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Relationships among nonlinearity criteria

Chapter


Abstract


  • An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.

Publication Date


  • 1995

Citation


  • Seberry, J., Zhang, X. M., & Zheng, Y. (1995). Relationships among nonlinearity criteria. In Unknown Book (Vol. 950, pp. 376-388). doi:10.1007/bfb0053452

International Standard Book Number (isbn) 13


  • 9783540601760

Scopus Eid


  • 2-s2.0-84948966990

Web Of Science Accession Number


Book Title


  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Start Page


  • 376

End Page


  • 388

Abstract


  • An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.

Publication Date


  • 1995

Citation


  • Seberry, J., Zhang, X. M., & Zheng, Y. (1995). Relationships among nonlinearity criteria. In Unknown Book (Vol. 950, pp. 376-388). doi:10.1007/bfb0053452

International Standard Book Number (isbn) 13


  • 9783540601760

Scopus Eid


  • 2-s2.0-84948966990

Web Of Science Accession Number


Book Title


  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Start Page


  • 376

End Page


  • 388