| 摘要: |
| 密码函数在密码学中具有重要的研究价值. 从组合的角度, 给出了一种密码函数不存在性证明的新方法, 并且得到了一些新结果, 部分结果优于已有结论, 这些结果可以部分证明不存在次数大于2的齐次旋转对称bent函数这一公开猜想. 同时, 利用多项式的最大公因子算法刻画了2次齐次旋转对称bent函数. 该方法也可以用于刻画其他形式的bent函数的存在性. |
| 关键词: 旋转对称布尔函数 bent函数 傅里叶变换 |
| DOI：10.13328/j.cnki.jos.006158 |
| 分类号:TP309 |
| 基金项目:国家自然科学基金(61572027) |
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| New Method for Existence Proof of Some Cryptographic Functions |
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YOU Qi-Di1,2, ZHANG Xi-Yong2, ZHOU Xuan2, WU Zhao-Yang2, YUAN Ye2
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1.Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China;2.State Key Laboratory of Space-Ground Integrated Information Technology, Beijing 100086, China
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| Abstract: |
| Cryptographic functions have important applications in the research of cryptography. This paper describes a more suitable approach to prove the nonexistence of some cryptographic functions, and obtain some new results, which support the conjecture that there are no homogeneous rotation symmetric bent functions of algebraic degree > 2. Also, homogeneous degree 2 rotation symmetric bent functions are characterizedby using GCD of polynomials. The method presented in this paper can also be used to characterize the existence of other forms of bent functions. |
| Key words: rotation-symmetric Boolean functions bent functions Fourier transform |
