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Efficient Simultaneous Inversion in Parallel and Application to Point Multiplication in ECC

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Information Security and Cryptology (CISC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3822))

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Abstract

Inversion is the costliest of all finite field operations. Some algorithms require computation of several finite field elements simultaneously (elliptic curve factorization for example). Montgomery’s trick is a well known technique for performing the same in a sequential set up with little scope for parallelization. In the current work we propose an algorithm which needs almost same computational resources as Montgomery’s trick, but can be easily parallelized. Our algorithm uses binary tree structures for computation and using 2r − 1 multipliers, it can simultaneously invert 2r elements in 2r multiplication rounds and one inversion round. We also describe how the algorithm can be used when 2, 4, ... number of multipliers are available. To exhibit the utility of the method, we apply it to obtain a parallel algorithm for elliptic curve point multiplication. The proposed method is immune to side-channel attacks and compares favourably to many parallel algorithms existing in literature.

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Author information

Authors and Affiliations

  1. Centre for Information Security and Cryptography (CISaC), University of Calgary, 2500 University Drive NW, Calgary, AB, Canada

    Pradeep Kumar Mishra

Authors
  1. Pradeep Kumar Mishra
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Editor information

Editors and Affiliations

  1. State Key Laboratory of Information Security, Institution of Software of Chinese Academy of Sciences, 100080, Beijing, China

    Dengguo Feng

  2. SKLOIS Lab, Institute of Software, Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Dongdai Lin

  3. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Mishra, P.K. (2005). Efficient Simultaneous Inversion in Parallel and Application to Point Multiplication in ECC. In: Feng, D., Lin, D., Yung, M. (eds) Information Security and Cryptology. CISC 2005. Lecture Notes in Computer Science, vol 3822. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11599548_28

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  • DOI: https://doi.org/10.1007/11599548_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30855-3

  • Online ISBN: 978-3-540-32424-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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