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Exploring the Design Space of Prime Field vs. Binary Field ECC-Hardware Implementations

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Information Security Technology for Applications (NordSec 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7161))

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Abstract

In this paper, we answer the question whether binary extension field or prime-field based processors doing multi-precision arithmetic are better in the terms of area, speed, power, and energy. This is done by implementing and optimizing two distinct custom-made 16-bit processor designs and comparing our solutions on different abstraction levels: finite-field arithmetic, elliptic-curve operations, and on protocol level by implementing the Elliptic Curve Digital Signature Algorithm (ECDSA). On the one hand, our \(\mathbb{F}_{2^{m}}\) based processor outperforms the \(\mathbb{F}_p\) based processor by 19.7% in area, 69.6% in runtime, 15.9% in power, and 74.4% in energy when performing a point multiplication. On the other hand, our \(\mathbb{F}_p\) based processor (11.6kGE, 41.4,μW, 1,313kCycles, and 54.3μJ) improves the state-of-the-art in \(\mathbb{F}_{p_{192}}\) ECC hardware implementations regarding area, power, and energy results. After extending the designs for ECDSA (signature generation and verification), the area and power-consumption advantages of the \(\mathbb{F}_{2^{m}}\) based processor vanish, but it still is 1.5-2.8 times better in terms of energy and runtime.

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Authors and Affiliations

  1. Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology, Inffeldgasse 16a, 8010, Graz, Austria

    Erich Wenger & Michael Hutter

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  1. Erich Wenger
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  2. Michael Hutter
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  1. Cybernetica AS, Ülikooli 2, 51003, Tartu, Estonia

    Peeter Laud

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Wenger, E., Hutter, M. (2012). Exploring the Design Space of Prime Field vs. Binary Field ECC-Hardware Implementations. In: Laud, P. (eds) Information Security Technology for Applications. NordSec 2011. Lecture Notes in Computer Science, vol 7161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29615-4_18

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  • DOI: https://doi.org/10.1007/978-3-642-29615-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29614-7

  • Online ISBN: 978-3-642-29615-4

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