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2024 06 v.29 42-47
一类逐重量完美平衡布尔函数的构造
基金项目(Foundation): 国家自然科学基金项目(61902314)
邮箱(Email):
DOI: 10.13682/j.issn.2095-6533.2024.06.006
中文作者单位:

西安邮电大学网络空间安全学院;西安邮电大学无线网络安全技术国家工程实验室;

摘要(Abstract):

考虑到已知的逐重量完美平衡(Weightwise Perfectly Balanced, WPB)布尔函数的q-重量非线性度不高,构造一类WPB布尔函数。通过修改四次函数的支撑集,得到一类新的WPB布尔函数,分析此类函数的逐重量平衡性和代数次数,并使用计算机程序对构造的WPB布尔函数的小变元函数的q-重量非线性度进行计算,结果表明,构造函数在16元时具有最高的8-重量非线性度。

关键词(KeyWords): 同态友好流密码;布尔函数;FLIP;逐重量完美平衡布尔函数;q-重量非线性度
参考文献 [1] GENTRY C.Fully homomorphic encryption using ideal lattices[C]//41st Annual ACM Symposium on Theory of Computing.New York:ACM,2009:169-178.
[2] GENTRY C,HALEVI S,SMART N.Homomorphic evaluation of the AES circuit[C]//Advances in Cryptology-CRYPTO 2012.Berlin:Springer,2012:850-867.
[3] ALBRECHT M,RECHBERGER C,SCHNEIDER T,et al.Ciphers for MPC and FHE[C]//International Association for Cryptologic Research.Advances in Cryptology-EUROCRYPT 2015.Berlin:Springer,2015:430-454.
[4] CANTEAUT A,CARPOV S,FONTAINE C,et al.Stream ciphers:A practical solution for efficient homomorphic-ciphertext compression[J].Journal of Cryptology,2018,31(3):885-916.
[5] MéAUX P,JOURNAULT A,STANDAERT F X,et al.Towards stream ciphers for efficient FHE with low-noise ciphertexts[C]//Advances in Cryptology-EUROCRYPT 2016.Berlin:Springer,2016:311-343.
[6] 郑东,严宏超,赵庆兰.一类旋转对称bent函数的构造[J].西安邮电大学学报,2018,23(2):17-21.ZHENG D,YAN H C,ZHAO Q L.Construction of a class of rotation symmetric bent functions[J].Journal of Xi’an University of Posts and Telecommunications,2018,23(3):17-21.(in Chinese)
[7] 郑东,赵庆兰,张应辉.密码学综述[J].西安邮电大学学报,2013,18(6):1-10.ZHENG D,ZHAO Q L,ZHANG Y H.A brief overview on cryptography[J].Journal of Xi’an University of Posts and Telecommunications,2013,18(6):1-10.(in Chinese)
[8] CARLET C,MEAUX P,ROTELLA Y.Boolean functions with restricted input and their robustness;application to the FLIP cipher[J].IACR Transactions on Symmetric Cryptology,2017,2017(3):192-227.
[9] MESNAGER S,ZHOU Z C,DING C S.On the nonlinearity of Boolean functions with restricted input[J].Cryptography and Communications,2019,11(1):63-76.
[10] ZHAO Q L,LI M R,CHEN Z X,et al.A unified construction of weightwise perfectly balanced Boolean functions[J].Cryptology ePrint Archive,2023,337:190-201.
[11] LI J J,SU S H.Construction of weightwise perfectly balanced Boolean functions with high weightwise nonlinearity[J].Discrete Applied Mathematics,2020,279:218-227.
[12] MESNAGER S,SU S H.On constructions of weightwise perfectly balanced Boolean functions[J].Cryptography and Communications,2021,13(6):951-979.
[13] ZHANG R,SU S H.A new construction of weightwise perfectly balanced Boolean functions[J].Advances in Mathematics of Communications,2023,17(4):757-770.
[14] GINI A,MéAUX P.Weightwise almost perfectly balanced functions:Secondary constructions for all n and better weightwise nonlinearities[C]//Cryptology-INDOCRYPT 2022.Cham:Springer,2023:492-514.
[15] 赵庆兰,李梦苒,李盼,等.一类新的逐重量完美平衡布尔函数的构造[J].西安邮电大学学报,2024,29(4):67-74.ZHAO Q L,LI M R,LI P,et al.A new construction of weightwise perfectly balanced Boolean functions[J].Journal of Xi’an University of Posts and Telecommunications,2024,29(4):67-74.(in Chinese)
[16] GINI A,MéAUX P.On the weightwise nonlinearity of weightwise perfectly balanced functions[J].Discrete Applied Mathematics,2022,322:320-341.
[17] MESNAGER S,SU S H,LI J J,et al.Concrete constructions of weightwise perfectly balanced (2-rotation symmetric) functions with optimal algebraic immunity and high weightwise nonlinearity[J].Cryptography and Communications,2022,14(6):1371-1389.
[18] TANG D,LIU J.A family of weightwise (almost) perfectly balanced Boolean functions with optimal algebraic immunity[J].Cryptography and Communications,2019,11(6):1185-1197.
[19] LIU J,MESNAGER S.Weightwise perfectly balanced functions with high weightwise nonlinearity profile[J].Designs,Codes and Cryptography,2019,87(8):1797-1813.

基本信息:

DOI:10.13682/j.issn.2095-6533.2024.06.006

中图分类号:TN918.4

引用信息:

[1]赵庆兰,王彦博.一类逐重量完美平衡布尔函数的构造[J].西安邮电大学学报,2024,29(06):42-47.DOI:10.13682/j.issn.2095-6533.2024.06.006.

基金信息:

国家自然科学基金项目(61902314)

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