Research And Design With Linear Secret Sharing Scheme

Secret sharing is an important research subject of information security and cryptography, which is a protocol to distribute a secret among a group of participants, where each participant holds a part of the secret. This distribution is done in such a way that any authorized subset of participants, pooling together their information, can reconstruct the secret; whereas any unauthorized subset of participants cannot get it. Since Shamir and Blakley introduced secret sharing schemes in1979separately, a large number of scholars have thrown themselves into the study of secret sharing and have gained fruitful achievements. However, the access structures, efficiency and the security of secret sharing schemes still remain further study. In the terms of the construction and performance of secret sharing schemes, this thesis presents and analyzes linear secret sharing schemes based on two classes of mathematical models.Main contributions of this paper are summarized as follows:1. In2010, Hsu proposed an ideal multi-secret sharing scheme based on monotone span programs(MSP), but there was obvious loopholes in that scheme. In this work, by using the knowledge of linear equations we analyze Hsu scheme, obtaining the condition to use monotone span programs for secret sharing(Hsu scheme). And finally, integrating MSP with two-variable one-way function, we design a verifiable multi-secret sharing scheme, which retains the original access structure of Hsu scheme.2. Furthermore, we analyze the attack models of enemies over multi-secret sharing schemes, and summary the security requirements that these schemes need to satisfy.3. Based on linear codes, we propose a novel space efficient single secret sharing scheme and a multi-secret sharing scheme, separately. In the new schemes, we partition the given linear codes into disjoint classes, and establish a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. The size of share of each participant is smaller than the size of the master secret. Thus, the scheme have higher information rate, reducing the cost and improving the space efficiency. Meanwhile, the anti-assault property of the schemes is based on the intractability of discrete logarithm, which makes secret sharing managements more effective and safer.