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一種計算旋轉(zhuǎn)對稱布爾函數(shù)的漢明重量和非線性度的新方法

張習(xí)勇,  祁應(yīng)紅,  高光普,  李玉娟

張習(xí)勇, 祁應(yīng)紅, 高光普, 李玉娟. 一種計算旋轉(zhuǎn)對稱布爾函數(shù)的漢明重量和非線性度的新方法[J]. 電子與信息學(xué)報, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
引用本文: 張習(xí)勇, 祁應(yīng)紅, 高光普, 李玉娟. 一種計算旋轉(zhuǎn)對稱布爾函數(shù)的漢明重量和非線性度的新方法[J]. 電子與信息學(xué)報, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
張習(xí)勇, 祁應(yīng)紅, 高光普, 李玉娟. A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions[J]. Journal of Electronics & Information Technology, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
Citation: 張習(xí)勇, 祁應(yīng)紅, 高光普, 李玉娟. A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions[J]. Journal of Electronics & Information Technology, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164

一種計算旋轉(zhuǎn)對稱布爾函數(shù)的漢明重量和非線性度的新方法

doi: 10.11999/JEIT 150164 cstr: 32379.14.JEIT 150164
  • 2.

    (信息工程大學(xué) 鄭州 450002) ②(數(shù)學(xué)工程與先進計算國家重點實驗室 無錫 214215) ③(洛陽外國語學(xué)校 洛陽 471003) ④(信息保障技術(shù)重點實驗室 北京 100072)

基金項目: 

國家自然科學(xué)基金(61402522, 60803154, 61572027)；數(shù)學(xué)工程與先進計算國家重點實驗室課題；信息保障技術(shù)重點實驗室開放基金(KJ-13-108)

A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions

Funds: 

The National Natural Science Foundation of China (61402522, 60803154, 61572027)

  • 摘要: 旋轉(zhuǎn)對稱布爾函數(shù)是一類重要的密碼學(xué)函數(shù)，研究其重量和非線性度等密碼學(xué)性質(zhì)具有很好的理論價值。區(qū)別于已有的計算方法，該文利用特定的正規(guī)基把這些布爾函數(shù)的問題轉(zhuǎn)化為有限域上的指數(shù)和問題，得到了4 ?? n和n=2s 時一些二次旋轉(zhuǎn)對稱布爾函數(shù)的重量和非線性度的新結(jié)果。使用所提的方法，可以計算幾乎全部的二次旋轉(zhuǎn)對稱布爾函數(shù)的重量和非線性度。所提的新方法對于研究一般的旋轉(zhuǎn)對稱布爾函數(shù)具有一定的參考意義。
    Abstract: Rotation-symmetric Boolean function is a class of Boolean functions with good cryptographic properties, and researches on its weight and nonlinearity cryptographic properties have good theoretical value. Different from the conventional calculation method, in this paper, these problems are converted to the evaluation of exponential sum on finite fields with a specific normal basis. Some new results about the weight and nonlinearity of some rotation-symmetric Boolean functions of degree 2 with4 ?? n and n=2s are obtained. Using the proposed method, the weight and nonlinearity of almost all Rotation-symmetric Boolean functions of degree 2 can be evaluated. This new method is also interesting for studies on the other Boolean functions.
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出版歷程
  • 收稿日期:  2015-01-29
  • 修回日期:  2015-06-11
  • 刊出日期:  2015-11-19

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