VECTORIAL BOOLEAN FUNCTIONS WITH GOOD CRYPTOGRAPHIC PROPERTIES
2011 ◽
Vol 22
(06)
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pp. 1271-1282
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In this paper we generalize two remarkable results on cryptographic properties of Boolean functions given by Tu and Deng [8] to the vectorial case. Firstly we construct vectorial bent Boolean functions [Formula: see text] with good algebraic immunity for all cases 1 ⩽ m ⩽ n, and with maximum algebraic immunity for some cases (n,m). Then by modifying F, we get vectorial balanced functions [Formula: see text] with optimum algebraic degree, good nonlinearity and good algebraic immunity for all cases [Formula: see text], and with maximum algebraic immunity for some cases (n,m). Moreover, while Tu-Deng's results are valid under a combinatorial hypothesis, our results (Theorems 4 and 5) are true without this hypothesis.
2012 ◽
Vol 23
(03)
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pp. 749-760
Keyword(s):
2016 ◽
Vol 10
(2)
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pp. 257-263
2020 ◽
Vol 17
(7)
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pp. 639-654
2013 ◽
Vol 774-776
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pp. 1721-1724
Keyword(s):
2014 ◽
Vol 25
(06)
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pp. 763-780
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2013 ◽
Vol 411-414
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pp. 45-48
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Keyword(s):
2013 ◽
Vol 24
(03)
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pp. 409-417