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Cryptographers’ Track at the RSA Conference

CT-RSA 2012: Topics in Cryptology – CT-RSA 2012 pp 84–97Cite as

A Duality in Space Usage between Left-to-Right and Right-to-Left Exponentiation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7178))

Abstract

Most exponentiation algorithms are categorised as being left-to-right or right-to-left because of the order in which they use the digits of the exponent. There is clear value in having a canonical way of transforming an algorithm in one direction into an algorithm in the opposite direction: it may lead to new algorithms, different implementations of existing algorithms, improved side-channel resistance, greater insights. There is already an historic duality between left-to-right and right-to-left exponentiation algorithms which shows they take essentially the same time, but it does not treat the space issues that are always so critical in resource constrained embedded crypto-systems. To address this, here is presented a canonical duality which preserves both time and space. As an example, this is applied to derive a new, fast yet compact, left-to-right algorithm which makes optimal use of recently developed composite elliptic curve operations.

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Author information

Authors and Affiliations

  1. Information Security Group, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom

    Colin D. Walter

Authors
  1. Colin D. Walter
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Editor information

Editors and Affiliations

  1. Computer Science Department, University of Haifa, 31905, Haifa, Israel

    Orr Dunkelman

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© 2012 Springer-Verlag Berlin Heidelberg

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Walter, C.D. (2012). A Duality in Space Usage between Left-to-Right and Right-to-Left Exponentiation. In: Dunkelman, O. (eds) Topics in Cryptology – CT-RSA 2012. CT-RSA 2012. Lecture Notes in Computer Science, vol 7178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27954-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-27954-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27953-9

  • Online ISBN: 978-3-642-27954-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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