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Investigating Cube Attacks on the Authenticated Encryption Stream Cipher ACORN

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Applications and Techniques in Information Security (ATIS 2016)

Abstract

The cube attack is an algebraic attack that allows an adversary to extract low degree polynomial equations from the targeted cryptographic primitive. This work applies the cube attack to a reduced round version of ACORN, a candidate cipher design in the CAESAR cryptographic competition. The cube attack on 477 initialization rounds of ACORN can recover the 128 bit key with a total attack complexity of about \(2^{35}\). We have also shown that linear equations relating the initial state of the full version of ACORN can be easily generated which can lead to state recovery attack with an attack complexity of about \(2^{72.8}\).

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References

  1. Dinur, I., Shamir, A.: Cube attacks on tweakable black box polynomials. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 278–299. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01001-9_16

    Chapter  Google Scholar 

  2. Wu, H., ACORN: A Lightweight Authenticated Cipher (v1). CAESAR Competition. http://competitions.cr.yp.to/round1/acornv1.pdf. Accessed 29 May 2015

  3. CAESAR: Competition for Authenticated Encryption: Security, Applicability, and Robustness. http://competitions.cr.yp.to/index.html. Accessed 10 Sep 2015

  4. Wu, H., ACORN: A Lightweight Authenticated Cipher (v2). CAESAR Competition. http://competitions.cr.yp.to/round2/acornv2.pdf. Accessed 10 Sep 2015

  5. Lai, X.: Higher order derivatives, differential cryptanalysis. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds.) Communications, Cryptography: Two Sides of One Tapestry. The Springer International Series in Engineering and Computer Science, vol. 276, pp. 227–233. Springer, US (1994)

    Chapter  Google Scholar 

  6. Vielhaber, M., Breaking One. Fivium by AIDA an Algebraic IV Differential Attack. IACR ePrint Archive 2007/413. https://eprint.iacr.org/2007/413.pdf. Accessed 28 May 2016

  7. Cannière, C.: Trivium: a stream cipher construction inspired by block cipher design principles. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds.) ISC 2006. LNCS, vol. 4176, pp. 171–186. Springer, Heidelberg (2006). doi:10.1007/11836810_13

    Chapter  Google Scholar 

  8. Mroczkowski, P. and Szmidt, J., The Cube Attack on Courtois Toy Cipher. IACR ePrint Archive 2009/497. https://eprint.iacr.org/2009/497.pdf. Accessed 17 June 2016

  9. Dinur, I., Shamir, A.: Breaking grain-128 with dynamic cube attacks. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 167–187. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21702-9_10

    Chapter  Google Scholar 

  10. Sarkar, S., Maitra, S., Baksi, A.: Observing biases in the state: case studies with Trivium and Trivia-SC. Des. Codes Crypt. 1–25 (2016)

    Google Scholar 

  11. Blum, M., Luby, M., Rubinfeld, R.: Self-testing/correcting with applications to numerical problems. J. Comput. Syst. Sci. 47, 579–595 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Stein, W., et al.: Sage Mathematics Software (Version 6.4.1), The Sage Development Team (2015). http://www.sagemath.org

Download references

Acknowledgements

Md Iftekhar Salam was supported by the QUT Postgraduate Research Award (QUTPRA), QUT Higher Degree Research Tuition Fee Sponsorship and QUT Excellence Top Up Scholarship. Josef Pieprzyk was supported by the Polish National Science Center Grant DEC-2014/15/B/ST6/05130.

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Salam, M.I., Bartlett, H., Dawson, E., Pieprzyk, J., Simpson, L., Wong, K.KH. (2016). Investigating Cube Attacks on the Authenticated Encryption Stream Cipher ACORN. In: Batten, L., Li, G. (eds) Applications and Techniques in Information Security. ATIS 2016. Communications in Computer and Information Science, vol 651. Springer, Singapore. https://doi.org/10.1007/978-981-10-2741-3_2

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  • DOI: https://doi.org/10.1007/978-981-10-2741-3_2

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  • Print ISBN: 978-981-10-2740-6

  • Online ISBN: 978-981-10-2741-3

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