Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria

WeiGuo Zhang; Enes Pasalic

Paper 2016/954

Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria

WeiGuo Zhang and Enes Pasalic

Abstract

In this paper, we improve the lower bound on the maximum nonlinearity of 1-resilient Boolean functions, for $n$ even, by proposing a method of constructing this class of functions attaining the best nonlinearity currently known. Thus for the first time, at least for small values of $n$ , the upper bound on nonlinearity can be reached in a deterministic manner in difference to some heuristic search methods proposed previously. The nonlinearity of these functions is extremely close to the maximum nonlinearity attained by bent functions and it might be the case that this is the highest possible nonlinearity of 1-resilient functions. Apart from this theoretical contribution, it turns out that the cryptographic properties of these functions are overall good apart from their moderate resistance to fast algebraic attacks (FAA). This weakness is repaired by a suitable modification of the original functions giving a class of balanced functions with almost optimal resistance to FAA whose nonlinearity is better than the nonlinearity of other methods.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Information Sciences
DOI: 10.1016/j.ins.2016.10.001
Keywords: Boolean functions nonlinearity resiliency algebraic immunity stream ciphers
Contact author(s): weiguozhang @ vip qq com
History: 2016-10-06: last of 3 revisions; 2016-10-04: received; See all versions
Short URL: https://ia.cr/2016/954
License: CC BY

BibTeX

@misc{cryptoeprint:2016/954,
      author = {WeiGuo Zhang and Enes Pasalic},
      title = {Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/954},
      year = {2016},
      doi = {10.1016/j.ins.2016.10.001},
      url = {https://eprint.iacr.org/2016/954}
}