## 1 Introduction
[PERSON] et al. [25] designed two novel generation schemes of pseudo-random patterns in the space-time dimension to increase the capacity of information embedding. In these studies, the interaction between multiple users is often ignored, which is worth researching and exploring. In the above schemes, the information carrier is either the object image or bucket values; their information capacity is limited. To increase the information capacity, one needs to either increase the pixel-size of the image or the number of the modulated patterns. [PERSON] et al. [26] proposed to an encryption scheme based on a customized data container, which is used as the encrypted image to enhance the ability to encrypt more information. Later, we proposed to build the mapping relationship of additive stitching images to be distributed and private key libraries to further increase the information capacity of the CKD protocol [27], but its susceptibility to attacks still needs to be improved. As we know, the quick response (QR) code has become a necessity in our daily lives, for it can be quickly identified by our smartphones and can store a great deal of information in the form of two-dimensional (2D) image encoding [28; 29; 30]. Besides, it also has high error tolerance capability. [PERSON] et al. [31; 32] directly used the QR code as a container of the secret information for optical image encryption. By utilizing its high-contrast binary image property, one can acquire higher robustness performance against noise in encryption. After that, [PERSON] et al. [33] introduced the QR code into the CGI to enlarge the information capacity of optical encrypted signal. On the other hand, the watermarking can be used as a privacy protection technology that embeds labels in visible images and texts [34], or a data hiding technology that hides the useful information in imperceptible signals to increase robustness to attacks or undetectability. Due to its security characteristics, the watermarking has been widely used in cryptosystems. As in the public network CKD protocol, the bucket values transmitted through public channels can be further embedded with watermarks to further increase the security [35]. If we could absorb both the excellent information capacity of the QR code and security characteristics of the watermarking technology, we could definitely build a CKD protocol with superior performance. In this work, we propose a multi-party interactive CKD protocol over a public network, which uses a QR code as the container of CKs and embeds \"watermark\" labels in the idle functional region of QR code image. In this protocol, the server splits the QR code image into multiple different fragment patterns (FPs), in each of which an independent image label that corresponds to each user is embedded in its unused functional region. By using a CGI setup, these FPs are separately encrypted into random bucket value sequences, which will be then sent to multiple legitimate users through public channels. This data hiding strategy also makes the watermark labels undetectable, confuses the audiovisual signal, increases the confidentiality and imperceptibility of the CKs and avoids content leakage. After receiving bucket values and performing image reconstruction, the receivers can conduct identity authentication and detect potential attacks, according to the content of their recovered watermark labels, and then send their results to a reliable intermediary for joint authentication. According to the cascade ablation result of FPs (complete QR code image) returned back from the intermediary, legitimate users can quickly extract their CKs by scanning the QR code. The cascade-ablation-based multi-party interactive identity authentication will improve the security of the protocol, the use of the QR code image increases the capacity of information and the watermarking technology is used for identity self-authentication and attack detection.