An Ideal Compartmented Secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations

Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure. We propose an ideal and efficient compartmented multi-secret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is $t$, our scheme can reduce the computational complexity from $O(n^{t-1})$ to $O(n^{\max(t_i-1)}\log n)$, where $t_i<t$. The security of the proposed scheme is based on Shamir\u27s threshold scheme. Moreover, it is efficient to share the multi-secret and to change the shared secrets in the proposed scheme. That is, the proposed scheme can improve the performances of the key management and the distributed system

Linear Regression Side Channel Attack Applied on Constant XOR

Linear regression side channel attack (LRA) used to be known as a robust attacking method as it makes use of independent bits leakage. This leakage assumption is more general than Hamming weight/ Hamming distance model used in correlation power attack (CPA). However, in practice, Hamming weight and Hamming distance model suit most devices well. In this paper, we restudy linear regression attack under Hamming weight/ Hamming distance model and propose our novel LRA methods. We find that in many common scenarios LRA is not only an alternative but also a more efficient tool compared with CPA. Two typical cases are recovering keys with XOR operation leakage and chosen plaintext attack on block ciphers with leakages from round output. Simulation results are given to compare with traditional CPA in both cases. Our LRA method achieves up to 400% and 300% improvements for corresponding case compared with CPA respectively. Experiments with AES on SAKURA-G board also prove the efficiency of our methods in practice where 128 key bits are recovered with 1500 traces using XOR operation leakage and one key byte is recovered with only 50 chosen-plaintext traces in the other case

A New Efficient Hierarchical Multi-secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations

Hierarchical secret sharing is an important key management technique since it is specially customized for hierarchical organizations with different departments allocated with different privileges, such as the government agencies or companies. Hierarchical access structures have been widely adopted in secret sharing schemes, where efficiency is the primary consideration for various applications. How to design an efficient hierarchical secret sharing scheme is an important issue. In 2007, a famous hierarchical secret sharing (HSS) scheme was proposed by Tassa based on Birkhoff interpolation, and later, based on the same method, many other HSS schemes were proposed. However, these schemes all depend on Polya\u27s condition, which is a necessary condition not a sufficient condition. It cannot guarantee that Tassa\u27s HSS scheme always exists. Furthermore, this condition needs to check the non-singularity of many matrices. We propose a hierarchical multi-secret sharing scheme based on the linear homogeneous recurrence (LHR) relations and the one-way function. In our scheme, we select $m$ linearly independent homogeneous recurrence relations. The participants in the highly-ranked subsets $\gamma_1, \gamma_2 ,\cdots, \gamma_{j-1}$ join in the $j$-th subset to construct the $j$-th LHR relation. In addition, the proposed hierarchical multi-secret sharing scheme just requires one share for each participant, and keeps the same computational complexity. Compared with the state-of-the-art hierarchical secret sharing schemes, our scheme has high efficiency