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Efficient Representation and Software Implementation of Resilient Maiorana-McFarland S-boxes

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Information Security Applications (WISA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3325))

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Abstract

We consider software implementation of resilient Maiorana-McFarland S-boxes. Such S-boxes have application in the design of stream ciphers and their efficient software implementation is important for software implementation of the corresponding stream ciphers. Most papers on construction of resilient Maiorana-McFarland S-boxes provide mathematical descriptions which are not sufficient for implementation purposes. Moreover, the mathematical descriptions do not bring out the fact that in most cases such S-boxes can be efficiently implemented using a small amount of memory. Our work shows that these S-boxes can be implemented using a small amount of memory and the output of an S-box can be computed using a small number of operations.

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References

  1. Camion, P., Carlet, C., Charpin, P., Sendrier, N.: On correlation immune functions. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 86–100. Springer, Heidelberg (1992)

    Google Scholar 

  2. Canteaut, A., Videau, M.: Degree of composition of highly nonlinear functions and applications to higher order differential cryptanalysis. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 518–533. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Chee, S., Lee, S., Lee, D., Sung, S.H.: On the correlation immune functions and their nonlinearity. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 232–243. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  4. Chepyzhov, V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 181–195. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Courtois, N., Meier, W.: Algebraic Attacks on Stream Ciphers with Linear Feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003), Extended version, available at http://www.cryptosystem.net/stream/

    Chapter  Google Scholar 

  6. Dobbertin, H.: Almost Perfect Nonlinear Power Functions on GF(2n): The Welch Case. IEEE Transactions on Information Theory 45(4), 1271–1275 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gupta, K.C., Sarkar, P.: Improved Construction of Nonlinear S-Boxes. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 466–483. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Johansson, T., Pasalic, E.: A construction of resilient functions with high nonlinearity. In: International Symposium on Information Theory (2000)

    Google Scholar 

  9. Kurosawa, K., Satoh, T., Yamamoto, K.: Highly nonlinear t-resilient functions. Journal of Universal Computer Science 3(6), 721–729 (1997)

    MATH  MathSciNet  Google Scholar 

  10. Meier, W., Pasalic, E., Carlet, C.: Algebraic attacks and decomposition of Boolean Functions. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 474–491. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Nyberg, K.: Perfect Nonlinear S-boxes. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 378–386. Springer, Heidelberg (1991)

    Google Scholar 

  12. Pasalic, E., Maitra, S.: Linear Codes in Generalized Construction of Resilient Functions with Very High Nonlinearity. IEEE Transactions on Information Theory 48(8), 2182–2191 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sarkar, P., Maitra, S.: Construction of Nonlinear Boolean Functions with Important Cryptographic Properties. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 485–506. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Seberry, J., Zhang, X.-M., Zheng, Y.: On construction and nonlinearity of correlation immune Boolean functions. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 181–199. Springer, Heidelberg (1994)

    Google Scholar 

  15. Zhang, M.: Maximum Correlation Analysis of Nonlinear Combining Functions in Stream Ciphers. Journal of Cryptology 13(3), 301–314 (2000)

    Article  MATH  Google Scholar 

  16. Zhang, M., Chan, A.H.: Maximum Correlation Analysis of Nonlinear S-boxes in Stream Ciphers. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 501–514. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Zhang, X.-M., Zheng, Y.: On Cryptographically Resilient Functions. IEEE Transactions on Information Theory 43(5), 1740–1747 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Cryptology Research Group, Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700108, India

    Kishan Chand Gupta & Palash Sarkar

Authors
  1. Kishan Chand Gupta
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  2. Palash Sarkar
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Editor information

Editors and Affiliations

  1. Dept. of Computer Engineering, Sejong University, 143-747, Seoul, Korea

    Chae Hoon Lim

  2. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, 10027, New York, NY, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Gupta, K.C., Sarkar, P. (2005). Efficient Representation and Software Implementation of Resilient Maiorana-McFarland S-boxes. In: Lim, C.H., Yung, M. (eds) Information Security Applications. WISA 2004. Lecture Notes in Computer Science, vol 3325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31815-6_26

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  • DOI: https://doi.org/10.1007/978-3-540-31815-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24015-0

  • Online ISBN: 978-3-540-31815-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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