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Highly-Parallel Montgomery Multiplication for Multi-Core General-Purpose Microprocessors

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Computer and Information Sciences III

Abstract

Popular public key algorithms such as RSA and Diffie-Hellman key exchange, and more advanced cryptographic schemes such as Paillier’s and Damgård-Jurik’s algorithms (with applications in private information retrieval), require efficient modular multiplication with large integers of size at least 1024 bits. Montgomery multiplication algorithm has proven successful for modular multiplication of large integers. While general purpose multi-core processors have become the mainstream on desktop as well as portable computers, utilization of their computing resources have been largely overlooked when it comes to performing computationally intensive cryptographic operations. In this work, we propose a new parallel Montgomery multiplication algorithm which exhibits up to 39 % better performance than the known best serial Montgomery multiplication variant for the bit-lengths of 2048 or larger. Furthermore, for bit-lengths of 4096 or larger, the proposed algorithm exhibits better performance by utilizing multiple cores available. It achieves speedups of up to 81 %, 3.37 times and 4.87 times for the used general-purpose microprocessors with 2, 4 and 6 cores, respectively. To our knowledge, this is the first work that shows with actual implementation results that Montgomery multiplication can be practically and scalably parallelized on general-purpose multi-core processors.

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Notes

  1. 1.

    Recommendation for Key Management, Special Publication 800-57 Part 1 Rev. 3, NIST, 05/2011.

  2. 2.

    OpenMP Tutorial at Supercomputing 2008, http://openmp.org/wp/2008/10/openmp-tutorial-at-supercomputing-2008/ (Last accessed on 26 February 2012).

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Authors and Affiliations

  1. Department of Computer Engineering, Bahçeşehir University, Istanbul, Turkey

    Selçuk Baktir

  2. Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey

    Erkay Savaş

Authors
  1. Selçuk Baktir
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  2. Erkay Savaş
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Correspondence to Selçuk Baktir .

Editor information

Editors and Affiliations

  1. , Dept of Electrical and Electronics Eng'g, Imperial College, London, SW7 2BT, United Kingdom

    Erol Gelenbe

  2. , EEE Dept., Imperial College, Exhibition Rd., London, SW72AZ, United Kingdom

    Ricardo Lent

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Baktir, S., Savaş, E. (2013). Highly-Parallel Montgomery Multiplication for Multi-Core General-Purpose Microprocessors. In: Gelenbe, E., Lent, R. (eds) Computer and Information Sciences III. Springer, London. https://doi.org/10.1007/978-1-4471-4594-3_48

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  • DOI: https://doi.org/10.1007/978-1-4471-4594-3_48

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4593-6

  • Online ISBN: 978-1-4471-4594-3

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