Skip to main content
SpringerLink
Log in

On cross-correlation indicators of an S-box

  • Research Article
  • Published:
Frontiers of Computer Science in China Aims and scope Submit manuscript

Abstract

Substitution boxes (S-boxes) are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global avalanche characteristics (GGAC) were introduced to measure the correlation between two arbitrary Boolean functions. In this paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying the related properties of the cross-correlation between two balanced Boolean functions, we propose the lower bounds on the sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang W G, Xiao G Z. Constructions of almost optimal resilient Boolean functions on large even number of variables. IEEE Transactions on Information Theory, 2009, 55(12): 5822–5831

    Article  MathSciNet  Google Scholar 

  2. Webster A F, Tavares S E. On the design of S-boxes. In: Proceedings of CRYPTO’85. 1986, 523–534

  3. Preneel B, Van Leekwijck W, Van Linden L, Govaerts R, Vandewalle J. Propagation characteristics of Boolean functions. In: Proceedings of Workshop on the Theory and Application of Cryptographic Techniques. 1991, 161–173

  4. Preneel B, Govaerts R, Vandewalle J. Boolean functions satisfying higher order propagation criteria. In: Proceedings of 1991 Workshop on the Theory and Application of Cryptographic Techniques. 1991, 141–152

  5. Zhang X M, Zheng Y L. GAC — the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1995, 1(5): 316–333

    MathSciNet  Google Scholar 

  6. Shannon C E. Communication theory of secrecy systems. Bell System Technical Journal, 1949, 28(4): 656–715

    MATH  MathSciNet  Google Scholar 

  7. Sarkar P, Maitra S. Cross-correlation analysis of cryptographically useful Boolean functions and S-boxes. Theory of Computing Systems, 2002, 35(3): 39–57

    MATH  MathSciNet  Google Scholar 

  8. Zhou Y, Xie M, Xiao G Z. On the global avalanche characteristics between two Boolean functions and the higher order nonlinearity. Information Sciences, 2010, 180(2): 256–265

    Article  MATH  MathSciNet  Google Scholar 

  9. Leander G, Poschmann A. On the classification of 4-bit S-boxes. In: Proceedings of 1st International Workshop on Arithmetic of Finite Fields. 2007, 159–176

  10. Biham E, Shamir A. Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 1991, 4(1): 3–72

    Article  MATH  MathSciNet  Google Scholar 

  11. Matsui M. Linear cryptanalysis method for DES cipher. In: Proceedings of Workshop on the Theory and Application of Cryptographic Techniques. 1994, 396–397

  12. Gligoroski D, Moe M E G. On deviations of the AES S-box when represented as vector valued Boolean function. International Journal of Computer Science and Network Security, 2007, 7(4): 156–163

    Google Scholar 

  13. Gao S, Ma W P, Guo N, Chen Q L. Design of cross-correlation test algorithm on S-box. Geomatics and Information Science of Wuhan University, 2010, 35(5): 558–561

    Google Scholar 

  14. Mister S, Adams C. Practical S-box design. In: Proceedings of the 3rd Annual Workshop on Selected Areas in Cryptography. 1996, 1–17

  15. Nyberg K. Perfect nonlinear S-boxes. In: Proceedings of 10th Annual International Conference on Theory and Application of Cryptographic. 1991, 378–385

  16. Porwik P. The spectral test of Boolean function linearity. Journal of Applied Mathematics and Computer Science, 2003, 13(4): 567–575

    MATH  MathSciNet  Google Scholar 

  17. National Bureau of Standards. Data encryption standard (DES). Federal Information Processing Standard, 1977

  18. Daemen J, Rijmen V. The block cipher Rijndael. http://www.nist.gov/aes

  19. Johansson T, Pasalic E. A construction of resilient functions with high nonlinearity. IEEE Transactions on Information Theory, 2003, 49(2): 494–501

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhang M, Chan A. Maximum correlation analysis of nonlinear Sboxes in stream ciphers. In: Proceedings of 20th Annual International Cryptology Conference on Advances in Cryptology. 2000, 501–514

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi’an, 710071, China

    Sheng Gao, Wenping Ma & Fenghe Wang

  2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Zepeng Zhuo

Authors
  1. Sheng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenping Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zepeng Zhuo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fenghe Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sheng Gao.

Additional information

Sheng Gao received his BSc in mathematics from Taiyuan Normal University in 2005 and his MSc in mathematics from Qinghai Normal University in 2008. Now he is a PhD candidate at Xidian University. His current research interests include cryptography, information security, cloud computing and cloud security.

Wenping Ma is Professor and PhD supervisor at Xidian University. He obtained his BSc and MSc in mathematics from Shanxi Normal University in 1987 and 1990, and the PhD in Communication and Information Systems from the School of Communication Engineering, Xidian University in 1999. His main research interests include coding theory, cryptography, and information theory.

Zepeng Zhuo received his BSc and MSc in mathematics from Huaibei Coal Industry Normal College in 2004 and 2007, respectively. Now he is a PhD candidate at Xidian University. His current research interests include cryptography and information theory.

Fenghe Wang received his BSc in mathematics from Yantai Normal University in 2001 and his MSc in cryptography from Xidian University in 2006. Now he is a PhD candidate at Xidian University. His current research interests include lattice public key cryptography and digital signatures.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, S., Ma, W., Zhuo, Z. et al. On cross-correlation indicators of an S-box. Front. Comput. Sci. China 5, 448–453 (2011). https://doi.org/10.1007/s11704-011-0177-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-011-0177-9

Keywords

Search

Navigation