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| on the construction of cryptographically significant boolean functions using objects in projective geometry spaces | |
| Pasalic Enes; Wei Yongzhuang | |
| 2012 | |
| Source | IEEE Transactions on Information Theory
 |
| ISSN | 189448 |
| Volume | 58Issue:10Pages:6681-6693 |
| English Abstract | Recently, several construction methods of highly nonlinear Boolean functions with relatively good algebraic properties were proposed. These approaches manage in optimizing most of the relevant cryptographic criteria, but not all of them at the same time. Usually, either the nonlinearity bounds are rather loose (though the actual nonlinearity is relatively high) or the functions do not provide a good resistance to fast algebraic cryptanalysis. In this paper, we develop a theoretical framework for using objects in suitable projective geometry spaces for construction of highly nonlinear Boolean functions. This allows us to establish tight bounds on the nonlinearity using simple counting arguments, thus avoiding rather complicated estimates of certain trace sums. Our method generates a class of almost fully optimized functions, that is the functions apart from very high nonlinearity also have the maximum algebraic degree and optimal algebraic immunity. Compared to the classes of functions proposed by Carlet and Feng, Wang , and Zeng , our functions achieve a slightly better nonlinearity which is traded-off against a little worse resistance against fast algebraic attacks. On the other hand, compared to the functions by Tang and Tu and Deng, our nonlinearity is somewhat lower, but the algebraic properties are slightly better. © 1963-2012 IEEE. |
| Indexed Type | ei |
| Department | (1) University of Primorska, FAMNIT, PINT, 6000, Koper, Slovenia; (2) State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China; (3) Department of Communication and Information Engineering, Guilin University of Electronic Technology, Guilin 541004, China |
| Language | 英语 |
| WOS ID | WOS:000308965600030 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14747 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Pasalic Enes,Wei Yongzhuang. on the construction of cryptographically significant boolean functions using objects in projective geometry spaces[J]. IEEE Transactions on Information Theory,2012,58(10):6681-6693. |
| APA | Pasalic Enes,&Wei Yongzhuang.(2012).on the construction of cryptographically significant boolean functions using objects in projective geometry spaces.IEEE Transactions on Information Theory,58(10),6681-6693. |
| MLA | Pasalic Enes,et al."on the construction of cryptographically significant boolean functions using objects in projective geometry spaces".IEEE Transactions on Information Theory 58.10(2012):6681-6693. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 06216427.pdf（4897KB） | 开放获取 | License | Application Full Text | |||
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