RG-Based (<i>k, n</i>)-Threshold Visual Cryptography with Abilities of OR and XOR Decryption

Abstract

A (k, n) visual cryptography (VCS) is used to build a system for secret sharing. The system divides a secret image (S) into n shares and recovers S by stacking shares bigger than or equal to k, while shares below k provide no information about S. The fundamental idea of VCS is that, rather than relying on mathematical or cryptographic skills, human vision can be used to decrypt the secret image. Typically, a Boolean OR operation can be used to indicate the stacking action in a VCS. The reconstructed secret image gradually darkens as more shares are stacked. However, this intractable issue can be overcome by designing an XOR-based VCS that uses the Boolean XOR operator rather than the OR operation. This indicates that by using the XOR-based VCS, higher image quality can be attained. Because the XOR operation requires the use of additional equipment, scholars consider that when no equipment is available, the traditional OR operation can still be used to reveal the secret images. That is, the secret image can be decrypted without a computing device by stacking enough shares, and if a lightweight computing device is available, a better-quality image can be produced via an XOR operation. In 2015, an RG-based (k, n) VCS to restore the secret image by using an OR or XOR operation was proposed. In this study, we improve the scheme and design a new (k, n) VCS, called (k, n) 2D_VCS to encrypt a secret image into n shares. The secret image can be recovered when k or more shares are gathered and stacked (OR operation) together or when an XOR procedure is utilized. Both the theoretical proof and experimental results show that the quality of the restored image obtained by our method is better than that of the previous methods.

Keywords

• secret sharing scheme
• visual cryptography
• (<i>k</i>, <i>n</i>)-threshold
• XOR operation
• random grids