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Efficient Cryptographic Hardware for Safety Message Verification in Internet of Connected Vehicles

Published:14 November 2022Publication History
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Abstract

An important security requirement in automotive networks is to authenticate, sign, and verify thousands of short messages per second by each vehicle. This requirement mandates the use of a high speed Elliptic Curve Cryptography (ECC) hardware. The Residue Number Systems (RNS) provide a natural parallelism and carry-free operations that could speed-up long integer arithmetics of cryptographic algorithms. In this article, we propose a high-speed RNS Montgomery modular reduction units with parallel computing to reduce the latency of the field modular operations. We propose a fully RNS-based ECC scalar multiplication co-processor for NIST-P256r1 and Brainpool256r1 standard curves and improved the scalar multiplication speed using NAF and DBC numbering systems. Compared to the literature, our scheme provides faster computation without compromising the security level. The performance of our fully RNS-ECC point multiplication meets the requirements of the automotive industry.

REFERENCES

  1. [1] IEEE 1609.2b-2019 –IEEE Standard for Wireless Access in Vehicular Environments –Security Services for Applications and Management Messages. ([n. d.]). Retrieved on 22 Mar, 2022 from https://standards.ieee.org/standard/1609_2b-2019.html.Google ScholarGoogle Scholar
  2. [2] ETSI TS 119 312 V1.3.1 (2019-02) Electronic Signatures and Infrastructures Cryptographic Suites. ([n. d.]). Retrieved on 22 Mar, 2022 from https://www.etsi.org/deliver/etsi_ts/119300_119399/119312/01.03.01_60ts_119312v010301p.pdf.Google ScholarGoogle Scholar
  3. [3] Cao T. and Wu M.Y.. 2013. Value analysis of transmission distance in urban vehicular networks. In Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering.Google ScholarGoogle Scholar
  4. [4] Esmaeildoust Mohammad, Schinianakis Dimitrios, Javashi Hamid, Stouraitis Thanos, and Navi Keivan. 2012. Efficient RNS implementation of elliptic curve point multiplication over GF (p). IEEE Transactions on Very Large Scale Integration (VLSI) Systems 8, 21 (1 2012). DOI:Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. [5] Bajard J.-C., Laurent-Stéphane Didier, and Kornerup Peter. 1998. An RNS montgomery modular multiplication algorithm. Computers, IEEE Transactions on 7, 47 (8 1998), 766776. DOI:Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. [6] Asif Shahzad, Hossain Md Selim, and Kong Yinan. 2017. High-throughput multi-key elliptic curve cryptosystem based on residue number system. IET Computers and Digital Techniques 11, 5 (9 2017), 165172. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  7. [7] Schinianakis Dr. Dimitrios, Fournaris Apostolos, Kakarountas Athanasios, and Stouraitis Thanos. 2006. An RNS architecture of an fp elliptic curve point multiplier. In Proceedings of the IEEE International Symposium on Circuits and Systems. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  8. [8] Mo Yifeng and Li Shuguo. 2017. Fast RNS implementation of elliptic curve point multiplication in GF(p) with selected base pairs. In Proceedings of the 2017 27th International Conference on Field Programmable Logic and Applications.16.Google ScholarGoogle Scholar
  9. [9] Bajard Jean-Claude, Eynard Julien, and Merkiche Nabil. 2018. Montgomery reduction within the context of residue number system arithmetic. Journal of Cryptographic Engineering 8, 3 (1 Sep. 2018), 189200. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  10. [10] Hankerson Darrel, Menezes Alfred J., and Vanstone Scott. 2003. Guide to Elliptic Curve Cryptography. Springer-Verlag, Berlin, Heidelberg.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. [11] 2000. SEC 2: Recommended Elliptic Curve Domain Parameter. https://www.secg.org/SEC2-Ver-1.0.pdf.Google ScholarGoogle Scholar
  12. [12] Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation. ([n. d.]). Retrieved on 22 Mar, 2022 from https://tools.ietf.org/html/rfc5639.Google ScholarGoogle Scholar
  13. [13] Dimitrov Vassil S. and Cooklev Todor. 1995. Two algorithms for modular exponentiation using nonstandard arithmetics. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 78, 1 (1995), 82–87.Google ScholarGoogle Scholar
  14. [14] Bernstein D. J., Chuengsatiansup C., and Lange T.. 2017. Double-base Scalar Multiplication Revisited. IACR.Google ScholarGoogle Scholar
  15. [15] Aburto Cristobal Leiva and Theriault Nicolas. 2019. Optimal 2-3 Chains for Scalar Multiplication. Springer, 89108. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  16. [16] Mehrabi M., Doche C., and Jolfaei A.. 2020. Elliptic curve cryptography point multiplication core for hardware security module. IEEE Transactions on Computers 1, 1 (Aug. 2020), 11. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  17. [17] Mohan P. V. Ananda. 2016. Residue Number Systems: Theory and Applications. Springer international Publishing Switzerland.Google ScholarGoogle ScholarCross RefCross Ref
  18. [18] Mehrabi Mohamad Ali. 2019. Improved sum of residues modular multiplication algorithm. Cryptography 3, 2 (5 2019), 116. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  19. [19] Kawamura Shinichi, Komano Yuichi, Shimizu Hideo, and Yonemura Tomoko. 2019. RNS montgomery reduction algorithms using quadratic residuosity. Journal of Cryptographic Engineering 9, 4 (1 Nov. 2019), 313331. DOI:Google ScholarGoogle ScholarCross RefCross Ref
  20. [20] Paravati G., Lamberti F., Gandino F., Bajard J., and Montuschi P.. 2012. An algorithmic and architectural study on montgomery exponentiation in RNS. IEEE Transactions on Computers 61, 8 (Aug. 2012), 10711083. DOI:Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. [21] Guillermin Nicolas. 2010. A high speed coprocessor for elliptic curve scalar multiplications over \( \mathbb {F}_p \). In Proceedings of the Cryptographic Hardware and Embedded Systems, CHES 2010, Mangard Stefan and Standaert François-Xavier (Eds.). Springer Berlin Heidelberg, Berlin, 4864.Google ScholarGoogle ScholarCross RefCross Ref
  22. [22] Explicit Formulas Database. ([n. d.]). Retrieved on 22 Mar, 2022 from https://hyperelliptic.org/EFD.Google ScholarGoogle Scholar
  23. [23] Lai J. and Huang C.. 2008. Elixir: High-throughput cost-effective dual-field processors and the design framework for elliptic curve cryptography. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 16, 11 (Nov. 2008), 15671580. DOI:Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. [24] Alrimeih H. and Rakhmatov D.. 2014. Fast and flexible hardware support for ECC over multiple standard prime fields. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 22, 12 (Dec. 2014), 26612674. DOI:Google ScholarGoogle ScholarCross RefCross Ref

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    • Published in

      cover image ACM Transactions on Internet Technology
      ACM Transactions on Internet Technology  Volume 22, Issue 4
      November 2022
      642 pages
      ISSN:1533-5399
      EISSN:1557-6051
      DOI:10.1145/3561988
      Issue’s Table of Contents

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 14 November 2022
      • Online AM: 3 February 2022
      • Accepted: 22 October 2020
      • Revised: 1 September 2020
      • Received: 9 April 2020
      Published in toit Volume 22, Issue 4

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