Abstract
Highly nonlinear permutations play an important role in the design of cryptographic transformations such as block ciphers, hash functions and stream ciphers. The substitution boxes of DES are relatively small in dimension and they can be generated by testing randomly chosen functions for required design criteria. Security may be increased by the use of substitution transformations of higher dimensions. But when the dimensions grow larger, analytic construction methods become necessary.
Finnish Defence Forces University of Helsinki (on leave)
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References
C. Carlet, Partially-bent functions, Codes, Designs and Cryptography (to appear).
X. Lai, Linear structures of functions over prime fields, Unpublished preprint (1990).
R. Lidl and H. Niederreiter, “Finite fields,” Encyclopedia of Mathematics and its applications, Vol. 20. Addison-Wesley, Reading, Massachusetts, 1983.
T. Matsumoto and H. Imai, Public quadratic polynomial-tuples for efficient signature-verification and message-encryption, Advances in Cryptology Eurocrypt’ 88. Lecture Notes in Computer Science, Springer-Verlag, 1989.
K. Nyberg, Constructions of bent functions and difference sets, Advances in Cryptology — Proceedings of Eurocrypt’ 90. Lecture Notes in Computer Science 473, Springer-Verlag, 1991.
J. Pieprzyk, On bent permutations, Technical Report CS91/11; The University of New South Wales, Department of Computer Science. Presented at the International Conference on Finite Fields, Coding Theory and Advances in Communications and Computing, Las Vegas, 1991.
B. Preneel et al., Cryptographic properties of quadratic Boolean functions, International Conference on Finite Fields, Coding Theory and advances in Communications and Computing, Las Vegas, 1991; Boolean functions satisfying higher order propagation criteria, Advances in Cryptology — Eurocrypt’ 91. Lecture Notes in Computer Science 547, Springer-Verlag, 1991.
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© 1993 Springer-Verlag Berlin Heidelberg
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Nyberg, K. (1993). On the construction of highly nonlinear permutations. In: Rueppel, R.A. (eds) Advances in Cryptology — EUROCRYPT’ 92. EUROCRYPT 1992. Lecture Notes in Computer Science, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47555-9_8
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DOI: https://doi.org/10.1007/3-540-47555-9_8
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