Biblio

As the computer architecture technology evolves, communication protocols have been demanded not only having reliable security but also flexible functionality. Advanced cryptography has been expected as a new generation cryptography which suffices such the requirements. A pairing is one of the key technologies of the cryptography and the pairing has been known as having a substantial amount of construction parameters. Recently, the elliptic curve with embedding degree 14 is evaluated as one of the efficient curves for pairing. In the paper, we implement an optimal ate pairing on the elliptic curve by applying several variants of multiplication algorithms of extension field of degree 7 on multiple devices. The best multiplication algorithm among the candidates is derived. Besides, for efficient calculations, we propose a pseudo 7-sparse algorithm and a fast calculation method of final exponentiation. As a result, we discover the proper multiplication algorithm bases on the rate of addition and multiplications on several different computer platforms. Our proposed pseudo 7-sparse algorithm is approximately 1.54% faster than a regular algorithm on almost all tested platforms. Eventually, for the total execution time of pairing we record 9.33ms on Corei5-9500.

The recent development of IoT technologies and cloud storages, many types of information including private information have been gradually outsourced. For such a situation, new convenient functionalities such as arithmetic and keyword search on ciphertexts are required to allow users to retrieve information without leaking any information. Especially, searchable encryptions have been paid much attention to realize a keyword search on an encrypted domain. In addition, an architecture of searchable symmetric encryption (SSE) is a suitable and efficient solution for data outsourcing. In this paper, we focus on an SSE scheme which employs a secure index for searching a keyword with optimal search time. In the conventional studies, it has been widely considered that the scheme searches whether a queried keyword is contained in encrypted documents. On the other hand, we additionally take into account the location of a queried keyword in documents by targeting a matrix-type data format. It enables a manager to search personal information listed per line or column in CSV-like format data.

This paper presents an efficient arithmetic in extension field based on Cyclic Vector Multiplication Algorithm that reduces calculation costs over cubic extension for elliptic curve pairing cryptography. In addition, we evaluate the calculation costs compared to Karatsuba-based method.