Secure Secret Sharing in the Cloud

In this paper, we show how a dealer with limited resources is possible to share the secrets to players via an untrusted cloud server without compromising the privacy of the secrets. This scheme permits a batch of two secret messages to be shared to two players in such a way that the secrets are reconstructable if and only if two of them collaborate. An individual share reveals absolutely no information about the secrets to the player. The secret messages are obfuscated by encryption and thus give no information to the cloud server. Furthermore, the scheme is compatible with the Paillier cryptosystem and other cryptosystems of the same type. In light of the recent developments in privacy-preserving watermarking technology, we further model the proposed scheme as a variant of reversible watermarking in the encrypted domain.

I. Introduction

Secret sharing is a study in cryptography invented independently by Blakley [1] and Shamir [2]. In general, there is one dealer who splits a secret into shares for players and only when any group of or more players work collectively will the secret be reconstructed from their shares. Any shares reveals restrictively no information about the secret. This refers to as a (t, n)-threshold secret sharing scheme. Conventionally, shares are of at least the same size of the secret itself. This n- fold increase in required storage is, however, space inefficient and thus has led to the notion of multi-secret sharing [3]– [5]. Over the past decade, businesses and individuals have entrusted an increasing amount of data to the cloud for the purposes of processing and storage. In the meanwhile, the advances in cloud computing have also led to growing concerns for data privacy. A standard solution to the concerns over privacy would be to encrypt the data. However, the desired functionality may not be achievable on the encrypted data. To address this problem, Rivest et al. [6] introduced the notion of homomorphic encryption, which permits mathematical operations to be performed on the encrypted data. In reality, encryption algorithms are inbuilt features in many widely available devices, while secret sharing algorithms have rather limited availability to the public. In addition to this, many secret sharing algorithms are patented and thus there are restrictions on the commercial use of these intellectual properties. For these reasons, it is of great interest to study secure secret sharing in the cloud, or from a scientific point of view, secret sharing in the encrypted domain.