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Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion

Conference Paper


Abstract


  • Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0- 1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearity 22k-2k and satisfying SAC, (ii) 0-1 balanced boolean functions on V2k (k ≥ 2) having nonlinearity 22k-1-2k and satisfying SAC. We demonstrate that the above non hnearities are very high not only for the 0-1 balanced functions satisfying SAC but also for all 0-1 balanced functions.

Publication Date


  • 1993

Citation


  • Seberry, J., & Zhang, X. M. (1993). Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 718 LNCS (pp. 145-155).

Scopus Eid


  • 2-s2.0-85028888814

Web Of Science Accession Number


Start Page


  • 145

End Page


  • 155

Volume


  • 718 LNCS

Abstract


  • Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0- 1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearity 22k-2k and satisfying SAC, (ii) 0-1 balanced boolean functions on V2k (k ≥ 2) having nonlinearity 22k-1-2k and satisfying SAC. We demonstrate that the above non hnearities are very high not only for the 0-1 balanced functions satisfying SAC but also for all 0-1 balanced functions.

Publication Date


  • 1993

Citation


  • Seberry, J., & Zhang, X. M. (1993). Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 718 LNCS (pp. 145-155).

Scopus Eid


  • 2-s2.0-85028888814

Web Of Science Accession Number


Start Page


  • 145

End Page


  • 155

Volume


  • 718 LNCS