Abstract
We develop several tools to derive linear independent multivariate equations from algebraic S-boxes. By applying them to maximally nonlinear power functions with the inverse exponents, Gold exponents, or Kasami exponents, we estimate their resistance against algebraic attacks. As a result, we show that S-boxes with Gold exponents have very weak resistance and S-boxes with Kasami exponents have slightly better resistance against algebraic attacks than those with the inverse exponents.
Chapter PDF
Similar content being viewed by others
References
Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology 4, 3–72 (1991)
Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer, Heidelberg (1993)
Cheon, J., Lee, D.: Almost Perfect Nonlinear Power Functions and Algebraic Attacks (2004) (manuscript)
Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)
Cheon, J., Chee, S., Park, C.: S-boxes with Controllable Nonlinearity. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 286–294. Springer, Heidelberg (1999)
Dobbertin, H.: Almost Perfect Nonlinear Power Functions on GF(2n): The Welch Case. IEEE Trans. Inform. Theory 45(4), 1271–1275 (1999)
Gold, R.: Maximal Recursive Sequences with 3-valued Recursive Cross-correlation Functions. IEEE Trans. Inform. Theory IT-14, 154–156 (1968)
Kasami, T.: The Weight Enumerators for Several Classes of Subcodes of the Second Order Binary Reed-Muller Codes. Infor. Contr. 18, 369–394 (1971)
Matsui, M.: Linear Cryptanalysis Method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1993)
Matsui, M.: New Block Encryption Algorithm MISTY. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 54–68. Springer, Heidelberg (1997)
Advances Encryption Standards, http://csrc.nist.gov/CryptoToolkit/aes/
New European Schemes for Signatures, Integrity, and Encryption, https://www.cosic.esat.kuleuven.ac.be/nessie/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheon, J.H., Lee, D.H. (2004). Resistance of S-Boxes against Algebraic Attacks. In: Roy, B., Meier, W. (eds) Fast Software Encryption. FSE 2004. Lecture Notes in Computer Science, vol 3017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25937-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-25937-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22171-5
Online ISBN: 978-3-540-25937-4
eBook Packages: Springer Book Archive