In conventional ( k , n ) threshold secret sharing, secret information or input can be recovered by collecting k shares from n servers, regardless of the honesty of the player. However, in asymmetric secret sharing, the input remains unrecoverable even if the attacker collects all shares from all data servers. Asymmetric secret sharing provides an asymmetric structure in which only an honest/authorized player can regain the input by combining shares from the data servers with pseudorandom numbers that are generated by the authorized player to complete the required k shares. Nevertheless, the asymmetric secret sharing scheme does not rely on information-theoretic security but rather on computational security. In this study, we first demonstrate the vulnerability of the conventional computationally secure asymmetric secret sharing scheme by presenting possible attacks on the scheme. We then show that by introducing true random numbers, an asymmetric secret sharing scheme with information-theoretic security can be achieved under certain conditions. We also identify and provide a detailed discussion of the conditions required to achieve information-theoretic security. However, the required conditions result in a reduction in storage efficiency on the server. We implemented our proposed method and evaluated its efficiency under these conditions, and showed that the execution time remains within the acceptable range and has a minimal effect on practical use. Moreover, we show that the proposed method can realize new applications that are not possible with conventional secret sharing schemes, such as secure data management that does not leak secret information even if the entire dataset in the cloud containing the shares is compromised, and communication, including IoT communication.

Secure computation methods include methods that use homomorphic encryption (HE) and those that use secret sharing (SS). Secure computation based on HE can be realized using one server, and the computation process can be made public if the encryption key is kept secure. However, HE generally requires a substantial computation cost. In contrast, SS has the advantage of low computation cost, allowing for high-speed processing; however, all servers must be managed independently. And the process of k or more servers cannot be disclosed. In particular, secret input will be leaked when the same organization manages multiple servers to implement SS. Therefore, a complex model where each server is independently managed is required. Iwamura et al. proposed a secure computation that is information-theoretic secure in n≥k instead of n≥2k−1 by assuming a trusted third party (TTP). In this paper, by making more effective use of a TTP, we demonstrate that secure computation based on SS is possible with only one computing server. Moreover, we show that the entire computation process can be disclosed if the key is managed safely. We realize a method that solves the disadvantages of conventional approaches with a faster computation than those methods.

e realize MPC of multiplication with the setting of N=k,n≥2k-1. We also show that our proposed method is information theoretic secure against a semi-honest adversary.

In recent years, the concept of Internet of Things (IoT) network has been extensively discussed. Hamasaki et al. proposed a method of group key sharing using geometric characteristic. Thereafter, a method for sharing a pairwise key by implementing the Hamasaki et al.'s method had been proposed by Nishigami et al. However, we found that in this method, when a node and its fellow nodes are attacked together, the keys of the rest of the nodes will be leaked. Therefore, in this paper, we propose a method that enables a pairwise key to be securely shared. In addition, we extend our method of pairwise key sharing to efficiently share pairwise, group, and global keys. Finally, we evaluate the efficiency of our proposed method.

Typically, when secrecy multiplication is performed in multiparty computation using Shamir's (k,n) threshold secret sharing scheme, the result is a polynomial with degree of 2k-2 instead of k-1 This causes a problem where, in order to reconstruct a multiplication result, the number of polynomials needed will increase from k to 2k-1. In this paper, we propose a multiparty computation that uses a secret sharing scheme that is secure against a product-sum operation but does not increase the degree of polynomial of the output. We prove that all combinations of the basic operations (addition, subtraction, multiplication, and division) can be performed securely using this scheme. We also propose three preconditions and finally show that our proposed method is information-theoretic secure against a passive adversary.