Journal
INFORMATION SCIENCES
Volume 415, Issue -, Pages 377-396Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2017.06.036
Keywords
Stream ciphers; Disjoint spectra; Non-overlap spectra; Resilient functions; Nonlinearity
Categories
Funding
- National Key R&D Program of China [2017YFB0802004]
- Natural Science Foundation of China [61572148]
- Guangxi Natural Science Foundation [2015GXNSFGA139007]
- project of Outstanding Young Teachers Training in Higher Education Institutions of Guangxi
- Slovenian Research Agency [P3-0384, J1-6720]
- National Science Foundation of China [61303263]
- Fundamental Research Funds for the Central Universities [2015XKMS086]
- National Natural Science Foundation of China [61672509, 61232009]
- EU [641985, 734325, PIRSES-GA-2013-612652]
- EPSRC [EP/L020009/1]
- EPSRC [EP/L020009/1] Funding Source: UKRI
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The design of n-variable t-resilient functions with strictly almost optimal (SAO) nonlinearity (> 2(n-1) - 2(n/2), n even) appears to be a rather difficult task. The known construction methods commonly use a rather large number (exactly Sigma(n/2)(i=t+1)((n/2)(i))) of affine subfunctions in n/2 variables which can induce some algebraic weaknesses, making these functions susceptible to certain types of guess and determine cryptanalysis and dynamic cube attacks. In this paper, the concept of non-overlap spectra functions is introduced, which essentially generalizes the idea of disjoint spectra functions on different variable spaces. Two, general methods to obtain a large set of non-overlap spectra functions are given and a new framework for designing infinite classes of resilient functions with SAO nonlinearity is developed based on these. Unlike previous construction methods, our approach employs only a few n/2-variable affine subfunctions in the design, resulting in a more favourable algebraic structure. It is shown that these new resilient SAO functions properly include all the existing classes of resilient SAO functions as a subclass. Moreover, it is shown that the new class provides a better resistance against (fast) algebraic attacks than the known functions with SAO nonlinearity, and in addition these functions are more robust to guess and determine cryptanalysis and dynamic cube attacks. (C) 2017 Elsevier Inc. All rights reserved.
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