### Citations

86 |
On correlation-immune functions
- Camion, Carlet, et al.
- 1991
(Show Context)
Citation Context ...ts7sBalanced t-th order correlation immune functions are called t-resilient functions.sFrom this point on, we will consider a balanced Boolean function as 0-resilient (thissconvention is accepted in =-=[CamCarCS1991]-=-, [SarMai1999], [PasJoh1999],s[Tara2000]) and an arbitrary Boolean function as (–1)-resilient.sThe importance of correlation immunity is that, it provides zero mutual informationsbetween any t-tuple s... |

50 |
Highly nonlinear mappings
- Carlet, Ding
(Show Context)
Citation Context ...he nonlinearity of f can be obtained from the Walsh-Hadamard transformsassω ω)(max 2 12 1 f n f Wnl −= −sThis measure of nonlinearity is important for linear cryptanalysis [Heys2000].sCarlet and Ding =-=[CarDin2004]-=- gives a more general definition for nonlinearity andsinvestigates perfect nonlinear functions.sA very well known theorem says that for any Boolean function f the sum of squaredsvalues of the Walsh-Ha... |

40 | A tutorial on linear and differential cryptanalysis,”
- Heys
- 2002
(Show Context)
Citation Context ...n H W gfd −−= −sTherefore, the nonlinearity of f can be obtained from the Walsh-Hadamard transformsassω ω)(max 2 12 1 f n f Wnl −= −sThis measure of nonlinearity is important for linear cryptanalysis =-=[Heys2000]-=-.sCarlet and Ding [CarDin2004] gives a more general definition for nonlinearity andsinvestigates perfect nonlinear functions.sA very well known theorem says that for any Boolean function f the sum of ... |

27 |
A spectral characterization of correlation immune combining functions
- Guo-Zhen, Massey
- 1988
(Show Context)
Citation Context ...( = ∈ω ωsDefinition 2.7. For a perfectly nonlinear Boolean function, also called bents[Roth1976], the squared spectrum is flat andsn fW 2)(2 =ω , for all ∈ GF(2)n.sDefinition 2.8. Xiao and Massey =-=[GouMas1988]-=- provided a spectralscharacterization of correlation immune functions. Here we state that as a definitionsof correlation immunity:sA Boolean function f is t-th order correlation immune if and only ifs... |

17 |
On the correlation immune functions and their nonlinearity
- Chee, Lee, et al.
- 1996
(Show Context)
Citation Context ...iorana-McFarland like technique is one of the construction techniques usedsto construct resilient Boolean functions and has been investigated previously in thesliterature ([CamCarCS1991], [Carl1997], =-=[CheLeeLS1996]-=-, [SarMai2000-3],s[SebZhaZ1994]). This technique of construction basically uses the following idea.sLet be a map from { }r1,0sto { }k1,0 , where for any x ∈ { }r1,0 , wt((x)) t + 1. Let fsbe a Bo... |

17 | New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity
- Pasalic, Maitra, et al.
- 2001
(Show Context)
Citation Context ...Mai2000-1] have found an upper bound for the nonlinearitysof t-resilient Boolean functions and inspired a number of researchers ([SarMai20001], [SarMai2000-2], [FedTar2001], [JohPas2003], [Tara2001], =-=[PasJohMS2001]-=-,s[Mait2000]) for discovering functions satisfying that upper bound, which iss11 22 +− −≤ tnfnlsfor 22 −> ntsand 1121 222 +−− −−≤ t n n fnlsfor 22 −≤ nt . Theyshave based their results to the fact tha... |

14 | Further results on the relation between nonlinearity and resiliency of Boolean functions
- Pasalic, Johansson
- 1999
(Show Context)
Citation Context ...lation immune functions are called t-resilient functions.sFrom this point on, we will consider a balanced Boolean function as 0-resilient (thissconvention is accepted in [CamCarCS1991], [SarMai1999], =-=[PasJoh1999]-=-,s[Tara2000]) and an arbitrary Boolean function as (–1)-resilient.sThe importance of correlation immunity is that, it provides zero mutual informationsbetween any t-tuple selected from the input vecto... |

11 | and Enes Pasalic. A Construction of Resilient Functions with High Nonlinearity
- Johansson
(Show Context)
Citation Context ...–1.sSarkar and Maitra [SarMai2000-1] have found an upper bound for the nonlinearitysof t-resilient Boolean functions and inspired a number of researchers ([SarMai20001], [SarMai2000-2], [FedTar2001], =-=[JohPas2003]-=-, [Tara2001], [PasJohMS2001],s[Mait2000]) for discovering functions satisfying that upper bound, which iss11 22 +− −≤ tnfnlsfor 22 −> ntsand 1121 222 +−− −−≤ t n n fnlsfor 22 −≤ nt . Theyshave based t... |

6 |
Construction of Cryptographically Important Boolean Functions
- Maity, Johansson
- 2002
(Show Context)
Citation Context ...f the document and also includes thesdiscussion on the nonlinearity bound of Sarkar and Maitra.sThe construction method described in Chapter 3 is a previously introduced methodsby Maity and Johansson =-=[MaiJoh2002]-=- to construct t-resilient Boolean functions ofsnonlinearity 1121 ' 222 +−− −−= t n n fnl , for t 2 ns- 2. In their method, Maity andsJohansson start with a bent function and complement some values o... |

5 |
More correlation immune and resilient functions over Galois fields and Galois rings
- Carlet
- 1997
(Show Context)
Citation Context ...niquesThe Maiorana-McFarland like technique is one of the construction techniques usedsto construct resilient Boolean functions and has been investigated previously in thesliterature ([CamCarCS1991], =-=[Carl1997]-=-, [CheLeeLS1996], [SarMai2000-3],s[SebZhaZ1994]). This technique of construction basically uses the following idea.sLet be a map from { }r1,0sto { }k1,0 , where for any x ∈ { }r1,0 , wt((x)) t + ... |

5 | On the constructing of highly nonlinear resilient Boolean functions by means of special matrices
- Fedorova, Tarannikov
(Show Context)
Citation Context ...then t + d n–1.sSarkar and Maitra [SarMai2000-1] have found an upper bound for the nonlinearitysof t-resilient Boolean functions and inspired a number of researchers ([SarMai20001], [SarMai2000-2], =-=[FedTar2001]-=-, [JohPas2003], [Tara2001], [PasJohMS2001],s[Mait2000]) for discovering functions satisfying that upper bound, which iss11 22 +− −≤ tnfnlsfor 22 −> ntsand 1121 222 +−− −−≤ t n n fnlsfor 22 −≤ nt . The... |

5 |
Improved Cost Function in the Design of Boolean Functions Satisfying Multiple Criteria
- Kavut, Yücel
- 2003
(Show Context)
Citation Context ... the Constructed FunctionssIn this section, we make a comparison of the functions constructed in the previousschapters of this work, together with some other functions provided by some previoussworks =-=[KavYüc2003]-=-. Table 5-1 gives the comparison of functions in terms ofsnonlinearity, order of resiliency, absolute indicator and sum-of-squared-errors.sTable 5-1. Comparison of 8-Variable FunctionssFunctionsf nlfs... |

2 | Computing Walsh Transform from the Algebraic Normal Form of a Boolean Function
- Gupta, Sarkar
- 2003
(Show Context)
Citation Context ... and is given by PiotrsPorwik [Porw2003].ssGupta and Sarkar have introduced an alternative computation method for computingsWalsh-Hadamard values of a Boolean function from its algebraic normal forms=-=[GupSar2003]-=-. Although their method is good for calculating the Walsh-Hadamardstransform at a specific point, the algorithm does not find all values of the spectrum,swhich is necessary for finding the nonlinearit... |

1 | Correlation Immune Boolean Functions with Very High Nonlinearity - Maitra - 2000 |