Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes

被引:7
作者
Isa, Herman [1 ,2 ,3 ]
Syed Junid, Syed Alwee Aljunid [1 ,2 ]
Z'aba, Muhammad Reza [3 ]
Endut, Rosdisham [1 ,2 ]
Ammar, Syed Mohammad [1 ]
Ali, Norshamsuri [1 ,2 ]
机构
[1] Univ Malaysia Perlis, Fac Elect Engn & Technol, Arau 02600, Perlis, Malaysia
[2] Univ Malaysia Perlis, Ctr Excellence Adv Commun Engn ACE, Arau 02600, Perlis, Malaysia
[3] MIMOS Berhad, Kuala Lumpur 57000, Malaysia
关键词
s-box; cryptographically strong s-box; binomial power function; non-permutation function; redundancy removal algorithm; BLOCK CIPHER; ENCRYPTION; ALGORITHM; IMPLEMENTATION; CRYPTANALYSIS; OPTIMIZATION; EFFICIENT;
D O I
10.3390/math11020446
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A Substitution box (S-box) is an important component used in symmetric key cryptosystems to satisfy Shannon's property on confusion. As the only nonlinear operation, the S-box must be cryptographically strong to thwart any cryptanalysis tools on cryptosystems. Generally, the S-boxes can be constructed using any of the following approaches: the random search approach, heuristic/evolutionary approach or mathematical approach. However, the current S-box construction has some drawbacks, such as low cryptographic properties for the random search approach and the fact that it is hard to develop mathematical functions that can be used to construct a cryptographically strong S-box. In this paper, we explore the non-permutation function that was generated from the binomial operation of the power function to construct a cryptographically strong S-box. By adopting the method called the Redundancy Removal Algorithm, we propose some enhancement in the algorithm such that the desired result can be obtained. The analytical results of our experiment indicate that all criteria such as bijective, nonlinearity, differential uniformity, algebraic degree and linear approximation are found to hold in the obtained S-boxes. Our proposed S-box also surpassed several bijective S-boxes available in the literature in terms of cryptographic properties.
引用
收藏
页数:22
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