Selective Encryption Scheme for Vector Map Data using Chaotic Map

Abstract

With the rapid interest in Geographic Information System (GIS) contents, a large volume of valuable GIS dataset has been distributed illegally by pirates, hackers, or unauthorized users. Therefore the problem focus on how to protect the copyright of GIS vector map data for storage and transmission. But GIS vector map data is very large and current data encryption techniques often encrypt all components of data. That means we have encrypted large amount of data lead to the long encrypting time and high complexity computation. This paper presents the selective encryption scheme using hybrid transform for GIS vector map data protection to store, transmit or distribute to authorized users. In proposed scheme, polylines and polygons in vector map are targets of selective encryption. We select the significant objects in polyline/polygon layer, and then they are encrypted by the key sets generated by using Chaotic map before changing them in DWT, DFT domain. Experimental results verified the proposed algorithm effectively and error in decryption is approximately zero.

1. INTRODUCTION

The vector map, is also called GIS vector map, is a vector–based collection of Geographic Information System (GIS) data about earth at various levels of detail. Vector map is created and developed by the merging system of cartography, statistical analysis, and database technology based on vector model [1,2]. Vector data provide a way to represent real world features within the GIS environment because vector data has advantages as need a small space or place for storage data; has a high spatial resolution and graphic representation spatial data closely likes handed map; easily for making projection and coordinates transformation [3,4]. For those advantages, vector map is used in many domains, and GIS applications use vector map have provided general users with easy access to services via mobile devices or internet access. But the producing process of a vector map is considerably complex and the maintenance of a digital map requires substantial monetary and human resources. And any companies can buy it, make illegal copies from them and distribute or sell them easily many times without taking any permission from the original GIS data provider. Moreover, applications of vector map in military domain require the high security, and must be kept away from unauthorized users. So vector map is necessary to be protected and prevent illegal duplication and distribution of it.

Our paper is organized as follows. In section 2, we discuss the related works and in section 3, we explain the proposed selective encryption algorithm in detail. Then, in section 4 we perform experiments and discuss about the experimental results, evaluate the performance of algorithm. Finally, we conclude this paper in section 5.

 

2. RELATED WORKS

The GIS vector map data includes layers. Each layer is a basic unit of geographical objects which are described and managed in a map. These objects describe the topography and geographical features of real objects or a certain place. Each layer consists of an amount of vector data which uses pairs of coordinates to describe as point, polyline and polygon [5,6], as shown Fig. 1.

Fig. 1.An example GIS vector map; (a) Forest layer, (b) Road layer.

Officially, the point is used to present simple or small objects in the reality on the map while polyline and polygon are used to present complex and large objects. Polyline is used to represent objects as road, contour line, and railway, so on. Polygon is used to represent objects as building, area, lake, boundaries and so on. The general approach of selective encryption is to separate the content into two parts. The first part is the public part, which is un-encrypted and accessible by all users [7-11]. The second part is the protected part; it is encrypted.

From these reasons, our algorithm only performs selective encryption for polylines and polygons in GIS vector map. Only authorized users have access to protected part. Polylines and polygons are selected, and encrypted by the key sets generate from Chaotic map before changing them in DWT, DFT domain based on their geographical features [12,13]. Our algorithm encrypts only some coefficients in DWT domain by changing DC value in DFT domain but it changes the whole map.

 

3. PROPOSED ALGORITHM

Our method aim to encrypt GIS vector map perceptually and entirely using a few of selected values, it is called as vector map selective encryption.

3.1 Encryption process

The schematic diagram of the proposed technique is illustrated in Fig. 2, and the step-by-step procedure is explained hereafter.

Fig. 2.Schematic diagram for proposed encryption technique.

3.1.1 Object classification

Our algorithm only performs selective encryption for polyline/polygon in GIS vector map. However, each polyline/polygon layer has many objects and if we encrypt all of them, we also need many computation time. Each object has attributes such as the number of points (P), the area of bounding box (A), as shown in Fig. 3(a). Many objects are created from a few points and the value of bounding box’s area is very small when compare with other objects in a layer. This object is very simple and mark it as an insignificant object, as shown in Fig. 3(b). With objects include many points and the area of bounding box is larger than, it also complex than and mark it as a significant object, as shown in Fig. 3(c).

Fig. 3.An example about objects in a layer.

Thus, we used probability distribution to define thresholds in each layer and identify which object is a significant or insignificant object by comparing object’s features with thresholds.

The area threshold (Aith) and the point threshold (Pith) in a layer are defined as following:

3.1.2 Chaotic map

The classical chaos system is a logistic map, which can be defined by following:

Here 0≤μ≤4 is the coefficient of the map, k=0, 1, 2, . . . and all the values of {xi} appear in the range [0,1] for the initial value x0∈[0,1]. It is noted that Eq. (3) has the chaotic behavior [14,15] when μ appears in the range [3.57,4], and especially the chaotic behavior called Pomeau–Manneville scenario [16] when appears in the range [3.57,3.82].

3.1.3 Encryption block

We used the key to create two key sets (length of key set is 8) for a layer. It is created randomly the first key in each key set by SHA-512 algorithm from user key with key length is 512 bit. Other keys are generated by using Chaotic map as Eq. (3). Therefore, we have two key sets: a={ai|i∈[1,8]}, b={bi|i∈[1,8]} and DC encryption value:

For a significant object, using encryption block to encrypt it, as shown in Fig. 4(a) and illustrate in Fig. 5, the step-by-step procedure is explained hereafter.

Fig. 4.Proposed (a) encryption and (b) decryption process for vector map.

Fig. 5.Selective encryption process.

3.2 Decryption process

The reverse process is applied to decrypt the encrypted map. To perform decryption, after we calculate thresholds in a layer, we use the decryption block to decrypt the encrypted significant objects, as shown in Fig. 4(b). If correct key is employed at the time of decryption, then the decrypted map would by a replica of the original map. In the case of an incorrect decryption key, the output map is vary.

 

4. EXPERIMENTAL RESULTS

4.1 Visualization

Experimental results figure 6 and figure 7 show the proposed algorithm changes whole maps. The proposed method has much lower computational complexity than AES (Advanced Encryption Standard ) or DES (Data Encryption Standard) because we only select some coefficients in DWT domain and one DC value in DFT domain, encrypt it by key values.

Fig. 6.Experimental results of polyline/polygon layer.

Fig. 7.Experimental result with full scaling layers 1:5000: (a) original map, (b) encrypted map.

4.2 Distance measure

The distance between original map and encrypted map is computed by equation (5):

With L is a original map, Eʹ(L) is corresponding encrypted map, N is the total number of objects in original map. And d(Pij) is distance between corresponding objects in Eʹ(L) and L.

We used same original map to experiment with different passwords K1 # K2. Then we calculate D(Eʹ,L) distance of each experimental time, as show in Table 1. .

Table 1Experimental distance measure

4.4 Decryption error

Our selective encryption scheme only changes values of vertices in polylines and polygons of map. It did not alter the size of encrypted file, as shown in Table 2. In addition, we use hybrid transform to encrypt coordinates, that means, if we have an input sequence zn, and we perform DFT to get Zk, and next we perform IDFT to get input sequence again zʹn, it shows that zʹn, is not absolutely equal to zn because sine and cosine value are not integer. However, in GIS vector map data, vertices are stored in double type such that the errors between original vertices and decrypted vertices values are approximately zero as given by Table 3.

Table 2.The result of loss accuracy

Table 3.The error between original coordinates and decrypted coordinates.

4.5 Security

Cryptographic security: In our algorithm, by using dynamic thresholds to define a significant object in a layer, about 70% of data is encrypted by using the key sets are generated from user's password and Chaotic map. It would be very difficult to break the encryption algorithm or try to predict the encrypted part.

Key sensitivity analysis: We test to encrypt the original layer with a slightly different encryption key, and evaluates the difference between the obtained encrypted layers.

To perform these test, slightly different keys are generated by modifying coefficient μ in Eq. (3) and a pair of first key in each key set a, b. In the modified keys, excluding one are kept same as that of original key. For the original key K1(3.52,0.34,0.62)(Key K is represented by three parameters (μ,a1,b1)), the modified keys are expressed as K2(3.42,0.34,0.62), K3(3.52,0.44,0.62) and K4(3.52,0.34,0.52). The original layer (Fig. 6(c)) is initially encrypted with key sets are generated from K1. The encrypted layer for this case is shown in Fig. 8(b). The original layer is then encrypted with key sets are generated from slightly modified key K2, K3 and K4. Fig. 8(b)-(d) indicates the corresponding encrypted layers. It is observed that layers encrypted with slightly different keys are completely incomprehensible.

Fig. 8.Key sensitivity analysis for encryption process: (a)-(d) Encrypted layer with corresponding key K1, K2, K3 and K4.

 

5. CONCLUSION

Our paper focuses on the issues how to encrypt GIS vector map selectivity with low complexity. This considers the properties of object in a layer and selectively encrypts only the significant objects by key sets in DWT, DFT domain. Only some values are selected to encrypt but it made changing whole map. Experimental results showed that the proposed algorithm has very effective with a large volume of GIS dataset. Decrypting results also show the error in decryption process approximates zero. The proposed algorithm can be applied to various file formats or standard vector map because only polyline and polygon objects are encrypted and can be used for map database security of GIS map service on/off-lines. Next time, we will continue to improve our algorithm by reducing number of selective values to reduce complexity while not change effectively.