An efficient verifiable (t,n)-threshold secret image sharing scheme with ultralight shares

Abstract

A secret sharing scheme partitions a secret into a set of shares and distributes them among the eligible participants, with each participant receiving one share of the secret. The sharing technique allows any qualified subset of participants to recover the secret. In (t,n)-threshold secret sharing schemes, the secret is distributed among n participants in the form of shares, such that every participant holds exactly one share. Individual share reveals nothing about the secret. Any subset of participants of size t or more (t ≤ n) can combine their shares and compute the secret, while any subset of size < t is not able to do so. This paper proposes a verifiable (t,n)-threshold secret image sharing (VSIS) scheme. In the proposed scheme, a secret image is shared among n participants with an intention that if t or more (t ≤ n) participants collaborate, then the secret image can be computed successfully. Still, any less than t participants get nothing. The scheme makes use of polynomial-based secret sharing and XOR operations to construct the shares and recover the secret image. Our scheme’s main advantage is that it presents the public shares as integer numbers (not image matrices produced in previous SIS schemes), much smaller than the secret image. It also generates a public share-image of the size the same as that of the secret image. Thus, the public shares can be efficiently transferred over the public network and efficiently stored in memory. The scheme applies to both grayscale and color images. The use of Elliptic Curve Cryptography (ECC) enables the participants to choose their own secret shadows and compute the pseudo shares (integer numbers) independently. Hence the entire communications can take place safely on public channels. The pseudo shares are verifiable to the participants as well as the combiner. The combination of small public shares and the elliptic curve cryptosystem makes this scheme ideal for resource-constrained devices. In contrast, public share-image can be safely stored with a Cloud Service Provider (CSP).