Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2016 | OriginalPaper | Chapter

Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes

Authors : Konstantinos Limniotis, Nicholas Kolokotronis

Published in: Cryptography and Information Security in the Balkans

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The construction of Boolean functions with an odd number of variables and maximum algebraic immunity is studied in this paper. Starting with any function f obtained by the Carlet–Feng construction, we develop an efficient method to properly modify f in order to provide new functions having maximum algebraic immunity. This new approach, which exploits properties of the punctured Reed–Muller codes, suffices to generate a large number of new functions with maximum algebraic immunity through swapping an arbitrary number of elements between the support of f and its complement.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
next chapter Results on Characterizations of Plateaued Functions in Arbitrary Characteristic
Literature
1.
Canteaut, A.: Open problems related to algebraic attacks on stream ciphers. In: Ytrehus, Ø. (ed.) WCC 2005. LNCS, vol. 3969, pp. 120–134. Springer, Heidelberg (2006)CrossRef
2.
Carlet, C., Dalai, D.K., Gupta, K.C., Maitra, S.: Algebraic immunity for cryptographically significant Boolean functions: analysis and construction. IEEE Trans. Inform. Theory 52, 3105–3121 (2006)CrossRefMathSciNetMATH
3.
Carlet, C.: Constructing balanced functions with optimum algebraic immunity. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), pp. 451–455 (2007)
4.
Carlet, C., Feng, K.: An infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 425–440. Springer, Heidelberg (2008)CrossRef
5.
Carlet, C., Gaborit, P.: On the construction of balanced Boolean functions with a good algebraic immunity. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), pp. 1101–1105 (2005)
6.
Carlet, C., Zeng, X., Li, C., Hu, L.: Further properties of several classes of Boolean functions with optimum algebraic immunity. Des. Codes Cryptogr. 52, 303–338 (2009)CrossRefMathSciNetMATH
7.
Carlet, C.: Comments on “constructions of cryptographically significant Boolean functions using primitive polynomials”. IEEE Trans. Inform. Theor. 57, 4852–4853 (2011)CrossRefMathSciNet
8.
Chen, Y., Lu, P.: Two classes of symmetric Boolean functions with optimum algebraic immunity: construction and analysis. IEEE Trans. Inform. Theor. 57, 2522–2538 (2011)CrossRefMathSciNet
9.
Courtois, N.T., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, Eli (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)CrossRef
10.
Courtois, N.T.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176–194. Springer, Heidelberg (2003)CrossRef
11.
Dalai, D.K., Maitra, S., Sarkar, S.: Basic theory in construction of Boolean functions with maximum possible annihilator immunity. Des. Codes Cryptogr. 40, 41–58 (2006)CrossRefMathSciNetMATH
12.
Li, N., Qi, W.: Construction and analysis of boolean functions of 2t+1 variables with maximum algebraic immunity. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 84–98. Springer, Heidelberg (2006)CrossRef
13.
Li, J., Carlet, C., Zeng, X., Li, C., Hu, L., Shan, J.: Two constructions of balanced Boolean functions with optimal algebraic immunity, high nonlinearity and good behavior against fast algebraic attacks. Des. Codes Cryptogr. 76, 279–305 (2015)CrossRefMathSciNetMATH
14.
Limniotis, K., Kolokotronis, N., and Kalouptsidis, N.: Constructing Boolean functions in odd number of variables with maximum algebraic immunity. In: IEEE International Symposium on Information Theory (ISIT), pp. 2686–2690 (2011)
15.
Limniotis, K., Kolokotronis, N., Kalouptsidis, N.: Secondary constructions of Boolean functions with maximum algebraic immunity. Cryptogr. Comm. 5, 179–199 (2013)CrossRefMathSciNetMATH
16.
Liu, M., Zhang, Y., Lin, D.: Perfect algebraic immune functions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 172–189. Springer, Heidelberg (2012)CrossRef
17.
Liu, M., Lin, D.: Fast algebraic attacks and decomposition of symmetric Boolean functions. IEEE Trans. Inform. Theory 57, 4817–4821 (2011)CrossRefMathSciNet
18.
MacWilliams, F.N., Sloane, N.: The Theory of Error Correcting Codes. North-Holland Publishing Company, Amsterdam (1977)MATH
19.
Meier, W., Pasalic, E., Carlet, C.: Algebraic attacks and decomposition of boolean functions. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 474–491. Springer, Heidelberg (2004)CrossRef
20.
Mesnager, S.: Bent and hyper-bent functions in polynomial form and their link with some exponential sums and dickson polynomials. IEEE Trans. Inform. Theory 57, 5996–6009 (2011)CrossRefMathSciNet
21.
Lidl, R., Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics and its Applications, vol. 20. Cambridge University Press, Cambridge (1996)CrossRefMATH
22.
Pasalic, E.: Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysis. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 399–414. Springer, Heidelberg (2009)CrossRef
23.
Qu, L., Feng, K., Liu, F., Wang, L.: Constructing symmetric Boolean functions with maximum algebraic immunity. IEEE Trans. Inform. Theory 55, 2406–2412 (2009)CrossRefMathSciNet
24.
Rizomiliotis, P.: On the resistance of Boolean functions against algebraic attacks using univariate polynomial representation. IEEE Trans. Inform. Theory 56, 4014–4024 (2010)CrossRefMathSciNet
25.
Sarkar, S., Maitra, S.: Construction of rotation symmetric Boolean functions on odd number of variables with maximum algebraic immunity. In: Boztaş, S., Lu, H.-F.F. (eds.) AAECC 2007. LNCS, vol. 4851, pp. 271–280. Springer, Heidelberg (2007)CrossRef
26.
Su, S., Tang, X., Zeng, X.: A systematic method of constructing Boolean functions with optimal algebraic immunity based on the generator matrix of the Reed-Muller code. Des. Codes Cryptogr. 72, 653–673 (2014)CrossRefMathSciNetMATH
27.
Su, S., Tang, X.: Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity. Des. Codes Cryptogr. 71, 183–199 (2014)CrossRefMathSciNetMATH
28.
Tang, D., Carlet, C., Tang, X.: Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks. IEEE Trans. Inform. Theory 59, 653–664 (2013)CrossRefMathSciNet
29.
Tu, Z., Deng, Y.: A conjecture on binary string and its applications on constructing Boolean functions of optimal algebraic immunity. Des. Codes Cryptogr. 60, 1–14 (2011)CrossRefMathSciNetMATH
30.
Wang, Q., Peng, J., Kan, H.: Constructions of cryptographically significant Boolean functions using primitive polynomials. IEEE Trans. Inform. Theory 56, 3048–3053 (2010)CrossRefMathSciNet
31.
Zeng, X., Carlet, C., Shan, J., Hu, L.: More balanced Boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks. IEEE Trans. Inform. Theory 57, 6310–6320 (2011)CrossRefMathSciNet
Metadata
Title
Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes
Authors
Konstantinos Limniotis
Nicholas Kolokotronis
Copyright Year
2016
Book
Cryptography and Information Security in the Balkans

Print ISBN: 978-3-319-29171-0

Electronic ISBN: 978-3-319-29172-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-29172-7_1

Premium Partner

    Image Credits