Montgomery Modular Multiplication on ARM-NEON Revisited View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015

AUTHORS

Hwajeong Seo , Zhe Liu , Johann Großschädl , Jongseok Choi , Howon Kim

ABSTRACT

Montgomery modular multiplication constitutes the “arithmetic foundation” of modern public-key cryptography with applications ranging from RSA, DSA and Diffie-Hellman over elliptic curve schemes to pairing-based cryptosystems. The increased prevalence of SIMD-type instructions in commodity processors (e.g. Intel SSE, ARM NEON) has initiated a massive body of research on vector-parallel implementations of Montgomery modular multiplication. In this paper, we introduce the Cascade Operand Scanning (COS) method to speed up multi-precision multiplication on SIMD architectures. We developed the COS technique with the goal of reducing Read-After-Write (RAW) dependencies in the propagation of carries, which also reduces the number of pipeline stalls (i.e. bubbles). The COS method operates on 32-bit words in a row-wise fashion (similar to the operand-scanning method) and does not require a “non-canonical” representation of operands with a reduced radix. We show that two COS computations can be “coarsely” integrated into an efficient vectorized variant of Montgomery multiplication, which we call Coarsely Integrated Cascade Operand Scanning (CICOS) method. Due to our sophisticated instruction scheduling, the CICOS method reaches record-setting execution times for Montgomery modular multiplication on ARM-NEON platforms. Detailed benchmarking results obtained on an ARM Cortex-A9 and Cortex-A15 processors show that the proposed CICOS method outperforms Bos et al’s implementation from SAC 2013 by up to 57 % (A9) and 40 % (A15), respectively. More... »

PAGES

328-342

References to SciGraph publications

  • 2014. Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and Their Implementation on GLV-GLS Curves in TOPICS IN CRYPTOLOGY – CT-RSA 2014
  • 2010. Montgomery Multiplication on the Cell in PARALLEL PROCESSING AND APPLIED MATHEMATICS
  • 2014. Montgomery Multiplication Using Vector Instructions in SELECTED AREAS IN CRYPTOGRAPHY -- SAC 2013
  • 2006. Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor in ADVANCES IN CRYPTOLOGY — CRYPTO’ 86
  • 2012. NEON Crypto in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2012
  • 2013. Fast Software Polynomial Multiplication on ARM Processors Using the NEON Engine in SECURITY ENGINEERING AND INTELLIGENCE INFORMATICS
  • 2013. NEON Implementation of an Attribute-Based Encryption Scheme in APPLIED CRYPTOGRAPHY AND NETWORK SECURITY
  • 2012. Software Implementation of Modular Exponentiation, Using Advanced Vector Instructions Architectures in ARITHMETIC OF FINITE FIELDS
  • Book

    TITLE

    Information Security and Cryptology - ICISC 2014

    ISBN

    978-3-319-15942-3
    978-3-319-15943-0

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-15943-0_20

    DOI

    http://dx.doi.org/10.1007/978-3-319-15943-0_20

    DIMENSIONS

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