Abstract
A Boolean function is called normal if it is constant on flats of certain dimensions. This property is relevant for the construction and analysis of cryptosystems. This paper presents an asymmetric Monte Carlo algorithm to determine whether a given Boolean function is normal. Our algorithm is far faster than the best known (deterministic) algorithm of Daum et al. In a first phase, it checks for flats of low dimension whether the given Boolean function is constant on them and combines such flats to flats of higher dimension in a second phase. This way, the algorithm is much faster than exhaustive search. Moreover, the algorithm benefits from randomising the first phase. In addition, by evaluating several flats implicitly in parallel, the time-complexity of the algorithm decreases further.
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Canteaut, Anne; Daum, Magnus; Dobbertin, Hans; and Leander, Gregor (2003).Normal and non-normal bent functions. In WCC03. 19 pages.
Carlet, Claude (2001). On the complexity of cryptographic Boolean functions. In 6 th Conference on Finite Fields and Applications, 21 th-25 th May, pages 53–69. Gary L. Mullen, Henning Stichtenoth, and Horacio Tapia-Recillas, editors, Spring
Daum, Magnus; Dobbertin, Hans; and Leander, Gregor (2003). An algorithm for checking normality of Boolean functions. In WCC03. 14 pages.
Dobbertin, Hans (1994). Construction of bent functions and balanced Boolean functions with high nonlinearity. In Fast Software Encryption-FSE 1994, volume 1008 of Lecture Notes in Computer Science, pages 61–74. Bart Preneel, editor, Springer.
Dubuc, Sylvie (2001).Etude des propriétés de dégénérescene et de normalité des fonctions booléennes et construction des fonctions q-aires parfaitement non-linéaires. PhD thesis, Université de Caen.
Kipnis, Aviad and Shamir, Adi (2004). New cryptographic primitives based on multiword T-functions. In Fast Software Encryption-FSE 2004. Bimal Roy and Willi Meier, editors. pre-proceedings, 14 pages.
Landau, David and Binder, Kurt (2000). A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press. ISBN 521-65314-2.
MacWilliams, F. J. and Sloane, N.J.A. (1991). The Theory of Error-Correcting Codes. Elsevier Science Publisher. ISBN 0-444-85193-3.
MAGMA. The MAGMA Computational Algebra System for Algebra, Number Theory and Geometry. Computational Algebra Group, University of Sydney. http://magma.maths.usyd.edu.au/magma/.
Rhoads, Glenn. Random number generator in C. http://remus.rutgers.edu/~rhoads/Code/rands.c.
Savage, Carla (1997). A survey of combinatorical Gray codes. SIAM Review 39(4): 605–629. http://www.csc.ncsu.edu/faculty/savage/AVAILABLE_FOR_MAILING/survey.ps.
WCC (2003). Workshop on Coding and Cryptography 2003. Daniel Augot, Pascal Charpin, and Grigory Kabatianski, editors, l’Ecole Suprieure et d’Application des Transmissions. ISBN 2-7261-1205-6.
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Braeken, A., Wolf, C., Preneel, B. (2004). A Randomised Algorithm for Checking The Normality of Cryptographic Boolean Functions. In: Levy, JJ., Mayr, E.W., Mitchell, J.C. (eds) Exploring New Frontiers of Theoretical Informatics. IFIP International Federation for Information Processing, vol 155. Springer, Boston, MA. https://doi.org/10.1007/1-4020-8141-3_7
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DOI: https://doi.org/10.1007/1-4020-8141-3_7
Publisher Name: Springer, Boston, MA
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