Visible to the public An Implementation and Evaluation of a Pairing on Elliptic Curves with Embedding Degree 14

TitleAn Implementation and Evaluation of a Pairing on Elliptic Curves with Embedding Degree 14
Publication TypeConference Paper
Year of Publication2020
AuthorsSong, Z., Matsumura, R., Takahashi, Y., Nanjo, Y., Kusaka, T., Nogami, Y., Matsumoto, T.
Conference Name2020 35th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)
Keywordsadvanced cryptography, Approximation algorithms, computer architecture technology, cryptographic protocols, efficient curves, elliptic curve, Elliptic curve cryptography, Elliptic curves, Encryption, exponentiation, Finite filed arithmetic, generation cryptography, multiple devices, multiplication algorithm bases, pairing-based cryptography, Protocols, pseudo7-sparse algorithm, pubcrawl, public key cryptography, Resiliency, Scalability
AbstractAs 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.
Citation Keysong_implementation_2020