On the correlation immune functions and their nonlinearity

Chee, Seongtaek; Lee, Sang-Jin; Lee, Daiki; Sung, Soo Hak

doi:10.1007/bfb0034850

Cited by 43 publications

(58 citation statements)

References 6 publications

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“…As already noticed [6], there is a binomial relationship between the parameters involved (note that )…”

Section: The MM Class Revisitedmentioning

confidence: 70%

“…Construction of resilient functions by concatenating the truth tables of small affine functions was first described in [1] and revisited in greater details in [33], [6]. The concatenation simply means that the truth tables of the functions are merged.…”

Section: The MM Class Revisitedmentioning

confidence: 99%

“…Hence, for such that (6) holds, then there will exist injective mappings and, consequently, the function will be -resilient functions with nonlinearity [6] (see also Theorem 1 below). Obviously, the aim is to minimize the parameter with respect to (6).…”

Section: The MM Class Revisitedmentioning

confidence: 99%

“…Obviously, the aim is to minimize the parameter with respect to (6). Therefore, for fixed integers and , we define…”

Section: The MM Class Revisitedmentioning

confidence: 99%

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Maiorana–McFarland Class: Degree Optimization and Algebraic Properties

Pašalić

2006

IEEE Trans. Inform. Theory

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Abstract-In this paper, we consider a subclass of the Maiorana-McFarland class used in the design of resilient nonlinear Boolean functions. We show that these functions allow a simple modification so that resilient Boolean functions of maximum algebraic degree may be generated instead of suboptimized degree in the original class. Preserving a high-nonlinearity value immanent to the original construction method, together with the degree optimization gives in many cases functions with cryptographic properties superior to all previously known construction methods. This approach is then used to increase the algebraic degree of functions in the extended Maiorana-McFarland (MM) class (nonlinear resilient functions F : GF (2) n 7 ! GF (2) m derived from linear codes). We also show that in the Boolean case, the same subclass seems not to have an optimized algebraic immunity, hence not providing a maximum resistance against algebraic attacks. A theoretical analysis of the algebraic properties of extended Maiorana-McFarland class indicates that this class of functions should be avoided as a filtering function in nonlinear combining generators.

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“…As already noticed [6], there is a binomial relationship between the parameters involved (note that )…”

Section: The MM Class Revisitedmentioning

confidence: 70%

Section: The MM Class Revisitedmentioning

confidence: 99%

Section: The MM Class Revisitedmentioning

confidence: 99%

“…Obviously, the aim is to minimize the parameter with respect to (6). Therefore, for fixed integers and , we define…”

Section: The MM Class Revisitedmentioning

confidence: 99%

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Maiorana–McFarland Class: Degree Optimization and Algebraic Properties

Pašalić

2006

IEEE Trans. Inform. Theory

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“…In [10,3], they focused on finding a bound on a resiliency of a vector Boolean function with algebraic degree one. In [6,7,16,17,18,21], they focused on constructing a resilient function with a single bit output having as high as nonlinearity as possible. In [23], Zhang and Zheng proposed a method to construct a nonlinear vector resilient function from a linear vector resilient function by permuting nonlinearly its output bits.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vector Resilient Functions

Cheon¹

2001

Advances in Cryptology — CRYPTO 2001

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Improved Construction of Nonlinear Resilient S-Boxes

Gupta

Sarkar

2002

Lecture Notes in Computer Science

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Abstract. We provide two new construction methods for nonlinear resilient functions. The first method is a simple modification of an elegant construction due to Zhang and Zheng and constructs n-input, m-output resilient S-boxes with degree d > m. We prove by an application of the Griesmer bound for linear error correcting codes that the modified Zhang-Zheng construction is superior to the previous method of Cheon in Crypto 2001. Our second construction uses a sharpened version of the Maiorana-McFarland technique to construct nonlinear resilient functions. The nonlinearity obtained by our second construction is better than previously known construction methods.

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On the correlation immune functions and their nonlinearity

Cited by 43 publications

References 6 publications

Maiorana–McFarland Class: Degree Optimization and Algebraic Properties

Maiorana–McFarland Class: Degree Optimization and Algebraic Properties

Nonlinear Vector Resilient Functions

Improved Construction of Nonlinear Resilient S-Boxes

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