Congruence and geometric feature-based commutative encryption-watermarking method for vector maps. (February 2022) - Ren, Na; Tong, Deyu; Cui, Hanchuan; Zhu, Changqing; Zhou, Qifei
Abstract: The commutative encryption-watermarking (CEW), in which the encryption and watermarking are distinct and commutative, has become a promising method for protecting data security. For vector maps, current methods combine encryption with watermarking directly, but cannot satisfy the CEW properties. For example, the watermark embedding and encryption are not commutative and lack flexibility. Considering the essential characteristics of vector maps, this paper proposes a CEW method based on the congruence relationship and geometric feature for vector maps. In the proposed CEW method, the angles and the distance ratios are selected as the geometric features which provide separate spaces for cryptography and watermarking operations. They are encrypted by making the original values and encrypted values congruent. At the same time, the watermark is embedded into their residue. As the residue keeps invariant under congruence operations, the watermark can be extracted from either the plaintext or the ciphertext. Experiments are conducted to verify the commutativity between encryption and watermarking. Besides, the superiority in terms of watermark robustness and capacity of the proposed method has been also compared with other encryption-combining-watermarking methods for vector maps. Highlights: A comprehensive combination of cryptography and watermarking for vector maps. The geometric features are used in both encryption and watermarking simultaneously. Cryptographic and watermarking operations are commutative without interference. High watermark capacity and robustness.