Constructions of Resilient S-Boxes With Strictly Almost Optimal Nonlinearity Through Disjoint Linear Codes

2015

Security Comm Networks

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Resilient Boolean functions with high nonlinearity and good algebraic properties play an important role in designing certain stream cipher schemes. In this paper, two construction methods are proposed to obtain such functions. It is shown that a class of resilient functions with high algebraic degree and currently best known nonlinearity can be constructed by using our technique. The algebraic immunity of the constructed functions is also analyzed.Maitra and Pasalic provided a generalized construction method for m-resilient functions in [8]. We first recall this construction that will play an important role in our paper.Security Comm. Networks (2015)

Section: Preliminariesmentioning

confidence: 99%

“…Both aforementioned constructions depend on the nonlinear functions h i and h. Note that (9,3,5,240) [16] and (15, 1, -, 2 14 -2 6 -2 5 -2 4 -2 3 ) [17] functions are available. Based on the functions obtained in Examples 1 and 2, we obtain some new functions with good nonlinearity as follows.…”

Section: Remarkmentioning

confidence: 99%

Construction of resilient Boolean functions with high nonlinearity and good algebraic degree

2015

Security Comm Networks

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“…Another approach, based on the use of a set of disjoint codes, has been proposed recently in [15,Corollary 3]. This method also first constructs a perfect nonlinear Sbox, a vectorial bent function F : F n 2 → F k 2 , and modify such an S-box by a suitable replacement of its output values.…”

Section: Remarkmentioning

confidence: 99%

“…Using the trace representation it can be shown [2] that the cardinality of different vectorial bent functions of the form T r n k ( t i=1 a i x i(2 k −1) ), where a i ∈ L, equals to (2 k + 1)!2 k−1 , whereas there are only 2 k ! permutations H. It is not clear whether the trace class includes the class in [15] or these classes are possibly equal to each other.…”

Section: Remarkmentioning

confidence: 99%

Highly Nonlinear Balanced S-Boxes With Good Differential Properties

IEEE Trans. Inform. Theory

Pašalić²

2014

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Substitution boxes (S-boxes) play a central role in the modern design of iterative block ciphers. While in substitution-permutation networks (SPN) the S-boxes are bijective, thus ensuring the invertibility of the encryption algorithm, the property of being bijective is not mandatory for Feistel kind of networks. In this article, two methods of constructing highly nonlinear balanced S-boxes (whose nonlinearity > 2 n−1 − 2 n/2 is better than the nonlinearity of the commonly used inverse S-box) with good algebraic and differential properties are given. The first method employs two vectorial Boolean functions from the Maiorana-McFarland class that need to fulfil certain conditions. In particular, these conditions are shown to be satisfied by maximum length sequences. The second method is based on a suitable modification of a certain class of vectorial bent functions. The differential properties of these boxes, measured as a deviation from an optimal uniform distribution, also appear to be better than those of the inverse S-box. Both methods are susceptible to further optimizations of the relevant cryptographic parameters due to the underlying design ideas.

“…Boolean functions are usually used for S-boxes design in block ciphers and utilized as nonlinear filters and combiners in stream ciphers [10,[14][15][16][17][18]. To resist various cryptanalytic attacks, they must satisfy several criteria.…”

Section: Introductionmentioning

confidence: 99%

Construction of balanced Boolean functions with high nonlinearity, good local and global avalanche characteristics

Sun

2016

Front. Math. China

Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered: high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.