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Instruction Set Extensions for Pairing-Based Cryptography

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Pairing-Based Cryptography – Pairing 2007 (Pairing 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4575))

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Abstract

A series of recent algorithmic advances has delivered highly effective methods for pairing evaluation and parameter generation. However, the resulting multitude of options means many different variations of base field must ideally be supported on the target platform. Typical hardware accelerators in the form of co-processors possess neither the flexibility nor the scalability to support fields of different characteristic and order. On the other hand, extending the instruction set of a general-purpose processor by custom instructions for field arithmetic allows to combine the performance of hardware with the flexibility of software. To this end, we investigate the integration of a tri-field multiply-accumulate (MAC) unit into a SPARC V8 processor core to support arithmetic in \({\mathbb{F}}_{p}\), \({\mathbb{F}}_{2^n}\) and \({\mathbb{F}}_{3^n}\). Besides integer multiplication, the MAC unit can also execute dedicated multiply and MAC instructions for binary and ternary polynomials. Our results show that the tri-field MAC unit adds only a small size overhead while significantly accelerating arithmetic in \({\mathbb{F}}_{2^n}\) and \({\mathbb{F}}_{3^n}\), which sheds new light on the relative performance of \({\mathbb{F}}_{p}\), \({\mathbb{F}}_{2^n}\) and \({\mathbb{F}}_{3^n}\) in the context of pairing-based cryptography.

The work described in this paper has been supported by the European Commission through the IST Programme under contract no. IST-2002-507932 ECRYPT. The information in this paper reflects only the authors’ views, is provided as is, and no guarantee or warranty is given or implied that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and liability.

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Author information

Authors and Affiliations

  1. Institute for Applied Information Processing and Communications, Graz University of Technology, Inffeldgasse 16a, A–8010 Graz, Austria

    Tobias Vejda

  2. University of Bristol, Department of Computer Science, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, U.K.

    Dan Page & Johann Großschädl

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  1. Tobias Vejda
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  2. Dan Page
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  3. Johann Großschädl
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Tsuyoshi Takagi Tatsuaki Okamoto Eiji Okamoto Takeshi Okamoto

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Vejda, T., Page, D., Großschädl, J. (2007). Instruction Set Extensions for Pairing-Based Cryptography. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds) Pairing-Based Cryptography – Pairing 2007. Pairing 2007. Lecture Notes in Computer Science, vol 4575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73489-5_11

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  • DOI: https://doi.org/10.1007/978-3-540-73489-5_11

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