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
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(i)
0–1 balanced boolean functions on V 2k+1 (k≥1) having nonlinearity 22k−2k and satisfying SAC,
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(ii)
0–1 balanced boolean functions on V 2k (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.
Supported in part by the Australian Research Council under the reference numbers A49130102, A9030136, A49131885 and A49232172.
Supported in part by the Australian Research Council under the reference number A49130102.
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Seberry, J., Zhang, XM. (1993). Highly nonlinear 0–1 balanced boolean functions satisfying strict avalanche criterion (extended abstract). In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_58
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DOI: https://doi.org/10.1007/3-540-57220-1_58
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