| 1. |
- Johansson, Thomas, et al.
(författare)
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A construction of resilient functions with high nonlinearity
- 2003
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 49:2, s. 494-501
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Tidskriftsartikel (refereegranskat)abstract
- We provide a construction technique for multiple-output resilient functions F: F-2(n) --> F-2(m) with high nonlinearity. The construction leads to the problem of finding a set of linear codes with a fixed minimum distance, having the property that the intersection between any two codes is the all-zero codeword only. This problem is considered, and existence results are provided. Moreover, the constructed functions obtain a nonlinearity superior to previous construction methods.
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| 2. |
- Maitra, S, et al.
(författare)
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Further constructions of resilient Boolean functions with very high nonlinearity
- 2002
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 48:7, s. 1825-1834
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Tidskriftsartikel (refereegranskat)abstract
- One well-known method of generating key stream sequences for stream ciphers is to combine the outputs of several linear-feedback shift registers (LFSR) using a combining Boolean function. Here we concentrate on the design of good combining Boolean functions. We provide resilient Boolean functions with currently best known nonlinearity. These functions were not known earlier and the issues related to their existence were posed as open questions in the literature. Some of the functions we construct here achieve the provable upper bound on nonlinearity for resilient Boolean functions. Our technique interlinks mathematical results with classical computer search.
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| 3. |
- Pasalic, Enes, et al.
(författare)
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Linear codes in generalized construction of resilient functions with very high nonlinearity
- 2002
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 48:8, s. 2182-2191
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we provide a new generalized construction method for highly nonlinear t-resilient functions, F: F-2(n) --> F-2(m). The construction is based on the use of linear error-correcting codes together with highly nonlinear multiple output functions. Given a linear [u, m, t + 1] code we show that it is possible to construct n-variable, m-output, t-resilient functions with very high nonlinearity for n > u. The method provides the currently best known nonlinearity results for most of the cases.
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