Biblio

The main searching functions realized by searchable encryption can be divided into searching using one query and searching using multiple queries. Searchable encryption using one query has been widely studied and researched; however, few methods of searchable encryption can accommodate search using multiple queries. In addition, most of the method proposed thus far utilize the concept of index search. Therefore, a new problem exists, in which an additional process of updating or deleting an index when new documents are added or removed is required. Hence, the overall computation cost increases. Another problem is that a document that is not registered in the index cannot be searched. Therefore, herein, using a secret-sharing scheme that is known to offer a low computational cost, we propose a method that can realize both logical conjunctive (AND) and logical disjunctive (OR) search over multiple conditions, without the construction of any index. Hence, we can realize direct searching over sentences, thus achieving a more efficient search method.

In Eurocrypt 2011, Obana proposed a (k, n) secret-sharing scheme that can identify up to ⌊((k− 2)/2)⌋ cheaters. The number of cheaters that this scheme can identify meets its upper bound. When the number of cheaters t satisfies t≤ ⌊((k− 1)/3)⌋, this scheme is extremely efficient since the size of share |Vi| can be written as |Vi| = |S|/ɛ, which almost meets its lower bound, where |S| denotes the size of secret and ε denotes the successful cheating probability; when the number of cheaters t is close to ⌊ ((k− 2)/2)⌋, the size of share is upper bounded by |Vi| = (n·(t + 1) · 2 |S|)/ɛ. A new (k, n) secret-sharing scheme capable of identifying ⌊((k − 2)/2)⌋ cheaters is presented in this study. Considering the general case that k shareholders are involved in secret reconstruction, the size of share of the proposed scheme is |Vi| = (2 |S| )/ɛ, which is independent of the parameters t and n. On the other hand, the size of share in Obana’s scheme can be rewritten as |Vi | = (n · (t + 1) · 2 |S|)/ɛ under the same condition. With respect to the size of share, the proposed scheme is more efficient than previous one when the number of cheaters t is close to ⌊((k− 2)/2)⌋.