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Encapsulated Scalar Multiplications and Line Functions in the Computation of Tate Pairing

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4484))

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Abstract

The efficient computation of the Tate pairing is a crucial factor to realize cryptographic applications practically. To compute the Tate pairing, two kinds of costs on the scalar multiplications and Miller’s line functions of elliptic curves should be considered. In the present paper, encapsulated scalar multiplications and line functions are discussed. Some simplified formulas and improved algorithms to compute f 3T , f 4T , f 2T±P , f 6T , f 3T±P and f 4T±P etc., are presented from given points T and P on the elliptic curve.

Supported by the NSF of China (10571005, 60473019), by 863 Project (No. 2006AA01Z434) and by NKBRPC (2004CB318000).

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Authors and Affiliations

  1. LMAM, School of Math. Sciences, Peking University, Beijing 100871, P.R. China

    Rongquan Feng & Hongfeng Wu

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  1. Rongquan Feng
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  2. Hongfeng Wu
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Jin-Yi Cai S. Barry Cooper Hong Zhu

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Feng, R., Wu, H. (2007). Encapsulated Scalar Multiplications and Line Functions in the Computation of Tate Pairing. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-72504-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72503-9

  • Online ISBN: 978-3-540-72504-6

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