One Note About the Tu-Deng Conjecture in Case
IEEE Access, 2019 Let k ≥ 2 be an integer, and define St := {(a, b) ∈ Z2|0 ≤ a, b ≤ 2k - 2, a + b = t(mod 2k - 1), w(a) + w(b) ≤ k - 1}, where t ∈ Z, 1 ≤ t ≤ 2k - 2.
Yindong Chen +3 more
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The Tu–Deng Conjecture holds Almost Surely [PDF]
The Electronic Journal of Combinatorics, 2019 The Tu–Deng Conjecture is concerned with the sum of digits $w(n)$ of $n$ in base $2$ (the Hamming weight of the binary expansion of $n$) and states the following: assume that $k$ is a positive integer and$1\leqslant t<2^k-1$. Then\[\Bigl \lvert\Bigl\{(a,b)\in\bigl\{0,\ldots,2^k-2\bigr\}^2:a+b\equiv t\bmod 2^k-1, w(a)+w(b)<k\Bigr\}\Bigr \rvert ...
Lukas Spiegelhofer, Michael Wallner 0001
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Constructing Two Classes of Boolean Functions With Good Cryptographic Properties
IEEE Access, 2019 Wu et al. proposed a generalized Tu-Deng conjecture over $\mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}}$ , and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open.
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A Lower Bound of Fast Algebraic Immunity of a Class of 1-Resilient Boolean Functions
IEEE Access, 2019 Boolean functions should possess high fast algebraic immunity when used in stream ciphers in order to stand up to fast algebraic attacks. However, in previous research, the fast algebraic immunity of Boolean functions was usually calculated by the ...
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A note on the Tu-Deng conjecture about binary strings
四川大学学报. 自然科学版In modern symmetric cryptography design and coding theory， Boolean functions with high algebraic immunity play an important role.In 2011， Tu and Deng proposed a combinatorial conjecture on binary sequences （ Tu-Deng conjecture） and， under the assumption ...
ZHU Qi-Ang, CHEN Long, TAN Qian-Rong
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