Perfectly Secure Shamir's Secret Sharing Scheme for Privacy Preserving Image Processing Over Cloud

Cloud computing is a highly prospective paradigm in which computational resources from third parties are used for processing outsourced data. Nonetheless, the distributed architecture of this concept poses many security and privacy threats for the data owners. Shamir's secret sharing is an effective technique for distributing and processing secret images over the encrypted domain. However, it has got some critical limitations primarily due to the presence of correlated information between the image pixels. Our study addresses this problem by proposing a perfectly secure Shamir's secret sharing scheme for images. Our work builds upon the formal notion of perfect secrecy for encoding the Shamir's shares in a particular manner such that they (i.e. encoded shares) do not reveal any additional information about the original image. Importantly, we have provided both theoretical and empirical validation of our proposed approach. We have also performed several image filtering operations on the stored shares and found the resulting PSNR and NCC values to be similar in the plain and encrypted domains. Hence our work provides a privacy-preserving and secure framework for working with images over a cloud-based architecture.