Formula omitted] Regional Secret Image Sharing over Finite Fields

Abstract

Secret image sharing (SIS), a tool capable of distributing a private image among certain number of shareholders, ensures both authorized recovery and unauthorized forbidding of the same. However, usually, in SIS every pixel is treated with equal weight. This is a hindrance in case of partial query to the original secret image, where usual SIS might over-inform the querier. To prevent this over-spilling of information, we introduce, in this work, the notion of Regional Secret Sharing, where access to a special region is not possible in general, unless an essential participant submits his shadow. We formally define (t,k,n)-Regional secret image sharing ((t,k,n)-RSIS) and provide a construction for the same using polynomial based secret image sharing. Our construction which is done over a finite field is completely lossless. We also formally prove the protocol’s behaviour in different cases of authorized access and unauthorized access. Moreover, we support our constructions with sufficient experimental results. This is the first usage of the notion of region in secret image sharing. Our construction is information theoretically secure, meaning we do not assume any computational assumptions for the adversary, in the semi-honest model and it does not require any preprocessing unlike most SIS schemes, making the scheme efficient as well.