Efficient Implementation of NIST-Compliant Elliptic Curve Cryptography for Sensor Nodes View Full Text


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Chapter Info

DATE

2013

AUTHORS

Zhe Liu , Hwajeong Seo , Johann Großschädl , Howon Kim

ABSTRACT

In this paper, we present a highly-optimized implementation of standards-compliant Elliptic Curve Cryptography (ECC) for wireless sensor nodes and similar devices featuring an 8-bit AVR processor. The field arithmetic is written in Assembly language and optimized for the 192-bit NIST-specified prime p = 2192 − 264 − 1, while the group arithmetic (i.e. point addition and doubling) is programmed in ANSI C. One of our contributions is a novel lazy doubling method for multi-precision squaring which provides better performance than any of the previously-proposed squaring techniques. Based on our highly optimized arithmetic library for the 192-bit NIST prime, we achieve record-setting execution times for scalar multiplication (with both fixed and arbitrary points) as well as multiple scalar multiplication. Experimental results, obtained on an AVR ATmega128 processor, show that the two scalar multiplications of ephemeral Elliptic Curve Diffie-Hellman (ECDH) key exchange can be executed in 1.75 s altogether (at a clock frequency of 7.37 MHz) and consume an energy of some 42 mJ. The generation and verification of an ECDSA signature requires roughly 1.91 s and costs 46 mJ at the same clock frequency. Our results significantly improve the state-of-the-art in ECDH and ECDSA computation on the P-192 curve, outperforming the previous best implementations in the literature by a factor of 1.35 and 2.33, respectively. We also protected the field arithmetic and algorithms for scalar multiplication against side-channel attacks, especially Simple Power Analysis (SPA). More... »

PAGES

302-317

References to SciGraph publications

  • 2005. Energy-Efficient Software Implementation of Long Integer Modular Arithmetic in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2005
  • 2011. Fast Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2011
  • 2008. Twisted Edwards Curves Revisited in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2008
  • 2008. NanoECC: Testing the Limits of Elliptic Curve Cryptography in Sensor Networks in WIRELESS SENSOR NETWORKS
  • 2004. Instruction Set Extensions for Fast Arithmetic in Finite Fields GF(p) and GF(2m) in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2004
  • 2010. Stealthy Compromise of Wireless Sensor Nodes with Power Analysis Attacks in MOBILE LIGHTWEIGHT WIRELESS SYSTEMS
  • 2014. MoTE-ECC: Energy-Scalable Elliptic Curve Cryptography for Wireless Sensor Networks in APPLIED CRYPTOGRAPHY AND NETWORK SECURITY
  • 2009. Energy-Efficient Implementation of ECDH Key Exchange for Wireless Sensor Networks in INFORMATION SECURITY THEORY AND PRACTICE. SMART DEVICES, PERVASIVE SYSTEMS, AND UBIQUITOUS NETWORKS
  • 1999. Differential Power Analysis in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2006. Efficient Implementation of Public Key Cryptosystems on Mote Sensors (Short Paper) in INFORMATION AND COMMUNICATIONS SECURITY
  • 2012. Smart Elliptic Curve Cryptography for Smart Dust in QUALITY, RELIABILITY, SECURITY AND ROBUSTNESS IN HETEROGENEOUS NETWORKS
  • 2012. Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors in INFORMATION SECURITY APPLICATIONS
  • 2004. Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2004
  • 2006. Curve25519: New Diffie-Hellman Speed Records in PUBLIC KEY CRYPTOGRAPHY - PKC 2006
  • 2013. NaCl on 8-Bit AVR Microcontrollers in PROGRESS IN CRYPTOLOGY – AFRICACRYPT 2013
  • Book

    TITLE

    Information and Communications Security

    ISBN

    978-3-319-02725-8
    978-3-319-02726-5

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-02726-5_22

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    http://dx.doi.org/10.1007/978-3-319-02726-5_22

    DIMENSIONS

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    30 schema:description In this paper, we present a highly-optimized implementation of standards-compliant Elliptic Curve Cryptography (ECC) for wireless sensor nodes and similar devices featuring an 8-bit AVR processor. The field arithmetic is written in Assembly language and optimized for the 192-bit NIST-specified prime p = 2192 − 264 − 1, while the group arithmetic (i.e. point addition and doubling) is programmed in ANSI C. One of our contributions is a novel lazy doubling method for multi-precision squaring which provides better performance than any of the previously-proposed squaring techniques. Based on our highly optimized arithmetic library for the 192-bit NIST prime, we achieve record-setting execution times for scalar multiplication (with both fixed and arbitrary points) as well as multiple scalar multiplication. Experimental results, obtained on an AVR ATmega128 processor, show that the two scalar multiplications of ephemeral Elliptic Curve Diffie-Hellman (ECDH) key exchange can be executed in 1.75 s altogether (at a clock frequency of 7.37 MHz) and consume an energy of some 42 mJ. The generation and verification of an ECDSA signature requires roughly 1.91 s and costs 46 mJ at the same clock frequency. Our results significantly improve the state-of-the-art in ECDH and ECDSA computation on the P-192 curve, outperforming the previous best implementations in the literature by a factor of 1.35 and 2.33, respectively. We also protected the field arithmetic and algorithms for scalar multiplication against side-channel attacks, especially Simple Power Analysis (SPA).
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