Differential Cryptanalysis of Round-Reduced Sparx-64/128

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10892)


Sparx is a family of ARX-based block ciphers designed according to the long-trail strategy (LTS) that were both introduced by Dinu et al. at ASIACRYPT’16. Similar to the wide-trail strategy, the LTS allows provable upper bounds on the length of differential characteristics and linear paths. Thus, the cipher is a highly interesting target for third-party cryptanalysis. However, the only third-party cryptanalysis on Sparx-64/128 to date was given by Abdelkhalek et al. at AFRICACRYPT’17 who proposed impossible-differential attacks on 15 and 16 (out of 24) rounds.

In this paper, we present chosen-ciphertext differential attacks on 16 rounds of Sparx-64/128. First, we show a truncated-differential analysis that requires \(2^{32}\) chosen ciphertexts and approximately \(2^{93}\) encryptions. Second, we illustrate the effectiveness of boomerangs on Sparx by a rectangle attack that requires approximately \(2^{59.6}\) chosen ciphertexts and about \(2^{122.2}\) encryption equivalents. Finally, we also considered a yoyo attack on 16 rounds that, however, requires the full codebook and approximately \(2^{126}\) encryption equivalents.


Symmetric-key cryptography Cryptanalysis Boomerang Truncated differential Yoyo ARX 


  1. 1.
    Abdelkhalek, A., Tolba, M., Youssef, A.M.: Impossible differential attack on reduced round SPARX-64/128. In: Joye, M., Nitaj, A. (eds.) AFRICACRYPT 2017. LNCS, vol. 10239, pp. 135–146. Springer, Cham (2017). Scholar
  2. 2.
    Ankele, R., List, E.: Differential cryptanalysis of round-reduced Sparx-64/128. Cryptology ePrint Archive, Report 2018/332 (2018).
  3. 3.
    Biham, E., Dunkelman, O., Keller, N.: The rectangle attack — rectangling the serpent. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 340–357. Springer, Heidelberg (2001). Scholar
  4. 4.
    Biham, E., Dunkelman, O., Keller, N.: New results on boomerang and rectangle attacks. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 1–16. Springer, Heidelberg (2002). Scholar
  5. 5.
    Biryukov, A., Khovratovich, D.: Related-key cryptanalysis of the full AES-192 and AES-256. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 1–18. Springer, Heidelberg (2009). Scholar
  6. 6.
    Cid, C., Huang, T., Peyrin, T., Sasaki, Y., Song, L.: Boomerang connectivity table (BCT) for Boomerang attack. In: EUROCRYPT. LNCS (2018, to appear)Google Scholar
  7. 7.
    Dinu, D., Perrin, L., Udovenko, A., Velichkov, V., Großschädl, J., Biryukov, A.: Design strategies for ARX with provable bounds: Sparx and LAX. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 484–513. Springer, Heidelberg (2016). Scholar
  8. 8.
    Daemen, J., Peeters, M., Van Assche, G., Rijmen, V.: Nessie Proposal: NOEKEON (2000).
  9. 9.
    Kelsey, J., Kohno, T., Schneier, B.: Amplified boomerang attacks against reduced-round MARS and serpent. In: Goos, G., Hartmanis, J., van Leeuwen, J., Schneier, B. (eds.) FSE 2000. LNCS, vol. 1978, pp. 75–93. Springer, Heidelberg (2001). Scholar
  10. 10.
    Leurent, G.: Improved differential-linear cryptanalysis of 7-round chaskey with partitioning. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 344–371. Springer, Heidelberg (2016). Scholar
  11. 11.
    Soos, M.: CryptoMiniSat SAT solver (2009).
  12. 12.
    Kölbl, S.: CryptoSMT: an easy to use tool for cryptanalysis of symmetric primitives (2015).
  13. 13.
    Tolba, M., Abdelkhalek, A., Youssef, A.M.: Multidimensional zero-correlation linear cryptanalysis of reduced round SPARX-128. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 423–441. Springer, Cham (2018). Scholar
  14. 14.
    Ganesh, V., Hansen, T., Soos, M., Liew, D., Govostes, R.: STP constraint solver (2017).
  15. 15.
    Wagner, D.: The boomerang attack. In: Knudsen, L. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999). Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Royal Holloway University of LondonEghamUK
  2. 2.Bauhaus-Universität WeimarWeimarGermany

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