Nonlinear Secret Image Sharing Scheme

Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log(2)⁡m⌉ bit-per-pixel (bpp), respectively.