Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2012: Advances in Cryptology – ASIACRYPT 2012 pp 244–261Cite as

  1. Home
  2. Advances in Cryptology – ASIACRYPT 2012
  3. Conference paper
Integral and Multidimensional Linear Distinguishers with Correlation Zero

Integral and Multidimensional Linear Distinguishers with Correlation Zero

  • Andrey Bogdanov18,
  • Gregor Leander19,
  • Kaisa Nyberg20 &
  • …
  • Meiqin Wang21 
  • Conference paper
  • 4588 Accesses

  • 58 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7658)

Abstract

Zero-correlation cryptanalysis uses linear approximations holding with probability exactly 1/2. In this paper, we reveal fundamental links of zero-correlation distinguishers to integral distinguishers and multidimensional linear distinguishers. We show that an integral implies zero-correlation linear approximations and that a zero-correlation linear distinguisher is actually a special case of multidimensional linear distinguishers. These observations provide new insight into zero-correlation cryptanalysis which is illustrated by attacking a Skipjack variant and round-reduced CAST-256 without weak key assumptions.

Keywords

  • zero-correlation cryptanalysis
  • integral distinguishers
  • multidimensional linear distinguishers
  • Skipjack
  • CAST-256

Download conference paper PDF

References

  1. Baignères, T., Junod, P., Vaudenay, S.: How Far Can We Go Beyond Linear Cryptanalysis? In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 432–450. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  2. Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of Skipjack Reduced to 31 Rounds Using Impossible Differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999)

    Google Scholar 

  3. Biham, E., Biryukov, A., Shamir, A.: Miss in the Middle Attacks on IDEA and Khufu. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 124–138. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  4. Biryukov, A., De Cannière, C., Quisquater, M.: On Multiple Linear Approximations. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 1–22. Springer, Heidelberg (2004)

    Google Scholar 

  5. Biryukov, A., Shamir, A.: Structural Cryptanalysis of SASAS. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 394–405. Springer, Heidelberg (2001)

    Google Scholar 

  6. Bogdanov, A., Leander, G., Nyberg, K., Wang, M.: Integral and Multidimensional Linear Distinguishers with Correlation Zero. IACR ePrint Archive report (2012)

    Google Scholar 

  7. Bogdanov, A., Rijmen, V.: Linear Hulls with Correlation Zero and Linear Cryptanalysis of Block Ciphers. Designs, Codes and Cryptography. Springer (to appear, 2012); preprint available as Cryptology ePrint Archive: Report 2011/123, http://eprint.iacr.org/2011/123

  8. Bogdanov, A., Wang, M.: Zero Correlation Linear Cryptanalysis with Reduced Data Complexity. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 29–48. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  9. Borst, J., Knudsen, L.R., Rijmen, V.: Two Attacks on Reduced IDEA. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 1–13. Springer, Heidelberg (1997)

    Google Scholar 

  10. Carlet, C.: Vectorial (multi-output) Boolean Functions for Cryptography. Cambridge University Press (to appear)

    Google Scholar 

  11. Carlet, C.: Boolean Functions for Cryptography and Error Correcting Codes. Cambridge University Press (to appear), preliminary version, http://www-rocq.inria.fr/codes/Claude.Carlet/chap-fcts-Bool.pdf

  12. Daemen, J., Knudsen, L.R., Rijmen, V.: The Block Cipher SQUARE. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  13. Englund, H., Maximov, A.: Attack the Dragon. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 130–142. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  14. Ferguson, N., Kelsey, J., Lucks, S., Schneier, B., Stay, M., Wagner, D., Whiting, D.: Improved Cryptanalysis of Rijndael. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  15. Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional Extension of Matsui’s Algorithm 2. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 209–227. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  16. Hermelin, M., Nyberg, K.: Linear cryptanalysis using multiple linear approximations. In: Junod, P., Canteaut, A. (eds.) Advanced Linear Cryptanalysis of Block and Stream Ciphers. IOS Press (2011)

    Google Scholar 

  17. Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional Linear Cryptanalysis of Reduced Round Serpent. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 203–215. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  18. Kaliski Jr., B.S., Robshaw, M.J.B.: Linear Cryptanalysis Using Multiple Approximations. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 26–39. Springer, Heidelberg (1994)

    Google Scholar 

  19. Knudsen, L.R., Robshaw, M.J.B., Wagner, D.: Truncated Differentials and Skipjack. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 165–180. Springer, Heidelberg (1999)

    Google Scholar 

  20. Knudsen, L.R., Wagner, D.: On the structure of Skipjack. Discrete Applied Mathematics 111(1-2), 103–116 (2001)

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Knudsen, L.R., Wagner, D.: Integral Cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  22. Leander, G.: On Linear Hulls, Statistical Saturation Attacks, PRESENT and a Cryptanalysis of PUFFIN. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 303–322. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  23. Lucks, S.: The Saturation Attack - A Bait for Twofish. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 1–15. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  24. Seki, H., Kaneko, T.: Differential Cryptanalysis of CAST-256 Reduced to Nine Quad-rounds. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences E84A(4), 913–918 (2001)

    Google Scholar 

  25. Skipjack and KEA Algorithm Specifications, Version 2.0, (May 29, 1998); The National Institute of Standards and Technology’s web page, http://csrc.nist.gov/groups/ST/toolkit/documents/skipjack/skipjack.pdf

  26. Wagner, D.: The Boomerang Attack. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  27. Wang, M., Wang, X., Hu, C.: New Linear Cryptanalytic Results of Reduced-Round of CAST-128 and CAST-256. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 429–441. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  28. Wang, Q., Chen, J.: 18-Round Impossible Differential for CAST-256 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ESAT/SCD/COSIC and IBBT, KU Leuven, Belgium

    Andrey Bogdanov

  2. Technical University of Denmark, Denmark

    Gregor Leander

  3. Aalto University, Finland

    Kaisa Nyberg

  4. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, 250100, China

    Meiqin Wang

Authors
  1. Andrey Bogdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregor Leander
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kaisa Nyberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Meiqin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Tsinghua University, 30 Shuangqing Road, 100084, Beijing, China

    Xiaoyun Wang

  2. Central Research Laboratories, NEC, 1754 Shimonumabe Nakahara, 211-8666, Kawasaki, Japan

    Kazue Sako

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 International Association for Cryptologic Research

About this paper

Cite this paper

Bogdanov, A., Leander, G., Nyberg, K., Wang, M. (2012). Integral and Multidimensional Linear Distinguishers with Correlation Zero. In: Wang, X., Sako, K. (eds) Advances in Cryptology – ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_16

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-34961-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34960-7

  • Online ISBN: 978-3-642-34961-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature