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A new construction of odd-variable rotation symmetric Boolean functions with good cryptographic properties. (English) Zbl 1501.94125

Summary: Rotation symmetric Boolean functions constitute a class of cryptographically significant Boolean functions. In this paper, based on the theory of ordered integer partitions, we present a new class of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity by modifying the support of the majority function. Compared with the existing rotation symmetric Boolean functions on odd variables, the newly constructed functions have the highest nonlinearity.

MSC:

94D10 Boolean functions
94A60 Cryptography
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[1] A. Canteaut and M. Trabbia, Improved fast correlation attacks using parity-check equations of weight 4 and 5, in Advances in Cryptology-EUROCRYPT 2000 (eds. B. Preneel), Springer, Berlin, Heidelberg, 2000,573-588. · Zbl 1082.94509
[2] C. Carlet, Boolean functions for cryptography and error correcting codes, to appear in Cambridge University Press. · Zbl 1209.94035
[3] C. Carlet and K. Feng, An infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity, in ASIACRYPT 2008 (eds. J. Pieprzyk), Lecture Notes in Computer Science, 5350, Springer, Heidelberg, 2008,425-440. · Zbl 1206.94060
[4] C. Carlet; G. Gao; W. Liu, A secondary construction and a transformation on rotation symmetric functions, and their action on bent and semi-bent functions, J. Combin. Theory Ser. A, 127, 161-175 (2014) · Zbl 1297.05239 · doi:10.1016/j.jcta.2014.05.008
[5] C. Carlet; X. Zeng; C. Li; L. Hu, Further properties of several classes of Boolean functions with optimum algebraic immunity, Des. Codes Cryptogr., 52, 303-338 (2009) · Zbl 1174.94012 · doi:10.1007/s10623-009-9284-0
[6] Y. Chen; F. Guo; J. Ruan, Constructing odd-variables RSBFs with optimal algebraic immunity, good nonlieanrity and good behavior against fast algebraic attarcks, Discrete Appl. Math., 262, 1-12 (2019) · Zbl 1445.94042 · doi:10.1016/j.dam.2019.02.041
[7] N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in EUROCRYPT 2003, Lecture Notes in Computer Science, 2656, Springer-Verlag, Heidelberg, 2003,345-359. · Zbl 1038.94525
[8] D. Dalai; S. Maitra; S. Sarkar, Basic theory in construction of Boolean functions with maximum possible annihilator immunity, Des. Codes Cryptogr., 40, 41-58 (2006) · Zbl 1202.94179 · doi:10.1007/s10623-005-6300-x
[9] C. Ding, G. Xiao and W. Shan, The stability theory of stream ciphers, in Lecture Notes in Computer Science, 561, Springer-Verlag, Berlin, 1991. · Zbl 0762.94008
[10] J. Du; Q. Wen; J. Zhang; S. Pang, Constructions of resilient rotation symmetric Boolean functions on given number of variables, IET Inform. Secur., 8, 265-272 (2014) · doi:10.1049/iet-ifs.2013.0090
[11] S. Fu; J. Du; L. Qu; C. Li, Construction of odd-variable rotation symmetric boolean functions with maximum algebraic immunity, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 99, 853-855 (2016) · Zbl 1352.94062 · doi:10.1016/j.dam.2016.06.005
[12] G. Gao, Constructions of quadratic and cubic rotation symmetric bent functions, IEEE Trans. Inform. Theory, 58, 4908-4913 (2012) · Zbl 1365.94670 · doi:10.1109/TIT.2012.2193377
[13] W. Meier, E. Pasalic and C. Carlet, Algebraic attacks and decomposition of Boolean functions, in Advances in Cryptology-EUROCRYPT 2004, Lecture Notes in Computer Science, 3027, Springer Heidelberg, 2004,474-491. · Zbl 1122.94041
[14] S. Sarkar and S. Maitra, Construction of rotation symmetric Boolean functions with maximum algebraic immunity on odd number of variables, in AAECC 2007, Lecture Notes in Computer Science, 4851, 2007,271-280. · Zbl 1193.94063
[15] P. Stnic; S. Maitra, Rotation symmetric Boolean functions-count and cryptographic properties, Discrete Appl. Math., 156, 1567-1580 (2002) · Zbl 1142.94016 · doi:10.1016/j.dam.2007.04.029
[16] S. Su, A new construction of rotation symmetric bent functions with maximal algebraic degree, Adv. Math. Commun., 13, 253-265 (2019) · Zbl 1426.94177 · doi:10.3934/amc.2019017
[17] S. Su; X. Tang, Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity, Des. Codes Cryptogr., 71, 183-199 (2014) · Zbl 1342.94099 · doi:10.1007/s10623-012-9727-x
[18] S. Su; X. Tang, Systematic constructions of rotation symmetric bent functions, 2-rotation symmetric bent functions, and bent idempotent functions, IEEE Trans. Inf. Theory, 63, 4658-4667 (2017) · Zbl 1370.94613 · doi:10.1109/TIT.2016.2621751
[19] L. Sun; F. Fu; X. Guang, Two classes of 1-resilient prime-variable rotation symmetric Boolean functions, IEICE Trans Fund. Electron. Comm. Comput. Sci., E100-A, 902-907 (2017) · doi:10.1587/transfun.E100.A.902
[20] H. Zhang; S. Su, A new construction of rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity, Discrete Appl. Math., 262, 13-28 (2019) · Zbl 1445.94044 · doi:10.1016/j.dam.2019.02.030
[21] Q. Zhao; G. Han; D. Zheng; X. Li, Constructing odd-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity, Chinese J. Electron., 28, 45-51 (2019) · Zbl 1425.94091 · doi:10.1007/s12190-019-01245-2
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