New Speed Records for Montgomery Modular Multiplication on 8-Bit AVR Microcontrollers View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2014

AUTHORS

Zhe Liu , Johann Großschädl

ABSTRACT

Modular multiplication of large integers is a performance-critical arithmetic operation of many public-key cryptosystems such as RSA, DSA, Diffie-Hellman (DH) and their elliptic curve-based variants ECDSA and ECDH. The computational cost of modular multiplication and related operations (e.g. exponentiation) poses a practical challenge to the widespread deployment of public-key cryptography, especially on embedded devices equipped with 8-bit processors (smart cards, wireless sensor nodes, etc.). In this paper, we describe basic software techniques to improve the performance of Montgomery modular multiplication on 8-bit AVR-based microcontrollers. First, we present a new variant of the widely-used hybrid method for multiple-precision multiplication that is 10.6% faster than the original hybrid technique of Gura et al. Then, we discuss different hybrid Montgomery multiplication algorithms, including Hybrid Finely Integrated Product Scanning (HFIPS), and introduce a novel approach for Montgomery multiplication, which we call Hybrid Separated Product Scanning (HSPS). Finally, we show how to perform the modular subtraction of Montgomery reduction in a regular fashion without execution of conditional statements so as to counteract Simple Power Analysis (SPA) attacks. Our AVR implementation of the HFIPS and HSPS method outperforms the Montgomery multiplication of the MIRACL Crypto SDK by up to 21.58% and 14.24%, respectively, and is twice as fast as the modular multiplication of the TinyECC library. More... »

PAGES

215-234

References to SciGraph publications

  • 2005. Energy-Efficient Software Implementation of Long Integer Modular Arithmetic in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2005
  • 2001. Distinguishing Exponent Digits by Observing Modular Subtractions in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2006. Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor in ADVANCES IN CRYPTOLOGY — CRYPTO’ 86
  • 2011. Fast Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2011
  • 2004. Simple Power Analysis of Unified Code for ECC Double and Add in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2004
  • 2007. Enabling Full-Size Public-Key Algorithms on 8-Bit Sensor Nodes in SECURITY AND PRIVACY IN AD-HOC AND SENSOR NETWORKS
  • 2003. Architectural Enhancements for Montgomery Multiplication on Embedded RISC Processors in ROBOCUP 2005: ROBOT SOCCER WORLD CUP IX
  • 2012. Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors in INFORMATION SECURITY APPLICATIONS
  • 2001-05-18. A Cryptographic Library for the Motorola DSP56000 in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’90
  • 2004. Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2004
  • 2002-09-13. Efficient Algorithms for Pairing-Based Cryptosystems in ADVANCES IN CRYPTOLOGY — CRYPTO 2002
  • 2004. Optimized RISC Architecture for Multiple-Precision Modular Arithmetic in SECURITY IN PERVASIVE COMPUTING
  • Book

    TITLE

    Progress in Cryptology – AFRICACRYPT 2014

    ISBN

    978-3-319-06733-9
    978-3-319-06734-6

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-06734-6_14

    DOI

    http://dx.doi.org/10.1007/978-3-319-06734-6_14

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1038724880


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