New Results on Boolean Functions with High Nonlinearity and Low Transparency Order. (17th April 2023)

• Record Type: Journal Article
• Authors: Zhang, Yibo; Wang, Yu; Wang, Qichun; Sun, Yinxia; Yu, Zhipeng
• Other Names: Rezai Abdalhossein Academic Editor.
• Is Part Of: Security and communication networks. Volume 2023(2023)
• Publication Date: 2023-04-17
• Subjects: Computer networks -- Security measures -- Periodicals; Computer security -- Periodicals; Cryptography -- Periodicals; 005.805
• DOI: 10.1155/2023/5189651
• Languages: English
• ISSNs: 1939-0114

Abstract

Abstract : We improve the steepest descent algorithm and increase the double threshold parameter, which significantly improves the algorithm's efficiency. And we design a new cost function so that in terms of search, various characteristics of Boolean functions can be taken into account simultaneously. Applying our algorithm, there are excellent results regarding the 9, 10, 11, and 12 variables. We find a Boolean function with a nonlinearity of 242 in 9 variables and the whole search space. Previously, this result only appeared in the rotational symmetry class. The best-achieved nonlinearity result for permutation (6, 5, 1, 4, 7, 2, 3, 0, 8) and (0, 7, 2, 5, 4, 1, 3, 6, 8) class is 238 and 239 introduced by Kavut in Information and Computation (2010). Still, applying our algorithm, we obtain a balanced Boolean function with a nonlinearity of 240 under the same permutation, indicating that our method is more general. Among the 11 variables, a Boolean function with a higher nonlinearity and a lower transparency level and the absolute value spectrum are maintained at a lower level. The algorithm performs well when considering all aspects of the property. There are similarly promising results in even-numbered variables.