Selective Encryption Algorithm Based on DCT for GIS Vector 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. At this point, GIS security techniques focusing on secure network and data encryption have been studied and developed to solve the copyright protection and illegal copy prevention for GIS digital map. 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 a novel selective encryption scheme for GIS vector map data protection to store, transmit or distribute to authorized users using K-means algorithm. The proposed algorithm only encrypts a small part of data based on properties of polylines and polygons in GIS vector map but it can change whole data of GIS vector map. Experimental results verified the proposed algorithm effectively and error in decryption is approximately zero.

1. INTRODUCTION

GIS is a system which designed to capture, store, manipulate, analyze, and manage all kinds of the geographic information and it is the merging system of cartography, statistical analysis, and database technology [1-2]. It consists of hardware, software, and GIS data. GIS allows us to view, understand, question, interpret, and visualize data in many ways that reveal relationships, patterns, and trends in the form of maps, globes, reports, and charts.

GIS has been used in military and commercial applications for many years. The main component of GIS is the data. The GIS data has two important properties. Firstly, the effort it takes to put it in a form suitable for use in the GIS applications. This effort increases its cost. Secondly, in most cases the GIS Data contains confidential information which must be kept away from unauthorized users. Such confidential information includes GIS layers containing troop locations and additional information like movements and mines places in a tactical environment. Hence, it is very important to protect the GIS data. Moreover, the GIS data is too expensive so we have to prevent illegal duplication and distribution of it. Nowadays, it is too easy for a company to buy some GIS layers, make illegal copies from them and distribute or sell them many times without taking any permission from the original GIS data provider. So we have to enforce some kinds of access control on it because the GIS data is sensitive and must not be accessed by unauthorized users.

In section 2, we introduce related works, and in section 3 we present selective encryption scheme for GIS vector map data protection. Finally, we implement the proposed scheme, and show experimental results in section 4.

 

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 [3-4], as shown Fig. 1. 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. Thus, our algorithm only performs selective encryption for polylines and polygons in GIS vector map.

Fig. 1.An example GIS vector map with city, river and country layers; (a) Railway layer, (b) Lake layer, (c) Building layer, and (d) Railway + Lake + Building layers.

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 [5-11]. The second part is the protected part; it is encrypted. Only authorized users have access to protected part. Polylines and polygons are selected, and encrypted by random keys combine with randomization and clustering process by K-means algorithm [12], random algorithms in DCT domain based on their geographical features [13]. Our algorithm encrypts only some selective DC values of polylines, polygons in DCT domain but it changes the whole map.

 

3. PROPOSED SELECTIVE ENCRYPTION ALGORITHM

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

3.1 Selective Encryption Process

The selective encryption algorithm follows as Fig. 2. Our algorithm consists of processes as data extraction to have polylines and polygons, polylines and polygons clustering using K clusters, vertices randomization of polylines and polygons by random coefficients using random key. Next, it applies DCT processing for randomized vertices to get DCT coefficients, and then multiply DC coefficients of each cluster with a random value which is created by another random key. Finally, it performs inverse discrete cosine transform (IDCT).

Fig. 2.Selective encryption algorithm for polyline/polygon.

In order to encrypt selectivity, we compute the total number of polylines NPLi, total number of polygons NPGi in ith layer. Each polyline/polygon has attributes such as the number of parts and the number of points. These attributes in each polyline/polygon is different. So, we used them to classify NPLi polylines, NPGi polygons into K clusters using K-means algorithm. We have NPLi polylines, NPGi polygons in ith layer, and we need to cluster them into K groups where K={kg|g∈[1,K]}. Each group kg in K groups is described by a centroid Cg={xcg,ycg}. Considering number of parts Npa-ij and number of points Npo-ij in jth polyline/polygon are coordinates in two dimensional space. And jth polyline/polygon is represented as a point which has coordinates (Npa-ij, Npo-ij) in that two dimensional space. The jth polyline/polygon is classified in group kg using the shortest Euclidean distance to Cg follow as equation (1). Djg is the Euclidean distance from jth polyline/polygon to centroid Cg, and calculated by equation (2).

Then, we find NLi-max of the max number of vertices in a polyline, and NGi-max of the max number of vertices in a polygon in ith layer. With values NLi-max, NGi-max and K, we generated random NLi-max coefficients where RL={rlk|k{1,NLi-max]} for polylines, random NGi-max coefficients where RG={rgk|k{1,NGi-max]} for polygons by random key R1 using equations (3) and (4):

From NLi-max and NGi-max coefficients, we randomize them with vertices in polylines, polygons follow as equations (5) and (6). These random coefficients will be applied to all polylines/polygons in a layer depend on the number of vertices in a polyline/polygon because number of vertices in a polyline NLi ≤ NLi-max, number of vertices in a polygon NGi ≤ NGi-max. And each layer will be applied different random coefficients. After randomization step polylines/polygons are encrypted by random key R1, and we receive NPLi new polylines with PL′i={pl′ij|j∈[1,NPLi]}={ul′i,j,k|j∈[1,NPLi],k∈[1,NLij]}, and NPGi new polygons with

PG′i={pg′ij|j∈[1,NPGi]}={ug′i,j,k|j∈[1,NPGi],k∈[1,NGij]}. Fig. 3(a) shows a randomized example for polyline.

Fig. 3.Example of randomization and multiplication for polyline, (a) Randomized example for polyline, (b) Multiplying DC coefficient with random value.

We continue to apply DCT for these new polylines/polygons to get a set of transformed polylines DLi by equation (7) and a set of transformed polygons DGi by equation (8).

After DCT processing, we continue to encrypt polylines/polygons one more time by multiplying DC coefficients of transformed polylines/polygons with one corresponding random value to their group, from K random values follow as equations (9), (10) and Fig. 3(b). K random values are Rv={rvg|g∈[1,K]}, and generated by random key R2 using the used random algorithm above.

Finally, we perform IDCT to get encrypted polylines EPLi, polygons EPGi by equations (12) and (13).

for i∈[1,NM].

3.2 Selective decryption process

The decryption algorithm for these polylines and polygons shown by Fig. 4 is the inverse process of selective encryption given at Fig. 2. Similar with the selective encryption process, we must also extract the protected data which consists of encrypted polylines and encrypted polygons, compute number of polylines and polygons, and find maximum number of vertices in polylines and polygons. The next step is to divide them into several groups by using K-means algorithm, similar with the encryption process, because the encryption changes the value of vertices only. Then, random coefficients and random values are generated again by random generator using random keys. Firstly, encrypted polylines and encrypted polygons are transformed using DCT and the DC coefficients are divided by random values. Secondly, they are inversed using IDCT to get randomized polylines and polygons again. Finally, we perform inverse randomization by dividing values of polylines/polygons in IDCT domain for random coefficients to have decrypted polylines and polygons.

Fig. 4.Selective decryption algorithm for polyline/polygon.

 

4. EXPERIMENTAL RESULTS

We used 1:5000, 1:10000, and 1:100000 scalingmaps in our experiments. Firstly, we experimented with each polyline layer and polygon layer with the scale of 1:5000. Then, we tested the full layers of 1:10000 and 1:100000 scale. Experimental results with polyline layer, polygon layer and full maps show that all maps are changed as given by Fig. 5 and Fig. 6. Unauthorized user cannot see anything on map because we changed polylines and polygons through four processes: randomization, DCT, multiplication, and IDCT using random keys R1,R2.

Fig. 5.Experimental result with scaling layers 1:5000; (a) original polyline layer, (b) encrypted polyline layer, (c) original polygon layer, and (d) encrypted polygon layer.

Fig. 6.Experimental result with full scaling map 1:10000, 1:100000; (a) original map 1:10000, (b) encrypted map 1:10000, (c) original map 1:100000, and (d) encrypted map 1:100000.

Our selective encryption scheme only changes values of vertices in polylines and polygons of the map. It did not alter the size of encrypted file. The result of loss accuracy is shown in Table 1. In addition, DCT and IDCT are not processes absolutely. That means, if we have an input sequence xn, and we perform DCT to get xk, and next we perform IDCT to get input sequence again x′n, it shows that x′n is not absolutely equal to xn because the cosine value is 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 2.

Table 1.The result of loss accuracy

Table 2.The error between original coordinates and decrypted coordinates

Finally, the distance between maps dM is computed by equation (14):

We used polyline map, polygon map to experiment other three times. Each time, we encrypted maps with different passwords which are used to create random keys as figure 3. Then we calculate dM distances of each experimental time. In Table 3, experimental results show that dM distance of two maps which are encrypted by different passwords from an original map is depend on passwords.

Table 3.Experimental distance measure

 

5. CONCLUSION

Our paper focuses on the issues how to encrypt GIS vector map selectivity with low complexity. We classified objects and encrypted them by random algorithms in DCT domain. Only some values are selected to encrypt by random processes 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. Our 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. Furthermore, our algorithm can be applied to various vector contents such as CAD and 3D content fields. Next time, we will continue to improve our algorithm by reducing number of selective values to reduce complexity while not change effectively.