Detection of Cheaters in Vector Space Secret Sharing Schemes

A perfect secret sharing scheme is a method of distributing shares of a secret among a set P of participants in such a way that only qualified subsets of P can reconstruct the secret from their shares and non-qualified subsets have absolutely no information on the value of the secret. In a secret sharing scheme, some participants could lie about the value of their shares in order to obtain some illicit benefit. Therefore, the security against cheating is an important issue in the implementation of secret sharing schemes. Two new secret sharing schemes in which cheaters are detected with high probability are presented in this paper. The first one has information rate equal to 1/2 and can be implemented not only in threshold structures, but in a more general family of access structures. We prove that the information rate of this scheme is almost optimal among all schemes with the same security requirements. The second scheme we propose is a threshold scheme in which cheaters are detected with high probability even if they know the secret. The information rate is in this case 1/3 In both schemes, the probability of cheating successfully is a fixed value that is determined by the size of the secret.     

滋长阶小于1的亚纯函数唯一性

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＢｙａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｗｅａｌｗａｙｓｍｅａｎａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ .ＷｅａｓｓｕｍｅｔｈａｔｔｈｅｒｅａｄｅｒｉｓｆａｍｉｌｉａｒｗｉｔｈＮｅｖａｎｌｉｎｎａｔｈｅｏｒｙｔｈａｔｃａｎｂｅｆｏｕｎｄ ,ｆｏｒｉｎｓｔａｎｃｅ ,ｉｎ [1 ] .Ｗｅｓａｙｔｈａｔｔｗｏｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓｆａｎｄ ｇｓｈａｒｅｔｈｅｖａｌｕｅａ∈ Ｃｐｒｏｖｉｄｅｄｔｈ…     

关于亚纯函数的唯一性定理

本文研究亚纯函数的唯一性问题,证明的结果与Ｈ．Ｕｅｄａ的一个工作相关。     

Efficient Mediated Quantum Secret Sharing Protocol in a Restricted Quantum Environment

The multiparty-mediated quantum secret sharing (MQSS) protocol proposed by Tsai et al. [Quantum Inf. Process., 2022 , 21, 63] allows n restricted users with limited quantum capabilities to share secret information using a dishonest third party with full quantum capabilities. Although the MQSS protocol allows restricted users to achieve secret sharing with lightweight quantum capabilities, the qubit efficiency of this protocol can be further improved. Therefore, this study proposes a measurement property of the graph state to design an efficient mediated quantum secret-sharing protocol in the same quantum environment as that of Tsai et al.’s protocol. The proposed MQSS protocol not only inherits the lightweight property of Tsai et al.’s protocol but also improves the qubit efficiency of Tsai et al.’s protocol by $2{}^{n-1}$ times. Security analysis is performed to show that the proposed MQSS protocol can avoid collective, collusion, and Trojan horse attacks. Furthermore, this study uses quantum network simulation software to implement Tsai et al.’s protocol and the proposed protocol to prove the feasibility of the proposed MQSS protocol and show that it is more efficient than Tsai et al.’s protocol.     

Sharing quantum nonlocality in star network scenarios

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.     

Two-weight or three-weight binary linear codes from cyclotomic mappings

Recently, linear codes with few weights have been studied extensively. These linear codes have wide applications in secret sharing schemes and authentication codes. In this paper, we introduce a new construction of defining sets using cyclotomic mappings and construct three new classes of binary linear codes with two or three weights. We also explicitly determine the weight distributions of these codes.     

纵场磁体电源变流器均流分析

在纵场磁体电源变流器均流特性分析中，通过对桥臂分段和提取支路分布参数矩阵的方法，建立了大功率变流器桥臂的等效电路模型，计算了各个支路电流和变流器的均流系数。通过变流器的仿真模拟得到了桥臂电流演化，模型的仿真结果与理论计算基本一致，其均流系数均小于1.2的工程设计目标。