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No Silver Bullet: Optimized Montgomery Multiplication on Various 64-Bit ARM Platforms

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Information Security Applications (WISA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13009))

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Abstract

In this paper, we firstly presented optimized implementations of Montgomery multiplication on 64-bit ARM processors by taking advantages of Karatsuba algorithm and efficient multiplication instruction sets for ARM64 architectures. The implementation of Montgomery multiplication can improve the performance of (pre-quantum and post-quantum) public key cryptography (e.g. CSIDH, ECC, and RSA) implementations on ARM64 architectures, directly. Last but not least, the performance of Karatsuba algorithm does not ensure the fastest speed record on various ARM architectures, while it is determined by the clock cycles per multiplication instruction of target ARM architectures. In particular, recent Apple processors based on ARM64 architecture show lower cycles per instruction of multiplication than that of ARM Cortex-A series. For this reason, the schoolbook method shows much better performance than the sophisticated Karatsuba algorithm on Apple processors. With this observation, we can determine the proper approach for multiplication of cryptography library (e.g. Microsoft-SIDH) on Apple processors and ARM Cortex-A processors.

This work was partly supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00264, Research on Blockchain Security Technology for IoT Services, 25%) and this work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2020R1F1A1048478, 25%) and this work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No. 2021-0-00540, Development of Fast Design and Implementation of Cryptographic Algorithms based on GPU/ASIC, 25%) and this work was partly supported by Institute for Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (<Q|Crypton>, No. 2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity, 25%).

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Notes

  1. 1.

    The proposed method is applicable to RSA, and ECC, as well.

  2. 2.

    https://github.com/microsoft/PQCrypto-SIDH/tree/master/src.

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Authors and Affiliations

  1. IT Department, Hansung University, Seoul, South Korea

    Hwajeong Seo

  2. Department of Computer and Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL, USA

    Pakize Sanal & Reza Azarderakhsh

  3. Department of Computer Engineering, Gachon University, Seongnam, Incheon, 13120, Korea

    Wai-Kong Lee

  4. PQSecure Technologies, LLC, Boca Raton, USA

    Reza Azarderakhsh

Authors
  1. Hwajeong Seo
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  2. Pakize Sanal
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  3. Wai-Kong Lee
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  4. Reza Azarderakhsh
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Editor information

Editors and Affiliations

  1. Sungkyunkwan University, Suwon-Si, Korea (Republic of)

    Hyoungshick Kim

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Seo, H., Sanal, P., Lee, WK., Azarderakhsh, R. (2021). No Silver Bullet: Optimized Montgomery Multiplication on Various 64-Bit ARM Platforms. In: Kim, H. (eds) Information Security Applications. WISA 2021. Lecture Notes in Computer Science(), vol 13009. Springer, Cham. https://doi.org/10.1007/978-3-030-89432-0_16

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  • DOI: https://doi.org/10.1007/978-3-030-89432-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89431-3

  • Online ISBN: 978-3-030-89432-0

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