In this paper, we propose a new type of non-recursive Mastrovito multiplier for $\text {GF}(2^{m})$ using an $n$ -term Karatsuba algorithm (KA), where $\text {GF}(2^{m})$ is defined by an irreducible trinomial, $x^{m}+x^{k}+1, m=nk$ . We show that such a type of trinomial combined with the $n$ -term KA can fully exploit the spatial correlation of entries in related Mastrovito product matrices and lead to a low-complexity architecture. The optimal parameter $n$ is further studied. As the main contribution of this paper, the lower bound of the space complexity of our proposal is about $O({m^{2}}/{2})+m^{3/2})$ . Meanwhile, the time complexity matches the best Karatsuba multiplier known to date. To the best of our knowledge, it is the first time that Karatsuba-based multiplier has reached such a space complexity bound while maintaining a relatively low time delay.

We continue the study of Mastrovito form of Karatsuba (MK) multipliers under the shifted polynomial basis (SPB). An MK multiplier utilizes Karatsuba algorithm and Mastrovito approach to optimize polynomial multiplication and modular reduction, which lead to a better space and time tradeoff for all trinomials. Based on this work, we make two types of contributions: 1) We derive a new modular reduction formulation for constructing Mastrovito matrix associated with special types of pentanomials, i.e., Types I, II, and Type C.1 pentanomial. Through related formulations, we demonstrate that Type I pentanomial is less efficient than Type II because of a more complicated modular reduction under the same SPB; conversely, Type C.1 pentanomial is as good as Type II under generalized polynomial basis (GPB). 2) We introduce a new MK multiplier for Type II pentanomial. It is shown that our proposal is only one TX slower than the fastest quadratic multipliers for Type II pentanomial, but its space complexity is roughly 3/4 of those schemes. To the best of our knowledge, it is the first time for hybrid multiplier to achieve such a time delay bound.

Searchable public key encryption scheme is a key technique for protecting data confidentiality in today’s cloud environment. Specifically, public key encryption with conjunctive and disjunctive keyword search (PECDK) can provide flexible search options without sacrificing keywords security and thus attracts a lot of attention nowadays. However, the most effective PECDK scheme is based on the inner product encryption (IPE), which needs more time and space cost. In this paper, by utilizing the bilinear pairing with a prime order group, we propose an efficient PECDK scheme needing less time and storage consumption. The proposed scheme is proven to be secure under a rigorous security definition. The theoretical analysis and experimental results demonstrate that our proposed scheme can significantly improve the time and space efficiency over the state-of-the-art scheme.

The searchable encryption scheme can perform keywords search operation directly over encrypted data without decryption, which is crucial to cloud storage, and has attracted a lot of attention in these years. However, it is still an open problem to develop an efficient public key encryption scheme supporting conjunctive and a disjunctive keyword search simultaneously. To achieve this goal, we introduce a keyword conversion method that can transform the query and index keywords into a vector space model. Through applying a vector space model to a predicate encryption scheme supporting inner product, we propose a novel public key encryption scheme with conjunctive and disjunctive keyword search. The experiment result demonstrates that our scheme is more efficient in both time and space as well as more suitable for the mobile cloud compared with the state-of-art schemes.

Searchable encryption (SE) is one of the effective techniques for searching encrypted data without decrypting it. This technique can provide a secure indexing mechanism for encrypted data and utilize a secure trapdoor to search for the encrypted data directly, thus realizing a secure ciphertext retrieval function. Existing schemes usually build a secure index directly on the whole dataset and implement the retrieval of encrypted data by implementing a secure search algorithm on the index. However, this approach requires testing many non-relevant documents, which diminishes the query efficiency. In this paper, we adopt a clustering method to preclassify the dataset, which can filter out quite a portion of irrelevant documents, thus improving the query. Concretely, we first partition the dataset into multiple document clusters using the k-means clustering algorithm; then, we design index building and searching algorithms for these document clusters; finally, by using the asymmetric scalar-product-preserving encryption (ASPE) scheme to encrypt the indexes and queries, we propose a fast searchable symmetric encryption scheme that supports ranked search. Detailed security analysis demonstrates that the proposed scheme can guarantee the data and query security of the search process. In addition, theoretical and experimental analysis indicates that our scheme outperforms other similar schemes in terms of query efficiency.