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An Improved EllipticNet Algorithm for Tate Pairing on Weierstrass’ Curves, Faster Point Arithmetic and Pairing on Selmer Curves and a Note on Double Scalar Multiplication

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Applications and Techniques in Information Security (ATIS 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 651))

Abstract

Elliptic Curve point arithmetic is at the heart of all cryptographic algorithms utilizing Elliptic Curves. Pairing based cryptography has been an area of intense research recently. In this context, we

(i) present an improved version of Stange’s Elliptic Net Algorithm to compute the Tate Pairing,

(ii) present an improved algorithm for Point arithmetic and Pairing on Selmer curves and

(iii) show that Co-Z based precomputation algorithms for elliptic curve double scalar multiplication are not necessarily faster than Conjugate-addition based precomputation algorithms as claimed in the literature.

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Acknowledgments

Many thanks to the anonymous reviewers of ATIS 2016 for their valuable feedback.

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Authors and Affiliations

  1. Mathematical Sciences Institute (MSI), The Australian National University (ANU), Canberra, Australia

    Srinivasa Rao Subramanya Rao

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  1. Srinivasa Rao Subramanya Rao
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Correspondence to Srinivasa Rao Subramanya Rao .

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Editors and Affiliations

  1. School of Information Technology, Deakin University, Burwood, Victoria, Australia

    Lynn Batten

  2. Deakin University , Burwood, Australia

    Gang Li

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Rao, S.R.S. (2016). An Improved EllipticNet Algorithm for Tate Pairing on Weierstrass’ Curves, Faster Point Arithmetic and Pairing on Selmer Curves and a Note on Double Scalar Multiplication. In: Batten, L., Li, G. (eds) Applications and Techniques in Information Security. ATIS 2016. Communications in Computer and Information Science, vol 651. Springer, Singapore. https://doi.org/10.1007/978-981-10-2741-3_8

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  • DOI: https://doi.org/10.1007/978-981-10-2741-3_8

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  • Print ISBN: 978-981-10-2740-6

  • Online ISBN: 978-981-10-2741-3

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