Abstract
Siegenthaler inequality shows the existence of a tradeoff between the correlation-immunity order and the nonlinearity order of a Boolean functions. We generalize this result to correlation-immune functions over any finite field. We then construct a family of correlation-immune functions achieving this bound; these functions are notably well-suited for combining linear feedback shift registers. We also apply this result to the cryptanalysis of any cryptographic primitive based on boxes connected by a network. Schnorr and Vaudenay have previously recommended that these boxes should be multipermutations; we here refine this condition since we show that each binary component of these multipermutations, seen as a Boolean function, should have low degree.
Centre National de la Recherche Scientifique
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L. Brynielsson. On the linear complexity of combined shift register sequences. In F. Pichler, editor, Advances in Cryptology — EUROCRYPT’ 85, number 219 in Lecture Notes in Computer Science, pages 156–160. Springer-Verlag, 1986.
K.A. Bush. Orthogonal arrays of index unity. Ann. Math. Stat., 23:426–434, 1952.
P. Camion, C. Carlet, P. Charpin, and N. Sendrier. On correlation-immune functions. In J. Feigenbaum, editor, Advances in Cryptology — CRYPTO’91, number 576 in Lecture Notes in Computer Science, pages 86–100. Springer-Verlag, 1992.
K. Gopalakrishnan and D.R. Stinson. Three characterizations of non-binary correlation-immune and resilient functions. Designs, Codes and Cryptography, 5:241–251, 1995.
T. Herlestam. On functions of linear shift register sequences. In F. Pichler, editor, Advances in Cryptology — EUROCRYPT’ 85, number 219 in Lecture Notes in Computer Science, pages 119–129. Springer-Verlag, 1986.
U.M. Maurer and J.L. Massey. Perfect local randomness in pseudo-random sequences. In G. Brassard, editor, Advances in Cryptology — CRYPTO’89, number 435 in Lecture Notes in Computer Science, pages 100–112. Springer-Verlag, 1990.
C.R. Rao. Factorial experiments derivable from combinatorial arrangements of arrays. J. Roy. Statist., 9:128–139, 1947.
R.A. Rueppel. Analysis and Design of stream ciphers. Springer-Verlag, 1986.
R.A. Rueppel and O.J. Staffelbach. Products of linear recurring sequences with maximum complexity. IEEE Trans. Inform. Theory, IT-33(1):124–131, 1987.
C.-P. Schnorr and S. Vaudenay. Black box cryptanalysis of hash networks based on multipermutations. In A. De Santis, editor, Advances in Cryptology — EUROCRYPT’94, number 950 in Lecture Notes in Computer Science, pages 47–57. Springer-Verlag, 1995.
C.P. Schnorr and S. Vaudenay. Parallel FFT-Hashing. In Fast Software Encryption, number 809 in Lecture Notes in Computer Science, pages 149–156. Springer-Verlag, 1994.
T. Siegenthaler. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Trans. Inform. Theory, IT-30(5):776–780, 1984.
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© 1996 Springer-Verlag Berlin Heidelberg
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Camion, P., Canteaut, A. (1996). Generalization of Siegenthaler Inequality and Schnorr-Vaudenay Multipermutations. In: Koblitz, N. (eds) Advances in Cryptology — CRYPTO ’96. CRYPTO 1996. Lecture Notes in Computer Science, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68697-5_28
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DOI: https://doi.org/10.1007/3-540-68697-5_28
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