# An Authentication Method for AMBTC Compressed Images Using Dual Embedding Strategies
## 1 Introduction  
With the progress and development of Internet, digital images are increasingly easy to be transmitted over the network. However, these images are likely to be tampered with either with malicious intent or otherwise, resulting in unauthentic images being received. Therefore, authentication of images has become an important issue. Fragile watermarking [1; 2; 3; 4; 5] is a common technique used in image authentication by embedding watermark data into images. If pixels were tampered with, the embedded data could be retrieved to authenticate the image. The fragile watermarking technique can be applied to images in spatial [6; 7; 8; 9; 10] or compressed [11; 12; 13] domains. In the spatial domain, data are embedded directly by modifying pixel values. Since images of spatial domain have many redundancies for embedding, higher payloads are expected. However, in recent years, most images are stored and transmitted in compressed formats. This is because compressed images have lower storage space and transmission bandwidth requirements. At present, vector quantization (VQ) [14; 15; 16], joint photographic expert group (JPEG) [17; 18; 19], and absolute moment block truncation coding (AMBTC) [20; 21] are some commonly used compression techniques. Amongst these techniques, AMBTC requires the least computational cost. Therefore, several authentication techniques based on AMBTC images [22; 23; 24; 25; 26; 27] have been proposed. AMBTC was proposed by [PERSON] and [PERSON] [28], where blocks were compressed into quantized values and bitmaps. In 2013, ref. [22] proposed an AMBTC image authentication method with joint image coding. This method used pseudo random sequence to generate authentication codes which were embedded into the bitmaps. The embedded bitmaps together with the quantized values were, then, losslessly compressed to obtain the finalbitstream. The advantage of their method was that it required less storage and achieved good detection accuracy. To improve image quality, ref. [23] in 2016 proposed a novel image authentication method based on a reference matrix. The matrix was employed to embed authentication codes into quantized values. The length of authentication codes was determined by the size of the matrix. Ref. [23] achieved a higher image quality compare to [22]. However, this method could not detect tampering in the bitmaps which were independently generated from the authentication codes. To improve security, ref. [24] also proposed an authentication method that used bitmaps to generate authentication codes. Furthermore, the resulting image had equivalent quality and higher detection accuracy to [23]. In 2018, ref. [25] proposed a tamper detection method for AMBTC images. The most significant bits (MSBs) of quantized values and bitmaps were hashed to generate the authentication codes. The codes were embedded into the least significant bits (LSBs) of the quantized values using the LSB embedding method. To obtain higher image quality, the MSBs of quantized values were perturbed within a small range and used to generate a set of authentication codes. The code with the smallest embedding error was selected for embedment to provide a higher image quality than [22; 23; 24]. In 2018, ref. [26] also proposed an AMBTC authentication method using adaptive pixel pair matching (APPM). Bitmaps and the position information were employed to generate the authentication codes, which were embedded in the quantized values using APPM. A threshold was used to classify blocks into edge and nonedge ones. If the difference of quantized values was larger than the threshold, the block was considered as an edge one; or otherwise, a nonedge block. Edges in an image were considered more informative than the nonedges; therefore, more bits were embedded in edge blocks than nonedge ones to provide more protection to edges. In 2019, ref. [27] proposed a high-precision authentication method for AMBTC images using matrix encoding (ME). Bitmaps and position information were used to generate 6-bit authentication codes.