Advertisement

New Applications of Differential Bounds of the SDS Structure

  • Jiali Choy
  • Khoongming Khoo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5222)

Abstract

In this paper, we present some new applications of the bounds for the differential probability of a SDS (Substitution-Diffusion-Substitution) structure by Park et al. at FSE 2003. Park et al. have applied their result on the AES cipher which uses the SDS structure based on MDS matrices. We shall apply their result to practical ciphers that use SDS structures based on {0,1}-matrices of size n×n. These structures are useful because they can be efficiently implemented in hardware. We prove a bound on {0,1}-matrices to show that they cannot be MDS and are almost-MDS only when n = 2,3, or 4. Thus we have to apply Park’s result whenever {0,1}-matrices where n ≥ 5 are used because previous results only hold for MDS and almost-MDS diffusion matrices. Based on our bound, we also show that the {0,1}-matrices used in E2, Camellia, and MCrypton are optimal or almost-optimal among {0,1}-matrices. Using Park’s result, we prove differential bounds for the E2 and MCrypton ciphers, from which we can deduce their security against boomerang attack and some of its variants. At ICCSA 2006, Khoo and Heng constructed block cipher-based universal hash functions, from which they derived Message Authentication Codes (MACs) which are faster than CBC-MAC. Park’s result provides us with the means to obtain a more accurate bound for their universal hash function. With this bound, we can restrict the number of MAC’s performed before a change of MAC key is needed.

Keywords

SPN branch number differential {0,1}-matrices universal hash functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aoki, K., Ichikawa, T., Kanda, M., Matsui, M., Moriai, S., Nakajima, J., Tokita, T.: Camellia: A 128-bit Block Cipher Suitable for Multiple Platforms - Design and Analysis. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Barreto, P.S.L.M., Rijmen, V.: The WHIRLPOOL Hashing Function. Primitive submitted to NESSIE, revised on May 2003 (September 2000), http://paginas.terra.com.br/informatica/paulobarreto/WhirlpoolPage.html
  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)CrossRefGoogle Scholar
  4. 4.
    Biham, E., Dunkelman, O., Keller, N.: Related-Key Boomerang and Rectangle Attack. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 507–525. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology 4 (1991)Google Scholar
  6. 6.
    Brassard, G.: On computationally secure authentication tags requiring short secret shared keys. In: Crypto 1983, pp. 79–86. Springer, Heidelberg (1983)Google Scholar
  7. 7.
    Daemen, J., Rijmen, V.: The Wide Trail Strategy. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 222–238. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Daemen, J., Rijmen, V.: The Design of Rijndael: AES, The Advanced Encryption Standard. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  9. 9.
    Daemen, J., Govaerts, R., Vandewalle, J.: Correlation Matrices. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 275–285. Springer, Heidelberg (1995)Google Scholar
  10. 10.
    Daemen, J., Knudsen, L., Rijmen, V.: The Block Cipher Square. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Hong, S., Lee, S., Lim, J., Sung, J., Cheong, D., Cho, I.: Provable Security against Differential and Linear Cryptanalysis for the SPN Structure. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 273–283. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Kanda, M., Moriai, S., Aoki, K., Ueda, H., Takashima, Y., Ohta, K., Matsumoto, T.: E2 - A New 128-bit Block Cipher. IEICE Transactions Fundamentals - Special Section on Cryptography and Information Security, vol. E83-A no. 1, pp. 48-59 (2000)Google Scholar
  13. 13.
    Kelsey, J., Kohno, T., Schneier, B.: Amplified Boomerang Attacks Against Reduced-Round MARS and Serpent. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 75–93. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Khoo, K., Heng, S.H.: New Constructions of Universal Hash Functions based on Function Sum. In: Gavrilova, M.L., Gervasi, O., Kumar, V., Tan, C.J.K., Taniar, D., Laganá, A., Mun, Y., Choo, H. (eds.) ICCSA 2006. LNCS, vol. 3982, pp. 416–425. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Lim, C.H., Korkishko, T.: mCrypton - A Lightweight Block Cipher for Security of Low-Cost RFID Tags and Sensors. In: Song, J.-S., Kwon, T., Yung, M. (eds.) WISA 2005. LNCS, vol. 3786, pp. 243–258. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
  17. 17.
    Nyberg, K.: Differentially Uniform Mappings for Cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 55–64. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Park, S., Sang, S.H., Lee, S., Lim, J.: Improving the Upper Bound on the Maximum Differential and the Maximum Linear Hull Probability for SPN Structures and AES. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 247–260. Springer, Heidelberg (2003)Google Scholar
  19. 19.
    Rijmen, V., Daemen, J., Preneel, B., Bosselars, A., Win, E.D.: The Cipher Shark. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 99–111. Springer, Heidelberg (1996)Google Scholar
  20. 20.
    Stinson, D.R.: On the connections between universal hashing, combinatorial designs and error-correcting codes. In: Congressus Numerantium, vol. 114, pp. 7–27 (1996)Google Scholar
  21. 21.
    Wagner, D.: The Boomerang Attack. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Wallen, J.: Design Principles of the KASUMI Block Cipher, http://citeseer.ist.psu.edu/wallen00design.html
  23. 23.
    Wegman, M.N., Carter, J.L.: New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences 22(3), 265–279 (1981)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jiali Choy
    • 1
  • Khoongming Khoo
    • 1
  1. 1.DSO National Laboratories Singapore

Personalised recommendations