On the Security of the Algebraic Eraser Tag Authentication Protocol

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9696)

Abstract

The Algebraic Eraser has been gaining prominence as SecureRF, the company commercializing the algorithm, increases its marketing reach. The scheme is claimed to be well-suited to IoT applications but a lack of detail in available documentation has hampered peer-review. Recently more details of the system have emerged after a tag authentication protocol built using the Algebraic Eraser was proposed for standardization in ISO/IEC SC31 and SecureRF provided an open public description of the protocol. In this paper we describe a range of attacks on this protocol that include very efficient and practical tag impersonation as well as partial, and total, tag secret key recovery. Most of these results have been practically verified, they contrast with the 80-bit security that is claimed for the protocol, and they emphasize the importance of independent public review for any cryptographic proposal.

Keywords

Algebraic Eraser Cryptanalysis Tag authentication IoT 

References

  1. 1.
    Ågren, M., Hell, M., Johansson, T., Meier, W.: Grain-128a: a new version of grain-128 with optional authentication. Int. J. Wirel. Mob. Comput. 5(1), 48–59 (2011). InderscienceCrossRefGoogle Scholar
  2. 2.
    Anshel, I., Atkins, D., Goldfeld, D., Gunnels, P.: Defeating the Ben-Zvi, Blackburn, and Tsaban Attack on the Algebraic Eraser. http://arxiv.org/pdf/1601.04780v1.pdf, http://eprint.iacr.org/2016/044.pdf
  3. 3.
    Anshel, I., Anshel, M., Goldfeld, D., Lemieux, S.: Key agreement, the Algebraic Eraser and Lightweight Cryptography. Contemporary Mathematics 418, pp. 1–34 (2006). www.securerf.com/wp-content/uploads/2014/03/SecureRF-Technical-White-Paper-06-with-Appendix-A-B.pdf
  4. 4.
    Atkins, D.: Algebraic Eraser: A lightweight, efficient asymmetric key agreement protocol for use in no-power, low-power, and IoT devices. www.csrc.nist.gov/groups/ST/lwc-workshop2015/papers/session8-atkins-paper.pdf
  5. 5.
    Atkins, D., Goldfeld, D.: Addressing the Algebraic Eraser Diffie–Hellman over-the-Air Protocol. http://eprint.iacr.org/2016/205.pdf (Pre-print)
  6. 6.
    Atkins, D., Gunnells, P.E.: Algebraic Eraser: A lightweight, efficient asymmetric key agreement protocol for use in no-power, low-power, and IoT devices. www.csrc.nist.gov/groups/ST/lwc-workshop2015/presentations/session8-atkins-gunnell.pdf
  7. 7.
    Ben-Zvi, A., Blackburn, S.R., Tsaban, B.: A Practical Cryptanalysis of the Algebraic Eraser. 7 October 2015. http://eprint.iacr.org/2015/1102 (Pre-print)
  8. 8.
    Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M.J.B., Seurin, Y., Vikkelsoe, C.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
  10. 10.
    Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Trans. Inf. Theor. IT–22(6), 644–654 (1976)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    EPCglobal. EPC Radio Frequency Identity Protocols, Generation 2 UHF RFID. Specification for RFID Air Interface Protocol for Communications at 860 MHz-960 MHz Version 2.0.1. www.gs1.org/gsmp/kc/epcglobal/uhfc1g2
  12. 12.
    Goldfeld, D., Gunnells, P.: Defeating the Kalka-Teicher-Tsaban linear algebra attack on the Algebraic Eraser, arXiv:1202.0598, February 2012
  13. 13.
    Gunnells, P.: On the cryptanalysis of the generalized simultaneous conjugacy search problem and the security of the Algebraic Eraser, arXiv:1105.1141, May 2011
  14. 14.
    ISO/IEC 29167-10:2015 - Information technology - Automatic identification and data capture techniques - Part 10: Crypto suite AES-128 security services for air interface communicationsGoogle Scholar
  15. 15.
    ISO/IEC 29167-11:2014 - Information technology - Automatic identification and data capture techniques - Part 11: Crypto suite PRESENT-80 security services for air interface communicationsGoogle Scholar
  16. 16.
    ISO/IEC 29167-13:2015 - Information technology - Automatic identification and data capture techniques - Part 13: Crypto suite Grain-128a security services for air interface communicationsGoogle Scholar
  17. 17.
    ISO/IEC 29167-12:2015 - Information technology - Automatic identification and data capture techniques - Part 12: Crypto suite ECC-DH security services for air interface communicationsGoogle Scholar
  18. 18.
    ISO/IEC 29167-16 - Information technology - Automatic identification, data capture techniques - Part 16: Crypto suite ECDSA-ECDH security services for air interface communicationsGoogle Scholar
  19. 19.
    ISO/IEC 29167-17:2015 - Information technology - Automatic identification and data capture techniques - Part 17: Crypto suite cryptoGPS security services for air interface communicationsGoogle Scholar
  20. 20.
    ISO/IEC 29167-20 - Information technology - Automatic identification, data capture techniques - Part 20: Crypto suite Algebraic Eraser security services for air interface communications. Working DraftGoogle Scholar
  21. 21.
    Kalka, A., Teicher, M., Tsaban, B.: Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser. Adv. Appl. Math. 49, 57–76 (2012)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Myasnikov, A., Ushakov, A.: Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux key agreement protocol. Groups Complex. Crypt. 1, 63–75 (2009)MathSciNetMATHGoogle Scholar
  23. 23.
    National Institute of Standards and Technology. FIPS 197: Advanced Encryption Standard, November 2001Google Scholar
  24. 24.
    SecureRF Corporation. Corporate materials. www.securerf.com
  25. 25.
    SecureRF Corporation. Algebraic Eraser OTA Authentication. 5 October 2015. www.securerf.com/wp-content/uploads/2015/10/Algebraic_Eraser_Over-the-Air_Authentication.pdf. Also posted at [9]
  26. 26.
    Seress, Á.: Permutation Group Algorithms. Cambridge University Press, Cambridge (2003)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Information Security GroupRoyal Holloway University of LondonEghamUK
  2. 2.ImpinjSeattleUSA

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