Commutative Encryption and Watermarking Algorithm Based on Feature Invariants for Secure Vector Map

Abstract

The existing commutative encryption and watermarking (CEW) methods based on feature invariants can achieve both the robustness of the watermarking algorithm and the security of the encryption algorithm. However, they are only applicable to the raster data such as images, videos, etc. In particular, the organization structure and storage structure of vector map have not been considered in these methods. Therefore, they cannot be used for vector map. This paper derives two feature invariants to solve this problem, which are the sum of inner angles and the storage direction of two adjacent objects according to the inherent characteristics of vector map. Based on these two feature invariants, a new CEW method is proposed in this paper, which includes the feature invariants based watermarking algorithm and the perceptual stream cipher based encryption algorithm on coordinates. Since the coordinate values used in encryption and the feature invariants used in watermarking are independent of each other, the commutativity is achieved for the proposed CEW method. The experiments are given to verify that the proposed CEW method can achieve the commutativity between encryption and watermarking without deteriorating accuracy of data. Besides, it has been verified that the proposed method is more robust to rotate, scaling, translation, and projection transformation compared with the existing CEW methods and has high security. The proposed algorithm has good scalability of encryption, and arbitrary encryption methods based on encrypting the coordinate values can be applied without affecting the extracted feature invariants.INDEX TERMS Commutative encryption and watermarking, feature invariant, vector map, perceptual stream cipher, lossless.

A Novel Invariant Based Commutative Encryption and Watermarking Algorithm for Vector Maps

“…Table 12 reflects the results of watermark extraction, it is obvious that the watermark can be extracted successfully and that the NC values are always 1, which shows that the extracted watermark is not affected by data format conversion. rithm is more robust in resisting vertex addition attack and vertex deletion attac shown in Figure 11c-f, the proposed algorithm has the same robustness as the exi methods [2,13,24] in resisting data format conversion, scaling and translation att whereas its robustness in resisting rotation attack is not as good as the existing met [2,13,24]. The above results show that the proposed algorithm is resistant to vertex att scaling and translation attacks, data format conversion attack.…”

“…Figure 11a-b reflect that the proposed algorithm is more robust in resisting vertex addition attack and vertex deletion attack. As shown in Figure 11c-f, the proposed algorithm has the same robustness as the existing methods [2,13,24] in resisting data format conversion, scaling and translation attacks, whereas its robustness in resisting rotation attack is not as good as the existing methods [2,13,24].…”

“…The key space is an important evaluation indicator of key security. The key space should be large enough to resist exhaustive attacks, and the size of the key space should be greater than the standard requirement (i.e., 2 100 ) [24]. The keys of proposed algorithm consist of the following two keys: the 512 bits hash value generated by user's input key and the map file respectively.…”

“…To further highlight the better performance of our method, the Railways map was used to implement the comparison with the existing methods [2,13,24]. We compared their robustness in vertex attacks, geometric attacks and data format conversion attack.…”

“…As mentioned above, it is obvious that the invariant based CEW is superior to the other two schemes in terms of balancing encryption security and watermark robustness. Based on this, Ren et al [24] analyzed the organization structure and storage structure of vector maps and proposed a CEW method by deriving two invariants: the sum of inner angles and the storage direction of two adjacent objects. This method has high robustness against geometric attacks.…”