Presentation
Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion
Faculty of Informatics - Papers (Archive)
Publication Date
1-1-1993
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 nonlinearities are very high not only for the 0-1 balanced functions satisfying SAC but also for all 0-1 balanced functions.
Disciplines
Citation Information
Jennifer Seberry and Xian-Mo Zhang. "Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion" (1993) Available at: http://works.bepress.com/jseberry/339/
Jennifer Seberry and Xian-Mo Zhang, Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion, (Jennifer Seberry and Yuliang Zheng, (Eds.)), Advances in Cryptography - Auscrypt'92, Conference held at the Gold Coast, Australia, December 1992, 718, Lecture Notes in Computer Science, Springer-Verlag, Berlin--Heidelberg--New York, (1993), 145-155.