Constructing Boolean functions by modifying Maiorana-McFarland's superclass functions

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E88-A, Issue 1, 2005, Pages 59-66

  Zeng, Xiangyong ^a   Hu, Lei ^b  

^a HUBEI UNIVERSITY   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Algebraic degree; Balancedness; Boolean function; Nonlinearity; Walsh spectrum

Indexed keywords

ALGEBRA; CONTROL NONLINEARITIES; CRYPTOGRAPHY; FUNCTIONS; RISK MANAGEMENT;

ALGEBRAIC DEGREE; BALANCEDNESS; NONLINEARITY; WALSH SPECTRUM;

BOOLEAN FUNCTIONS;

EID: 27544449113     PISSN: 09168508     EISSN: 17451337     Source Type: Journal    
DOI: 10.1093/ietfec/E88-A.1.59     Document Type: Conference Paper

References (20)

1. M. Matsui, "Linear cryptanalysis method for DES cipher," Advances in Cryptology-Eurocrypt'93, Workshop on the Theory and Application of Cryptographic Techniques, LNCS 765, pp.386-397, Lofthus, Norway, May 1993.
2. O. Rothaus, "On bent functions," J. Comb. Theory A, vol.20, pp.300-305, Jan. 1976.
3. W. Meier and O. Staffelbach, "Nonlinearity criteria for cryptographic functions," Proc. workshop on the theory and application of cryptographic techniques on Advances in cryptology, LNCS 434, pp.549-562, Houthalen, Belgium, Nov. 1990.
4. C. Carlet, "Partially-bent functions," Des., Codes Cryptog., vol.3, no.2, pp.135-145, May 1993.
5. X.M. Zhang and Y. Zheng, "On plateaud functions," IEEE Trans. Inf. Theory, vol.47, no.3, pp.1215-1223, March 2001.
6. G. Gong and K. Khoo, "Additive autocorrelation of resilient Boolean functions," CACR Technical Report, CORR 2003-11, 2003, available: http://www.cacr.math.uwaterloo.ca/tech_reports.html
7. X. Zeng and L. Hu, "A composition construction of bent-like Boolean functions from quadratic polynomials," available: http://eprint.iacr.org/ 2003/204
8. C. Carlet and E. Prouff, "On plateaued functions and their construction," Proc. Fast Software Encryption, 10th International Workshop, FSE 2003, LNCS 2887, pp.54-73, Lund, Sweden, Feb. 2003.
9. Y. Zheng, X.M. Zhang, and H. Imai, "Duality of Boolean functions and its cryptographic applications," Proc. 1997 International Conference on Information and Communications Security (ICICS'97), LNCS 1334, pp. 159-169, Beijing, China, Nov. 1997.
10. A. Canteau and M. Videau, "Degree of composition of highly nonlinear functions and applications to higher order differential cryptoanalysis," Advances in Cryptology-Eurocrypt2002, LNCS 2332, pp.518-533, Amsterdam, Netherlands, April 2002.
11. N.J. Patterson and D.H. Wiedemann, "The covering radius of the Reed-Muller code is at least 16276," IEEE Trans. Inf. Theory, vol.IT-29, no.3, pp.354-356, May 1983.
12. S. Maitra and P. Sarkar, "Modifications of Patterson-Wiedemann functions for cryptographic applications," IEEE Trans. Inf. Theory, vol.48, no.1, pp.278-284, Jan. 2002.
13. C. Carlet, "A larger class of cryptographic Boolean functions via a study of the Maiorana-Mcfarland construction," Advances in Cryptology-Crypto'2002, LNCS 2442, pp.549-564, Santa Barbara, USA, Aug. 2002.
14. H.Dobbertin, "Construction of bent functions and balanced Boolean functions with high nonlinearity," Proc. Fast Software Encryption, Second International Workshop, LNCS 1008, pp.61-74, Leuven, Belgium, Dec. 1994.
15. P. Camion, C. Carlet, P. Charpin, and N. Sendrier, "On correlation immune functions," Advances in Cryptology-Crypto'91, Workshop on the Theory and Application of Cryptographic Techniques, LNCS 547, pp.86-100, Brighton, UK, April 1991.
16. S. Chee, S. Lee, D. Lee, and S.H. Sung, "On correlation immune functions and their nonlinearity," Advances in Cryptology-Asiacrypt'96, International Conference on the Theory and Applications of Cryptology and Information Security, LNCS 1163, pp.232-243, Kyongju, Korea, Nov. 1996.
17. J. Seberry, X.M. Zhang, and Y. Zheng, "On construction and nonlinearity of correlation immune Boolean functions," Advances in Cryptology-Eurocrypt'93, Workshop on the Theory and Application of of Cryptographic Techniques, LNCS 765, pp.181-199, Lofthus, Norway, May 1993.
18. S. Maitra and P. Sarkar, "Cryptographically significant Boolean functions with five valued walsh spectra," Theor. Comput. Sci., vol.276, no.1-2, pp.133-146, April 2002.
19. P. Sarkar and S. Maitra, "Construction of nonlinear Boolean functions with important cryptographic properties," Advances in Cryptology-Eurocrypt'2000, LNCS 1807, pp.485-506, Bruges (Brugge), Belgium, May 2000.
20. Z.X. Wan, ed., Geometry of Classical Groups over Finite Fields, Chartwell-Bratt Ltd., Bromley, 1993.