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Computing Mod with a Variable Lookup Table

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Security in Computing and Communications (SSCC 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 625))

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Abstract

Encryption algorithms are designed to be difficult to break without knowledge of the secrets or keys. To achieve this, the algorithms require the keys to be large, with some having a recommend size of 2048-bits or more. However most modern processors only support computation on 64-bits at a time. Therefore standard operations with large numbers are more complicated to implement. One operation that is particularly challenging to efficiently implement is modular reduction. In this paper we propose a highly-efficient algorithm for solving large modulo operations; it has several advantages over current approaches as it supports the use of a variable sized lookup table, has good spatial and temporal locality allowing data to be streamed, and only requires basic processor instructions. Our proposed algorithm is theoretically compared to widely used modular algorithms, and shows improvements over other algorithms using predefined lookup tables.

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Acknowledgements

This research is supported by STRATUS (Security Technologies Returning Accountability, Trust and User-Centric Services in the Cloud) (https://stratus.org.nz), a science investment project funded by the New Zealand Ministry of Business, Innovation and Employment (MBIE). The authors would also like to thank Sabu M. Thampi for his kind invitation to submit this invited paper for the SSCC 2016 proceedings.

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Authors and Affiliations

  1. Cyber Security Lab, The University of Waikato, Hamilton, New Zealand

    Mark A. Will & Ryan K. L. Ko

Authors
  1. Mark A. Will
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  2. Ryan K. L. Ko
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Corresponding author

Correspondence to Mark A. Will .

Editor information

Editors and Affiliations

  1. IBM ZURICH RESEARCH LABORATORY, IBM ZURICH RESEARCH LABORATORY, RUESCHLIKON, Switzerland

    Peter Mueller

  2. Technology and Management, Indian Institute of Information Technology and Management, Kerala, India

    Sabu M. Thampi

  3. Temple University, New York, New York, USA

    Md Zakirul Alam Bhuiyan

  4. Computer Science, University of Waikato Computer Science, Hamilton, New Zealand

    Ryan Ko

  5. Deakin University , Burwood, Victoria, Australia

    Robin Doss

  6. University of the West of Scotland , Paisley, Glasgow, United Kingdom

    Jose M. Alcaraz Calero

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© 2016 Springer Nature Singapore Pte Ltd.

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Will, M.A., Ko, R.K.L. (2016). Computing Mod with a Variable Lookup Table. In: Mueller, P., Thampi, S., Alam Bhuiyan, M., Ko, R., Doss, R., Alcaraz Calero, J. (eds) Security in Computing and Communications. SSCC 2016. Communications in Computer and Information Science, vol 625. Springer, Singapore. https://doi.org/10.1007/978-981-10-2738-3_1

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  • DOI: https://doi.org/10.1007/978-981-10-2738-3_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2737-6

  • Online ISBN: 978-981-10-2738-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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