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Since the advent of pairing-based cryptography, various optimization methods that increase the speed of pairing computations have been exploited, as well as new types of pairings. This paper extends the work of (Kinoshita and Suzuki Advances in Information and Computer Security - 15th International Workshop on Security, IWSEC 2020, Fukui, Japan, September 2-4, 2020, Proceedings, Lecture Notes in Computer Science, Springer, 2020) who proposed a new formula for the β\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \beta $$\end{document}-Weil pairing on curves with even embedding degree by eliminating denominators and exponents during the computation of the Weil pairing. We provide novel formulas suitable for the parallel computation for the β\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\beta $$\end{document}-Weil pairing on curves with odd embedding degree which involve vertical line functions useful for sparse multiplications. For computations we used Miller’s algorithm combined with storage and multifunction methods. Applying our framework to BLS-27, BLS-15 and BLS-9 curves at respectively the 256 bit, the 192 bit and the 128 bit security level, we obtain faster β\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\beta $$\end{document}-Weil pairings than the previous state-of-the-art constructions. The correctness of all the formulas and bilinearity of pairings obtained in this work is verified by a SageMath code.
Mathematics in Computer Science – Springer Journals
Published: Sep 1, 2022
Keywords: β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-Weil pairing; Optimal Ate pairing; Multifunction technique; Storage technique; BLS curves; Primary 14H52; Secondary 1990S
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