 Salsa20 7.9970 RC4 −0.0020 −0.0037 0.0039 DES 7.9959 Salsa20 0.0430 0.0383 0.0117 3DES 7.9966 DES 0.0159 0.0558 0.0069 AES 7.9965 3DES 0.0332 0.0455 −0.0049 ECC 6.7694 AES −0.0045 0.0039 −0.0042 Chaotic map[49] 7.9972 ECC 0.3279 −0.3445 0.3502 Hyper-chaotic map[50] 7.9972 Chaotic map[49] 0.0007 0.0086 −0.0057 Measuring entropy in the encrypted images is shown in Table Hyper-chaotic map[50] −0.0015 −0.0032 0.0008 7 where Salsa20 and RC4 have high entropy but the chaotic and hyper-chaotic maps are the highest. Depending on the analysis provided by Table 4, chaotic map and hyper-chaotic map cryptography appears to be the PSNR Analysis unrivalled as it has the least correlation of all among adjacent pixels. On the other hand, the AES cryptography and RC4 This section includes results for key and pixel sensitivity on stream cipher manifest less correlation but not least. three different size of images. Table 8: PSNR Analysis

Sensitivity Analysis Cipher PSNR This section includes results for pixel sensitivity of images. Vigenère 9.7637 Table 6: NPCR and UACI analysis for modified pixel RC4 8.3781 Salsa20 8.4642 Plain image sensitivity NPCR UACI DES 8.4698 Vigenère 0.0015 0.00006 3DES 8.4548 RC4 99.6172 33.5834 AES 8.4021 Salsa20 0.0015 0.0006 ECC 7.9017 DES 0.0216 0.0040 Chaotic map[49] 8.2674 3DES 0.0217 0.0063 Hyper-chaotic map[50] 8.1216 AES 0.0354 0.0137 Elliptic Curve 97.0156 33.4745 PSNR analysis is shown by Table 8. For a good encryption, low Chaotic map[49] 99.65 33.55 values of PSNR are appreciated. Hyper-chaotic has good PSNR Hyper-chaotic map[50] 99.61 33.46 value closely followed by chaotic. ECC shows the best PSNR results.

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Computational Time Analysis The present study investigates the different types of methodologies used for image encryption via providing an in- Table 9: Computational Time Analysis depth comparison. The similar and the different points of Cipher Encryption time ciphers depending on the chaotic encryption technique are Vigenère 0.01634 mentioned whether these ciphers are traditional, modern or even more recent ones. This idea is highlighted in cases where RC4 0.23275 chaotic techniques brings about the best encryption results. Salsa20 1.3875 Table 10 is a synopsis of all the outcomes in situations where DES 49.1286 the schemes are scored depending on their achievements. The 3DES 143.7368 overall score is the decisive factor for showing chaotic techniques as the best among all. There are many positive AES 169.4769 attributes of chaotic techniques. It is the best among all because ECC 202.1892 the pixels are extremely uncorrelated. The time needed for the Chaotic map[49] 0.37168 process of searching is enhanced in having safe measures in Hyper-chaotic map[50] 0.45343 hyper-chaotic technique. Another feature which puts the chaotic techniques in the first place is its uniformity of

histograms. PSNR value of ECC is the lowest, as a Encryption should be done in least time and hence RC4 and consequence, AES, RC4 exhibits effective outcomes closely chaotic map cryptographies are better than others as shown in followed by chaotic techniques. To add more, it has a high Table 9. But Vigenère proves to be the fastest amongst all. value of entropy and it is highly sensitive to a single bit change in original pixel or key. CONCLUSION Table 10: Analytical comparison of cryptographic techniques

Techniques Key space Histogram Correlation Pixel sensitivity Entropy PSNR Computationa Implemented analysis analysis l time Vigenère Poor Very poor Very poor Very poor Moderate Moderate Excellent RC4 Good Good Good Excellent Good Good Good Salsa20 Excellent Good Moderate Very poor Good Good Good DES Very poor Moderate Moderate Very poor Good Good Very poor 3-DES Poor Moderate Moderate Very poor Good Good Very poor AES Poor Good Moderate Very poor Good Good Very poor ECC Poor Moderate Moderate Good Poor Excellent Very poor Chaotic map[49] Poor Excellent Excellent Excellent Excellent Good Good Hyper-chaotic map[50] Good Excellent Excellent Excellent Excellent Good Good

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