New construction of highly nonlinear resilient S-boxes via linear codes

Haixia ZHAO, Yongzhuang WEI

PDF(852 KB)
PDF(852 KB)
Front. Comput. Sci. ›› 2022, Vol. 16 ›› Issue (3) : 163805. DOI: 10.1007/s11704-020-0182-y
Information Security
RESEARCH ARTICLE

New construction of highly nonlinear resilient S-boxes via linear codes

Author information +
History +

Abstract

Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers. During the past three decades, the main idea of construction of highly nonlinear resilient functions are benefited from concatenating a large number of affine subfunctions. However, these resilient functions as core component of ciphers usually suffered from the guess and determine attack or algebraic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most n/2 variables of them. How to design highly nonlinear resilient functions (S-boxes) without concatenating a large number of n/2 variables affine subfunctions appears to be an important task. In this article, a new construction of highly nonlinear resilient functions is proposed. These functions consist of two classes subfunctions. More specially, the first class (nonlinear part) contains both the bent functions with 2 k variables and some affine subfunctions with n/2 − k variables which are attained by using [ n/2 − k, m, d] disjoint linear codes. The second class (linear part) includes some linear subfunctions with n/2 variables which are attained by using [ n/2, m, d] disjoint linear codes. It is illustrated that these resilient functions have high nonlinearity and high algebraic degree. In particular, It is different from previous well-known resilient S-boxes, these new S-boxes cannot be directly decomposed into some affine subfunctions with n/2 variables by fixing at most n/2 variables. It means that the S-boxes (vectorial Boolean functions) which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.

Keywords

stream cipher / S-box / disjoint linear codes / resiliency / nonlinearity

Cite this article

Download citation ▾
Haixia ZHAO, Yongzhuang WEI. New construction of highly nonlinear resilient S-boxes via linear codes. Front. Comput. Sci., 2022, 16(3): 163805 https://doi.org/10.1007/s11704-020-0182-y

References

[1]
Menezes A J , Vanstone S A , Van Oorschot P C . Handbook of Applied Cryptography. 1st ed. Cleveland: CRC Press, 1997,
[2]
Ding C S , Shan W J , Xiao G Z . The stability theory of stream ciphers. Lecture Notes in Computer Science, 1991, 561 : 13– 28
[3]
Siegenthaler T . Correlation-immunity of nonlinear combining functions for cryptographic applications (Corresp.). IEEE Transactions on Information Theory, 2003, 30( 5): 776– 780
CrossRef Google scholar
[4]
Courtois N . Fast algebraic attacks on stream ciphers with linear feedback. In: Proceedings of Advances in Cryptology — EUROCRYPT 2003: International Conference on the Theory and Applications of Cryptographic Techniques, 2003, 176– 194
[5]
Zhou Y , Hu Y P , Dong X F . The Design and Analysis of Boolean Function. 1st ed. Beijin: National Defense Industry Press, 2015,
[6]
Camion P , Carlet C , Charpin P , Sendrier N . On correlation-immune functions. In: Proceedings of International Cryptology Conference on Advances in Cryptology, 1991, 86– 100
[7]
Carlet C . A larger class of cryptographic boolean functions via a study of the Maiorana-McFarland construction. In: Proceedings of International Cryptology Conference on Advances in Cryptology, 2002, 549– 564
[8]
Pasalic E . Maiorana-McFarland class: degree optimization and algebraic properties. IEEE Transactions on Information Theory, 2006, 52( 10): 4581– 4594
CrossRef Google scholar
[9]
Pasalic E , Maitra S . Linear codes in generalized construction of resilient functions with very high nonlinearity. IEEE Transactions on Information Theory, 2002, 48( 8): 2182– 2191
CrossRef Google scholar
[10]
Johansson T , Pasalic E . A construction of resilient functions with high nonlinearity. IEEE Transactions on Information Theory, 2003, 49( 2): 494– 501
CrossRef Google scholar
[11]
Zhang W G , Pasalic E . Constructions of resilient S-boxes with strictly almost optimal nonlinearity through disjoint linear codes. IEEE Transactions on Information Theory, 2014, 60( 3): 1638– 1651
CrossRef Google scholar
[12]
Zhang W G , Xiao G Z . Constructions of almost optimal resilient Boolean functions on large even number of variables. IEEE Transactions on Information Theory, 2009, 55( 12): 5822– 5831
CrossRef Google scholar
[13]
Zhang W G , Pasalic E . Generalized Maiorana-McFarland construction of resilient Boolean functions with high nonlinearity and good algebraic properties. IEEE Transactions on Information Theory, 2014, 60( 10): 6681– 6695
CrossRef Google scholar
[14]
Khoo K , Chew G , Gong G , Lee H K . Time-memory-data trade-off attack on stream ciphers based on Maiorana-McFarland functions. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2009, 92( 1): 11– 21
[15]
Mihaljevic M , Gangopadhyay S , Paul G , Imaiand H . Internal state recovery of Grain-v1 employing normality order of the filter function. Information Security Iet, 2012, 6( 2): 55– 64
CrossRef Google scholar
[16]
Pasalic E . On guess and determine cryptanalysis of LFSR-based stream ciphers. IEEE Transactions on Information Theory, 2009, 55( 7): 3398– 3406
CrossRef Google scholar
[17]
Boura C , Canteaut A . A new criterion for avoiding the propagation of linear relations through an S-box. In: Proceedings of International Workshop on Fast Software Encryption, 2013, 585– 604
[18]
Wei Y Z , Pasalic E , Zhang F R . New constructions of resilient functions with strictly almost optimal nonlinearity via non-overlap spectra functions. Information Sciences, 2017, 415 : 377– 396
[19]
Cusick T W , Stanica P . Cryptographic Boolean Functions and Applications. 1st ed. San Diego: Elsevier, 2009,
[20]
Xiao G Z , Massey J L . A spectral characterization of correlation immune combining functions. IEEE Transactions on Information Theory, 1988, 34( 3): 569– 571
CrossRef Google scholar
[21]
Wen Q Y , Niu X X , Yang Y X . Boolean Functions in Modern Cryptography. 1st ed. Beijing: Science Press, 2000,
[22]
Zhang X M , Zheng Y L . Cryptographically resilient functions. IEEE Transactions on Information Theory, 1997, 43( 5): 1740– 1747
CrossRef Google scholar
[23]
Wang X M , Xiao G Z . Error Correcting Code – Principle and Method. 1st ed. Xian: Xidian University Press, 2003,
[24]
Fu S J , Li C , Qu L J . A recursive construction of highly nonlinear resilient vectorial functions. Information Science, 2014, 269 : 388– 396
CrossRef Google scholar

Acknowledgements

The work was supported in part by the National Natural Science Foundation of China (Grant No. 61872103), in part by Guangxi Science and Technology Foundation (Guike AB18281019, Guike AD18281026), in part by Guangxi Natural Science Foundation (2019GXNSFGA245004), in part by the Foundation of Ministry of Education Key Laboratory of Cognitive Radio and Information Processing (Guilin University of Electronic Technology)(CRKL180107).

RIGHTS & PERMISSIONS

2022 Higher Education Press
AI Summary AI Mindmap
PDF(852 KB)

Accesses

Citations

Detail

Sections
Recommended

/