Skip to main content
Log in

Characterizing the Structures of Cryptographic Functions Satisfying the Propagation Criterion for Almost All Vectors

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Many practical information authentication techniques are based on such cryptographic means as data encryption algorithms and one-way hash functions. A core component of such algorithms and functions are nonlinear functions. In this paper, we reveal a relationship between nonlinearity and propagation characteristic, two critical indicators of the cryptographic strength of a Boolean function. We also investigate the structures of functions that satisfy the propagation criterion with respect to all but six or less vectors. We show that these functions have close relationships with bent functions, and can be easily constructed from the latter.

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

Access this article

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. C. M. Adams and S. E. Tavares, Generating and counting Ňinary Ňent sequences, IEEE Transactions on Information Theory, Vol. IT-36 No. 5 (1990) pp. 1170–1173.

    Google Scholar 

  2. Claude Carle, Partially-Ňent functions, Designs, Codes and Cryptography, Vol. 3 (1993) pp. 135–145.

    Google Scholar 

  3. J. F. Dillon, A survey of Ňent function, The NSA Technical Journal, (1972) pp. 191–215, (unclassified).

  4. J. H. Evertse, Linear structures in Ňlockciphers, Advances in Cryptology —EUJROCRYPT '87, Lecture Notes in Computer Science, Springer Verlag, Berlin, HeidelŇerg, New York, 304 (1988) pp249–266.

    Google Scholar 

  5. F. J. MacWilliams and N. J. A. Sloane. The Theory of Error-Correcting Codes, North-Holland, Amsterdam, New York, Oxford, (1977).

  6. W. Meier and O. StaffelŇach, Nonlinearity criteria for cryptographic functions, Advances in Cryptology—EUROCRYPT '89, Lecture Notes in Computer Science, Springer Verlag, Berlin, HeidelŇerg, New York, 434 (1990) pp. 549–562.

    Google Scholar 

  7. K. NyŇerg, On the construction of highly nonlinear permutations, Advances in Cryptology—EUROCRYPT '92, Lecture Notes in Computer Science, Springer Verlag, Berlin, HeidelŇerg, New York, 658 (1993) pp. 92–98.

    Google Scholar 

  8. K. NyŇerg, Differentially uniform mappings for cryptography, Advances in Cryptology—EUROCRYPT '93, Lecture Notes in Computer Science, Springer Verlag, Berlin, HeidelŇerg, New York, 765 (1994) pp. 55–65.

    Google Scholar 

  9. B. Preneel, R. Govaerts, and J. Vandewalle, Boolean functions satisfying higher order propagation criteria, Advances in Cryptology—EUROCRYPT '91, Lecture Notes in Computer Science, Springer-Verlag, Berlin, HeidelŇerg, New York, 547 (1991 ) pp. 141–152.

    Google Scholar 

  10. B. Preneel, W. V. Leekwijck, L. V. Linden, R Govaerts, and J. Vandewalle, Propagation characteristics of Ňoolean functions, Advances in Cryptology—EUROCRYPT '90, Lecture Notes in Computer Science, Springer-Verlag, Berlin, HeidelŇerg, New York, 437 (1991) pp. 155–165.

    Google Scholar 

  11. O. S. Rothaus, On "Ňent" functions, Journal of ComŇinatorial Theory, Ser. A, No 20 (1976) pp. 300–305.

    Google Scholar 

  12. J. SeŇerry, X. M. Zhang, and Y. Zheng, Relationships among nonlinearity criteria, Presented at EUROCRYPT '94 (1994).

  13. J. SeŇerry, X. M. Zhang, and Y. Zheng, Nonlinearity and propagation characteristics of Ňalanced Ňoolean functions, Information and Computation, Vol. 119, No. 1 (1995) pp. 1–13.

    Google Scholar 

  14. J. SeŇerry, X. M. Zhang, and Y. Zheng, Nonlinearity and propagation characteristics and nonlinearity of cryptographic functions, Journal of Universal Computer Science, Vol. 1, No. 2 (1995) pp. 136–150. (availaŇle at http://hgiicm.tu-graz.ac.at/)

  15. A. F. WeŇster, Plaintext/ciphertext Ňit dependencies in cryptographic system, Master's Thesis, Department of Electrical Engineering, Queen's University, Ontario (1985).

    Google Scholar 

  16. A. F. WeŇster and S. E. Tavares, On the design of S-Ňoxes, Advances in Cryptology—CRYPTO '85, Lecture Notes in Computer Science, Springer-Verlag, Berlin, HeidelŇerg, New York, 219 (1986) pp. 523–534.

    Google Scholar 

  17. R. Yarlagadda and J. E. Hershey, Analysis and synthesis of Ňent sequences, IEE Proceedings (Part E), Vol. 136 (1989) pp. 112–123.

    Google Scholar 

  18. X. M. Zhang and Y. Zheng, Cac—the criterion for gloŇal avalanche characteristics of cryptographic functions, Journal of Universal Computer Science, Vol. 1, No. 5 (1995) pp. 316–333. (availaŇle at http://hgiicm.tu-graz.ac.at/).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, XM., Zheng, Y. Characterizing the Structures of Cryptographic Functions Satisfying the Propagation Criterion for Almost All Vectors. Designs, Codes and Cryptography 7, 111–134 (1996). https://doi.org/10.1023/A:1018009032032

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018009032032

Navigation