4t-1元旋转对称2-弹性函数的构造

doi:10.11959/j.issn.1000-436x.2020213

Abstract

Abstract:

Some properties of rotation symmetric orbits were proposed in n dimensional vector space over finite field of characteristic 2,a matrix on the distributions of number pairs such as 00,01 and 11 was defined,and a new characterization of 2-resilient rotation symmetric functions was introduced.Constructions of rotation symmetric 2-resilient Boolean functions with 4t-1 number of variables were presented by modifying the support of the linear rotation symmetric functions,such as f₀(x)=x₁+x₂+…+x_n,where n=4t-1.At last,an example was demonstrated to introduce the spirit of the proposed method to construct 2-resilient rotation symmetric functions with 4t-1 number of variables.

Key words: cryptography, rotation symmetric function, orthogonal array, resilient function, support table

CLC Number:

TN918.1

Jiao DU,Chunhong LIU,Shanqi PANG. Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables[J]. Journal on Communications, 2020, 41(11): 169-175.

References 23

[1]	PIEPRZYK J , QU C X . Fast hashing and rotation symmetric functions[J]. Journal Universal Computer Science, 1999,5(1): 20-31.
[2]	FILIOL E , FONTAINE C . Highly nonlinear balanced boolean functions with a good correlation-immunity[C]// International Conference on the Theory and Application of Cryptographic Techniques. Berlin:Springer, 1998: 475-488.
[3]	CUSICK W , STANICA P , MAITRA S . Fast evaluation,weight and nonlinearity of rotation symmetric functions[J]. Discrete Mathematics, 2002,258(1-3): 289-301.
[4]	STANICA P , MAITRA S , CLARK J . Results on rotation symmetric bent and correlation immune Boolean functions[C]// Fast Software Encryption Workshop (FSE 2004). Berlin:Springer, 2004: 161-177.
[5]	KAVUT S , MAITRA S , SARKAR S ,et al. Enumeration of 9-variable Rotation symmetric Boolean functions having nonlinearity>240[C]// International Conference on Cryptology. Berlin:Springer, 2006: 266-279.
[6]	KAVUT S , MAITRA S , YUCEL M D . Search for Boolean functions with excellent profiles in the rotation symmetric class[J]. IEEE Transactions on Information Theory, 2007,53(5): 1743-1751.
[7]	CARLET C , DALAI D K , GUPTA K C ,et al. Algebraic immunity for cryptographically significant Boolean functions:analysis and construction[J]. IEEE Transactions on Information Theory, 2006,52(7): 3105-3121.
[8]	STANICA P , MAITRA S . Rotation symmetric Boolean functions count and cryptographic properties[J]. Discrete Applied Mathematics, 2008,156: 1567-1580.
[9]	王永娟, 韩文报, 李世取 . 满足 CI 的 RotS 函数的构造与计数[J]. 通信学报, 2007,28(11): 6-9.
	WANG Y J , HAN W B , LI S Q . Construction and numeration of correlation immunity RotS Boolean function[J]. Journal on Communications, 2007,28(11): 6-9.
[10]	FU S J , LI C , QU L J . On the number of rotation symmetric Boolean functions[J]. Science China Information Sciences, 2010,53(3): 537-545.
[11]	张鹏, 付绍静, 屈龙江 ,等. 平衡旋转对称布尔函数的计数[J]. 应用科学学报, 2012,30(1): 45-51.
	ZHANG P , FU S J , QU L J ,et al. Enumeration of balanced rotation-symmetric Boolean functions[J]. Journal of Applied Sciences-Electronics and Information Engineering, 2012,30(1): 45-51.
[12]	庞善起, 杜蛟, 席金彦 . 相关免疫函数阶的判别方法[J]. 应用数学学报, 2009,32(3): 445-453.
	PANG S Q , DU J , XI J Y . Some methods for judging the order of correlation-immune functions[J]. Acta Mathematicae Applicatae Sinica, 2009,32(3): 445-453.
[13]	杜蛟, 温巧燕, 张劼 ,等. 素数元旋转对称弹性布尔函数的构造与计数[J]. 通信学报, 2013,34(3): 6-13.
	DU J , WEN Q Y , ZHANG J ,et al. Construction and count of resilient rotation symmetric Boolean functions with prime number of variables[J]. Journal on Communications, 2013,34(3): 6-13.
[14]	SUN L , FU F W , GUANG X . Two classes of 1-resilient prime-variable rotation symmetric Boolean functions[J]. IEICE Transactions on Fundamentals of Electronics Communications ＆ Computer Sciences, 2017,100(3): 902-907.
[15]	DU J , WEN Q Y , ZHANG J ,et al. Constructions of resilient rotation symmetric Boolean functions on given number of variables[J]. IET Information Security, 2014,8(5): 265-272.
[16]	杜蛟, 温巧燕, 张劼 ,等. 2p元2-阶旋转对称弹性布尔函数的构造与计数[J]. 北京邮电大学学报, 2013,35(5): 36-40.
	DU J , WEN Q Y , ZHANG J ,et al. Construction and counting of resilient 2-rotation symmetric Boolean functions with 2p variables[J]. Journal of Beijing University of Posts and Telecommunications, 2013,35(5): 36-40.
[17]	PANG S Q , WANG X N , WANG J ,et al. Construction and count of 1-resilient rotation symmetric Boolean functions[J]. Information Sciences, 2018,450: 336-342.
[18]	SUN L , LIU J , FU F W . Secondary constructions of RSBFs with good cryptographic properties[J]. Information Processing Letters, 2019,147: 44-48.
[19]	杜蛟, 庞善起, 温巧燕 ,等. GF(p)上q元旋转对称弹性函数的一个等价刻画[J]. 通信学报, 2014,35(8): 179-183.
	DU J , PANG S Q , WEN Q Y ,et al. Equivalent characterization of resilient rotation symmetric functions with q number of variables over GF(p)[J]. Journal on Communications, 2014,35(8): 179-183.
[20]	DU J , FU S J , QU L J ,et al. New constructions of q-variable 1-resilient rotation symmetric functions over F_p[J]. Science China Information Science, 2016,59(7): 1-3.
[21]	SU S H , TANG X H . Systematic constructions of rotation symmetric bent functions,2-rotation symmetric bent functions,and bent idempotent functions[J]. IEEE Transactions on Information Theory, 63(7): 4658-4667.
[22]	GOPALAKRISHNAN K , STINSON D R . Three characterizations of non-binary correlation-immune and resilient functions[J]. Designs Codes ＆ Cryptography, 1995,5: 241-251.
[23]	STINSON D R . Resilient functions and large sets of orthogonal arrays[J]. Congressus Numerantium, 1993,92: 105-110.

Metrics

Recommended 0

No Suggested Reading articles found!

Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References 23

Related Articles 15

Metrics

Recommended 0

[1]	Huawei HUANG. Security analysis of public-key cryptosystems based on matrix action problem against quantum attack [J]. Journal on Communications, 2023, 44(3): 220-226.
[2]	Ziyuan WANG, Ruizhong DU. Certificateless public key cryptography based provable data possession scheme in edge environment [J]. Journal on Communications, 2022, 43(7): 62-72.
[3]	Zhu WANG, Siqi YANG, Fenghua LI, Kui GENG, Tingting PENG, Mengyao SHI. Efficient and provably-secure certificateless sequential aggregate signature scheme [J]. Journal on Communications, 2022, 43(5): 58-67.
[4]	Bin LI, Xiaojie CHEN, Feng FENG, Qinglei ZHOU. FPGA multi-unit parallel optimization and implementation of post-quantum cryptography CRYSTALS-Kyber [J]. Journal on Communications, 2022, 43(2): 196-207.
[5]	Youliang TIAN, Xiaoxia JIANG. Fair and rational delegation of computation in the universally composable framework [J]. Journal on Communications, 2021, 42(9): 106-119.
[6]	Hui LIU, Xinyan LIU, Yan XU, Hong ZHONG, Meng WANG. Privacy protection of warning message publishing protocol in VANET [J]. Journal on Communications, 2021, 42(8): 120-129.
[7]	Jiangtao DONG, Peiwen YAN, Ruizhong DU. Verifiable access control scheme based on unpaired CP-ABE in fog computing [J]. Journal on Communications, 2021, 42(8): 139-150.
[8]	Huaqun WANG, Zhe LIU, Debiao HE, Jiguo LI. Identity-based provable data possession scheme for multi-source IoT terminal data in public cloud [J]. Journal on Communications, 2021, 42(7): 52-60.
[9]	Wenbo ZHANG, Wenhua HUANG, Jingyu FENG. Secure communication mechanism for VSN based on certificateless signcryption [J]. Journal on Communications, 2021, 42(7): 128-136.
[10]	Fei TANG, Jiali BAO, Yonghong HUANG, Dong HUANG, Huili WANG. Multi-authority attribute-based identification scheme [J]. Journal on Communications, 2021, 42(3): 220-228.
[11]	Bin WANG, Si CHEN, Jiadong CHEN, Xing WANG. DWB-AES: an implementation of dynamic white-box based on AES [J]. Journal on Communications, 2021, 42(2): 177-186.
[12]	Houzhen WANG, Xinwei CAI, Yan GUO, Huanguo ZHANG. 5-pass zero-knowledge identity authentication scheme based on matrix completion problem [J]. Journal on Communications, 2021, 42(11): 79-86.
[13]	Miaomiao TIAN, Jing CHEN, Hong ZHONG. Identity-based incremental signature scheme from lattices [J]. Journal on Communications, 2021, 42(1): 108-117.
[14]	Liguo FANG,Zhengxin FU,Hao HU,Gang SHEN,Bin YU. Research on algorithm for raster map multi-level sharing based on region incrementing color visual cryptography [J]. Journal on Communications, 2019, 40(9): 24-32.
[15]	Miaomiao TIAN,Chuang GAO,Jie CHEN. Identity-based cloud storage integrity checking from lattices [J]. Journal on Communications, 2019, 40(4): 128-139.

Constructions of rotation symmetric 2-resilient functions with 4t-1 number of variables

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References 23

Related Articles 15

Metrics

Recommended 0

Constructions of rotation symmetric 2-resilient functions with 4t_-1 number of variables