# Color Visual Secret Sharing for QR Code with Perfect Module Reconstruction
## 1 Introduction  
QR (Quick Response) code has been widely used since 1994 when it was invented by the DENSO WAVE corporation of Japan. Now it becomes an integral part of our everyday lives and makes our lives more and more convenient. QR code can be used in information storage, website access, online transaction and online banking etc. These applications call for protection of data security and privacy. However, QR code itself does not provide such mechanism. It can be scanned and read by anyone using a standard QR code decoder. To ensure security, an extra mechanism should be designed and incorporated into the standard QR code, such as encryption, authentication, privacy protection, hiding, and secret sharing. Encryption, authentication and privacy protection can be ensured by resorting to classicalcryptography techniques [1; 2; 3], such as private key cryptography, message authentication code, public key cryptography [4; 5], and digital signature, etc. Data hiding and secret sharing are new techniques for multimedia security, but can also be tailored to ensure QR code security. [PERSON] et al. hided secret data into QR code by using error correction capability [6]. [PERSON] et al. proposed a data embedding mechanism to hide secret data into QR code by using Reed-Solomon code and turtle shell matrix [7]. Furthermore, reversible data hiding (RDH) can be combined with QR code to ensure data security and data recovery. [PERSON] et al. proposed a RDH algorithm for QR code [8]. The background image covered by QR code is embedded into other regions of the background image using RDH [9; 10; 11; 12; 13; 14; 15; 16]. Once scanned, the QR code can be removed and the background image can be partially recovered. VSS (Visual Secret Sharing) was first proposed by [PERSON] and [PERSON] in 1994 [17]. The main idea of VSS is that the secret image can be divided into multiple share images, from which the secret images can be recovered by stacking or logical \"OR\" operation. The idea of VSS can be combined with many multimedia security applications [18; 19; 20; 21; 22], such as QR code security. QR code image poses some special features than the natural image or binary image that are used as input to ordinary VSS algorithm. For example, the observer of a QR code is not the human vision system (HVS), but a QR code decoder [23]. These features bring new ingredients into the VSS algorithm design. [PERSON] [24] applied VSS to share a secret QR code. [PERSON]'s algorithm can completely reconstruct the secret QR code from shares. However, this algorithm is pixel-based, i.e., each secret pixel of the QR code image is encrypted independently. The computational complexity is proportional to the number of pixels in a QR code, which is significantly larger than module-based processing. However, if this algorithm is applied directly to each module of the QR code, the error probability of the reconstructed module is about 50%, which exceeds the ECC of QR code. [PERSON] et al. also proposed VSS algorithm using QR code as cover images [25]. The secret data was split into \(n\) shares using a random grid approach. Each share is then embedded into one QR code such that the modification of each QR code is within its error correction capability. However, this algorithm uses QR codes as cover images, not as the secret image. Furthermore, it needs computation when reconstructing the secret image. Recently, [PERSON] et al. proposed QRCSS (QR Code Secret Sharing) algorithm to achieve QR code secret sharing [26]. The distortion between the reconstructed QR code and the secret QR code can be controlled such that the reconstructed QR code is readable by a QR code decoder. To achieve this goal, QRCSS utilizes the error correction capability of the QR code. However, this damages the error tolerance of the QR code, leaving smaller margin for error correction. Furthermore, QRCSS needs to get all the \(n\) shares in order to to reconstruct the secret QR code. To relax this constraint, [PERSON] et al.