A Simple Chaos Based Image Encryption Scheme Using Diffusion Technique Computer Science Essay

With the proliferation of the Internet and ripening of the digital signal processing engineering, applications of digital imagination are prevailing and are still continuously and quickly increasing in recent old ages. Yet the chief hurdle in the widespread deployment of digital image services has been implementing security and guaranting authorised entree to sensitive informations. Compared with text encoding, which most bing encoding criterions purpose at, image encoding ( or more by and large, multimedia encoding ) has its ain intrinsic features and particular characteristics with many alone specifications. In this respect, the pandemonium based cryptanalytic algorithms have suggested developing a new and efficient manner of unafraid image encoding techniques.

In this respect, we propose a new attack for image encoding strategy based on helter-skelter logistic maps in order to run into the demands of the secure image transportation. In the proposed image encoding strategy, an external secret key of 15 denary figures and two helter-skelter logistic maps are employed. The initial conditions for the both logistic maps are derived utilizing the external secret key by supplying different weightage to all its spots. Further, in the proposed encoding procedure, simple type of operations is used to code the pels of an image and is decided by the result of the logistic map. To do the cypher more robust against any onslaught, the secret key may be modified after coding and logistic map is used twice a clip. From the consequences of several experimental, cardinal infinite analysis, statistical analysis, and cardinal sensitiveness trials show that the proposed image cryptosystems provides an efficient and unafraid manner for real-time image encoding and transmittal from the web security point of view.

KEYWORDS: Chaos, Logistic map, Image Encryption and Cipher.

1. Introduction

In recent old ages all communicating system, including orbiter and cyberspace, it is impossible to forestall unauthorised people from listen ining. When information is broadcasted from a orbiter or transmitted through the cyberspace, there is a high hazard of information interception. Security of still image, picture, multimedia and information has become progressively of import for many applications including picture conferencing, secure autotype, medical, and military applications. Two chief groups of engineerings have been developed for this intent. In the first group is content protection through encoding, for which a key is required for proper decoding of the information. In the 2nd group is digital watermarking, which aims to implant a message into the multimedia informations. These two engineerings could be used complementary to each other.

In secured communications utilizing encoding, which is the focal point of the recent work, the information under consideration is converted from the apprehensible signifier to an unintelligible construction utilizing certain crude operations at the sender.In the go outing Data encoding technique is chiefly performed by scrambling the content of informations, such as text, image, sound, picture and so forth to do the information indecipherable, unseeable or inexplicable during transmittal. The encrypted signifier of the information is so transmitted through the insecure channel, i.e. cyberspace, orbiter, etc to the receiving system. At the intended receiver side, nevertheless, the information is once more converted back to an apprehensible signifier utilizing decoding or contrary operation and therefore the information is conveyed firmly. It should be noted that the same keys steer both these encoding and decoding operations. Such encoding system is grouped under private cardinal cryptanalysis.

In peculiar, an image-scrambling strategy transforms an image into another unintelligible image, based on keys merely known to the transmitters and the receiving systems. The cardinal techniques to code a block of pels are permutation and substitution. Substitution replaces a pel with another one ; substitution changes the sequence of the pels in a block to do them indecipherable.

In recent old ages, helter-skelter maps have been employed for image encoding. Most helter-skelter image encodings ( or encoding systems ) use the permutation-substitution architecture. These two procedures are repeated for several unit of ammunitions, to obtain the concluding encrypted image. For illustration, in [ 4 ] , Fridrich suggested a helter-skelter image encoding method composed of substitution and permutation. All the pels are moved utilizing a 2D helter-skelter map. The new pels moved to the current place are taken as a substitution of the original pels. In the permutation procedure, the pel values are altered consecutive. Chen et. Al. employed a 3-dimensional ( 3D ) Arnold cat map [ 5 ] and a 3D Baker map [ 6 ] in the substitution phase. Guan et Al. used a 2D cat map for pixel place substitution and the discretized Chen ‘s helter-skelter system for pixel value dissembling [ 7 ] . Lian et Al. [ 8 ] used a helter-skelter criterion map in the substitution phase and a quantal logistic map in the permutation phase. The parametric quantities of these two helter-skelter maps are determined by a key-stream generated in each unit of ammunition. Mao et. Al. build a new image encoding strategy based on the drawn-out helter-skelter Baker map [ 6 ] . Zhang et. Al. first permute the pels of images with distinct exponential helter-skelter map, and so utilize ”XOR plus mod ” operation for permutation [ 9 ] . Gao et. Al. show the image encoding algorithm based on a new nonlinear helter-skelter algorithm utilizing a power map and a tangent map alternatively of a additive map. It besides uses a helter-skelter sequence generated by a nonlinear helter-skelter algorithm to code image informations utilizing XOR operation [ 10 ] . Zhou et. al. , suggest a parallel image encoding algorithm utilizing discretized kolmogorov flow map. All the pels are foremost permuted with a discretized helter-skelter map and so encrypted under the cypher block concatenation mode [ 11 ] .

There are nevertheless, some other helter-skelter image encoding systems with different constructions. For illustration, Pisarchik et Al. suggested an algorithm to change over image pels to helter-skelter maps coupled to organize a helter-skelter map lattice. The encrypted image is obtained by repeating the helter-skelter map lattice with secret system parametric quantities and figure of rhythms [ 12 ] . Pareek et Al. extended the construct of their text encoding to image encoding by utilizing two logistic maps and a cardinal [ 13 ] .

In this paper, a new permutation-substitution architecture utilizing helter-skelter maps and Tompkins-Paige algorithm is proposed. Our designed technique for address scrambling [ 14 ] is extended to planar ( 2-D ) substitution, and is applied to image substitution [ 15 ] . We have improved our work by utilizing helter-skelter maps and adding a permutation portion to an image encoding system. In the substitution stage, a logistic map is used to bring forth a spot sequence, which is used to bring forth pseudo random Numberss in Tompkins-Paige algorithm. A tent map is besides used in the permutation stage to merchandise a pseudo random image that is used to blend it with the permuted image. The substitution and permutation operations need two different keys, Key-P and Key-S, severally. Satisfactory security public presentation of the proposed system is achieved in merely one unit of ammunition and hence the entire encoding clip is short.

It has been proved that in many facets helter-skelter maps have correspondent but different features as compared with conventional encoding algorithms [ 1, 2, 3, 4 ] . Equally early as in 1989 [ 5 ] , a helter-skelter map was already used to plan a cryptanalytic algorithm. Although dedicated chaos-based image encoding strategies do non frequently appear in the literature, there does be some, which are briery discussed here. In [ 6 ] , an encoding method called CKBA ( helter-skelter key-based algorithm ) was proposed. The algorithm foremost generates a clip series based on a helter-skelter map, and so uses it to make a binary sequence as a key. Harmonizing to the binary sequence so generated, image pels are rearranged and so XOR or XNOR operated with the selected key. This method is really simple but has obvious defects in security, as pointed out recently in [ 14 ] : this method is really weak to the chosen/known-plaintext onslaught utilizing merely one plain-image, and moreover its security to brute-force onslaught is besides questionable. In [ 7 ] a helter-skelter Kolmogorov flow-based image encoding algorithm was designed. In this strategy, the whole image is taken as a individual block and permuted through a key-controlled chaotic system based on the Kolmogorov flow. In order to confound the informations, a permutation based on a shift-registered pseudo-random figure generator is applied, which alters the statistical belongings of the cipher-image. It was advocated that the strategy is computationally unafraid and superior to modern-day majority encoding systems when taking at efficient image and picture informations encoding. In [ 8 ] , a systematical method was suggested for accommodating an invertible planar helter-skelter map on a toroid or on a square, so as to make a symmetric block encoding strategy. Most image scrambling algorithms make usage of the quantisation scheme of coefficient. But it is unknown weather the map keeps chaos belongings after quantisation.

In this paper we perform a simple diffusion operations aims at cut downing clip complexness and pertinence in low power devices. The helter-skelter sequence is generated from logistic map, utilizing secret key agreement, initial seed, by utilizing two pandemonium maps which extends the cardinal infinite. The algorithm reduces iterative figure and makes usage of non deterministic helter-skelter belongings of map. Because of the strong abnormality of the new algorithm, the encrypted image possesses high-ranking security. In subdivision 2, a helter-skelter map system is discussed. We analyze the kineticss action of the logistic map in finite preciseness. In subdivision 3, the item of image encoding is described. In subdivision 4, we test the new algorithm and demo the high degree security. Section 5 is a decision.


The pandemonium can be generated by utilizing assorted helter-skelter maps. Here 1 D helter-skelter map is used to bring forth the helter-skelter sequence which is used to command the encoding procedure.

Logistic Map

A simple and well-studied illustration of a 1D map that exhibits complicated behaviour is the logistic map from the interval into, parameterized by I? :

Where 0 a‰¤ I? a‰¤ 4. This map constitutes a discrete-time dynamical system in the sense that the map generates a semi-group through the operation of composing of maps. The province development is described by.we denote

( ntimes ) – ( 2 )

For all, a “ discrete-time ” flight, where, can be generated. The set of points is called the ( forward ) orbit of x. A periodic point of g is a point such that for some positive whole number n. The least positive whole number N is called the period of x. A periodic point of period 1 is called a fixed point.

For differentiable g, a periodic point ten with period N is stable if

and unstable if


In the logistic map, as I? is varied from 0 to 4, a period-doubling bifurcation occurs. In the part, the map gI? possesses one stable fixed point. As I? is increased past 3, the stable fixed point becomes unstable and two new stable periodic points of period 2 are created. As I? is further increased, these stable periodic points in bend become unstable and each spawns two new stable periodic points of period 4. Thus the period of the stable periodic points is doubled at each bifurcation point. Each period-doubling episode occurs in a shorter “ parametric quantity ” interval, diminishing at a geometric rate each clip. Furthermore, at a finite I? , the period-doubling episode converges to an infinite figure of period doublings at which point pandemonium is observed.


1. Reading of Original image ( Im ) :

The original image is converted to grey graduated table if it is colour image.

Im = { Im I, J } , where and, H and W, severally, are height and breadth of the Original image in pels.

2. The secret key:

The secret key in the proposed encoding technique is a set of two drifting point Numberss and one whole number XINT= ( Aµ , Xo, rw ) ,

Where value is 3.987654321000001, Xo is initial value of the helter-skelter map, it is cardinal and its typical value is 0.123456789000001 ; and W is width of the image.

y= ( Aµ , X ( row ) , column )

Where its typical value is 3.963852741000001, X ( row ) is last value of x map and column is Height of the image.

Y k/R is the logistic map generated with the value said above and it is multiplied with the figure of columns and fixed as Column.

Similarly Y k/c is the logistic map generated with the value said above and multiplied with the figure of rows and fixed as row.

3. Then helter-skelter key value Y K is XOR’ed with original image.

FOR i=1 to row

y= ( Aµ , Y ( I ) , gap )

Y = Y * column ;

Y K = whole number ( Y )

FOR j=1 to column

Im ( I, J ) = Im ( I, J ) Yk ( J )



4.Again helter-skelter key value Y K is XOR’ed with original image.

FOR i=1 to row

y= ( Aµ , Y ( I ) , gap )

Y = y * row ;

Y K = whole number ( Y )

FOR j=1 to column

Im ( I, J ) = Im ( I, J ) Yk ( I )



Original Image

Secret Key

15 digit drifting point figure

Low-level formatting

For helter-skelter Maps

Chaotic Map- Logistic Map X/Row

Pixel values are XOR’ed with Chaotic bomber key

Transmitted through unbarred channel


Ykey /col

Ykey /row

Chaotic Map- Logistic Map Y/ColThe Proposed Scheme:




The proposed crypto system has a simple two helter-skelter maps. A logistic map was used to bring forth a spot sequence, which was in bend used to bring forth another logistic map, in this algorithm ; pels are transformed by simple diffusion procedures,

The security of the algorithm needs two different keys, YK-Row and YK-Column, severally. The entire cardinal length was 45 spots. Therefore, the cardinal infinite was 245, which was big plenty to protect the system against any brute-force onslaughts.

The image was a 2-D array of pels, each with 256 grey graduated tables. To better security of the proposed encoding system, the histogram needed to go unvarying.

All parts of the proposed helter-skelter encoding system were simulated utilizing a MATLAB 7.6 version. The histogram of the encrypted image was approximated a unvarying distribution. Therefore, the proposed encoding system was immune against any statistical onslaught. To quantify the difference between encrypted image and matching plain-image, three steps were used: Correlation and cardinal infinite analysis is performed. It was concluded that the correlativity and KSA standards of the proposed system were satisfactory when compared to other research consequences as was the security public presentation of the proposed system.