Abstract
Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. In this paper, we investigate n-variable (n even and n ⩾ 12) RSBFs to achieve maximum algebraic immunity (AI), and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI. We also prove that our construction provides high algebraic degree in some case.
Similar content being viewed by others
References
Stanica P, Maitra S. Rotation symmetric Boolean functions—count and cryptographic properties. Electron Notes Discrete Math, 2003, 15: 139–145
Dalai D K, Maitra S, Sarkar S. Results on rotation symmetric bent functions. In: Proceedings of the 2nd International Workshop on Boolean Functions: Cryptography and Applications, Rouen, France, 2006. 137–156
Maximov A, Hell M, Maitra S. Plateaued rotation symmetric Boolean functions on odd number of variables. In: Proceedings of the 1st Workshop on Boolean Functions: Cryptography and Applications, Rouen, France, 2005. 83–104
Stanica P, Maitra S, Clark J. Results on rotation symmetric bent and correlation immune Boolean functions. In: Proceedings of Fast Software Encryption Workshop, Delhi, India, 2004. 161–177
Pieprzyk J, Qu C X. Fast hashing and rotation-symmetric functions. J Univ Comput Sci, 1999, 5: 20–31
Cusick T W, Stanica P. Fast evaluation, weights and nonlinearity of rotation-symmetric functions. Discrete Math, 2002, 258: 289–301
Courtois N, Pieprzyk J. Cryptanalysis of block ciphers with overdefined systems of equations. In: Advances in Cryptology-ASIACRYPT, Queenstown, New Zealand, 2002. 267–287
Courtois N, Meier W. Algebraic attacks on stream ciphers with linear feedback. In: Advances in Cryptology-EUROCRYPT, Warsaw, Poland, 2003. 345–359
Dalai D K, Gupta K C, Maitra S. Results on algebraic immunity for cryptographically significant Boolean functions. In: Proceedings of the 5th International Conference on Cryptology, Chennai, India, 2004. 92–106
Meier W, Pasalic E, Carlet C. Algebraic attacks and decomposition of Boolean functions. In: Advances in Cryptology-EUROCRYPT, Santa Barbara, USA, 2004. 474–491
Carlet C, Zeng X Y, Li C L, et al. Further properties of several classes of Boolean functions with optimum algebraic immunity. Des Codes Cryptogr, 2009, 52: 303–338
Carlet C, Dalai D K, Gupta K C, et al. Algebraic immunity for cryptographically significant Boolean functions: Analysis and construction. IEEE Trans Inf Theory, 2006, 52: 3105–3121
Dalai D K, Maitra S, Sarkar S. Basic theory in construction of Boolean functions with maximum possible annihilator immunity. Des Codes Cryptogr, 2006, 40: 41–58
Qu L J, Li C, Feng K Q. A note on symmetric Boolean functions with maximum algebraic immunity in odd number of variables. IEEE Trans Inf Theory, 2007, 53: 2908–2910
Qu L J, Feng K Q, Liu F, et al. Constructing symmetric Boolean functions with maximum algebraic immunity. IEEE Trans Inf Theory, 2009, 55: 2406–2412
Sarkar S, Maitra S. Construction of rotation symmetric Boolean functions with maximum algebraic immunity on odd number of variables. In: Proceedings of International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting codes, Bangalore, India, 2007. 271–280
Fu S J, Li C, Matsuura K, et al. Construction of rotation symmetric Boolean functions with maximum algebraic immunity. In: Proceedings of the 8th International Conference on Cryptology and Network Security, Kanazawa, Ishikawa, Japan, 2009. 402–412
Sarkar S, Maitra S. Construction of rotation symmetric Boolean functions with optimal algebraic immunity. Comput Syst, 2009, 12: 267–284
Carlet C. A method of construction of balanced functions with optimum algebraic immunity. In: Proceedings of the International Workshop on Coding and Cryptography, The Wuyi Mountain, Fujiang, China, 2007
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fu, S., Li, C., Matsuura, K. et al. Construction of even-variable rotation symmetric Boolean functions with maximum algebraic immunity. Sci. China Inf. Sci. 56, 1–9 (2013). https://doi.org/10.1007/s11432-011-4350-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-011-4350-4