Some efficient algorithms for the final exponentiation of ηT pairing

Masaaki Shirase; Tsuyoshi Takagi; Eiji Okamoto

doi:10.1093/ietfec/e91-a.1.221

Some efficient algorithms for the final exponentiation of η_T pairing

Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and nt pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the nt pairing in the extension field double-struck F sign;_36n. Indeed, we propose some efficient algorithms using the torus T ₂(double-struck F sign;_33n) that can efficiently compute an inversion and a powering by 3ⁿ + 1. Consequently, the total processing cost of computing the nt pairing can be reduced by 16% for n = 97.

Original language	English
Pages (from-to)	221-228
Number of pages	8
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E91-A
Issue number	1
DOIs	https://doi.org/10.1093/ietfec/e91-a.1.221
Publication status	Published - 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1093/ietfec/e91-a.1.221

Cite this

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abstract = "Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and nt pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the nt pairing in the extension field double-struck F sign;36n. Indeed, we propose some efficient algorithms using the torus T 2(double-struck F sign;33n) that can efficiently compute an inversion and a powering by 3n + 1. Consequently, the total processing cost of computing the nt pairing can be reduced by 16% for n = 97.",

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AU - Shirase, Masaaki

AU - Takagi, Tsuyoshi

AU - Okamoto, Eiji

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Some efficient algorithms for the final exponentiation of η_T pairing

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