Predicting Outcomes of ElimLin Attack on Lightweight Block Cipher Simon

Nicolas T. Courtois, Pouyan Sepehrdad, Guangyan Song, Iason Papapanagiotakis-Bousy

2016

Abstract

There are two major families in cryptanalytic attacks on symmetric ciphers: statistical attacks and algebraic attacks. In this position paper we argue that algebraic cryptanalysis has not yet been developed properly due to the weakness of the theory which has substantial difficulty to prove most basic results on the number of linearly independent equations in algebraic attacks. Consequently most authors present a restricted range of attacks which are shown experimentally to work with their computer but refrain from claiming results which would work on a larger computer but have not yet been tested. For example in recent 2015 work of Raddum we discover that (experimentally) ElimLin attack breaks up to 16 rounds of Simon block cipher however it is hard to know what happens for 17 rounds. In this paper we argue that one CAN predict and model the behavior of such attacks and evaluate complexity of the attacks which we cannot yet execute. To the best of our knowledge this has never been done before.

References

  1. Courtois, N. (2000-2016b). Algebraic cryptanalysis software,. http://www.cryptosystem.net/aes/tools.html.
  2. Courtois, N. (2007a). Ctc2 and fast algebraic attacks on block ciphers revisited. In eprint. eprint.iacr.org/2007/152/.
  3. Courtois, N. (2007b). How fast can be algebraic attacks on block ciphers? In Dagstuhl Seminar 07021, Symmetric Cryptography. dagstuhl.de.
  4. Courtois, N. (2008). New frontier in symmetric cryptanalysis. In Invited talk at Indocrypt 2008. http://www.nicolascourtois.com/papers/front indocry pt08.pdf.
  5. Courtois, N. (2016a). Algebraic attacks vs. design of block and stream ciphers. In slides used in UCL GA18 course “Cryptanalysis”, University College London . http://www.nicolascourtois.com/papers/algat all teac h 2015.pdf.
  6. Courtois, N. (2016c). Software and algebraic cryptanalysis lab,. In University College London. http://www.nicolascourtois.com/papers/ga18/AC Lab 1 ElimLin Simon CTC2.pdf.
  7. Courtois, N. and Debraize, B. (2008). Specific s-box criteria in algebraic attacks on block ciphers with several known plaintexts. In WEWoRC 2007, pp 100-113. Springer.
  8. J.-M. Chen, N. C. and Yang, B.-Y. (2004). On Asymptotic Security Estimates in XL and Gr öbner Bases-Related Algebraic Cryptanalysis. In ICICS'04, pp. 401-413. Springer.
  9. M. Bardet, J.-C. Faugère], B. S. (2004). On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In ICPSS, Proceedings of International Conference on Polynomial System Solving.
  10. N. Courtois, T. Mourouzis, G. S. P. S. and Susil, P. (2014). Combined algebraic and truncated differential cryptanalysis on reduced-round simon,. In proc. of SECRYPT 2014. INSTICC.
  11. N. Courtois, G. V. B. (2007). Algebraic cryptanalysis of the data encryption standard,. In IMA Cryptography and Coding, pp. 152-169. Springer.
  12. N. Courtois, J. P. (2003). About the xl algorithm over gf(2). In CT-RSA 2003, pp. 141-157. Springer.
  13. N. Courtois, A. Shamir, J. P. A. K. (2000). Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In Eurocrypt'2000, pp. 392- 407. Springer.
  14. N. Courtois, P. Sepherdad, P. S. S. V. (2012). Elimlin algorithm revisited. In FSE 2012. Springer.
  15. Nash, J. (2012). letter to the nsa. In declassified material from 1955. www.nsa.gov.
  16. P. Susil, P. Sepehrdad, S. V. N. C. (2016). On selection of samples in algebraic attacks and a new technique to find hidden low degree equations. In Int. J. Inf. Sec. vol. 15 iss. 1, pp. 51-65. Springer.
  17. Raddum, H. (2015). Algebraic analysis of the simon block cipher family. In LatinCrypt 2015, pp. 157-169. Springer.
  18. T.J. Hodges, S.D. Molina, J. S. (2015). On the existence of semi-regular sequences. In DIMACS Workshop on the Mathematics of Post-Quantum Cryptography. arxiv.org/1412.7865.
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Paper Citation


in Harvard Style

Courtois N., Sepehrdad P., Song G. and Papapanagiotakis-Bousy I. (2016). Predicting Outcomes of ElimLin Attack on Lightweight Block Cipher Simon . In Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016) ISBN 978-989-758-196-0, pages 465-470. DOI: 10.5220/0005999504650470


in Bibtex Style

@conference{secrypt16,
author={Nicolas T. Courtois and Pouyan Sepehrdad and Guangyan Song and Iason Papapanagiotakis-Bousy},
title={Predicting Outcomes of ElimLin Attack on Lightweight Block Cipher Simon},
booktitle={Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016)},
year={2016},
pages={465-470},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005999504650470},
isbn={978-989-758-196-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016)
TI - Predicting Outcomes of ElimLin Attack on Lightweight Block Cipher Simon
SN - 978-989-758-196-0
AU - Courtois N.
AU - Sepehrdad P.
AU - Song G.
AU - Papapanagiotakis-Bousy I.
PY - 2016
SP - 465
EP - 470
DO - 10.5220/0005999504650470