Constructions of bent functions and difference sets
- 1.9k Downloads
Based on the work of Rothaus , Olsen, Scholtz and Welch suggested the bent functions to be used as feed-forward functions to generate binary sequences which possess high linear complexity and very nearly optimum crosscorrelation properties . In  Meier and Staffelbach discovered, that binary bent functions give a solution to the correlation problem when used as combining functions of several binary linear shiftregister sequences. One of their results is that bent functions are at maximum distance to the set of affine functions. We refer to  for the cryptographic background and motivation. The general theory of the bent functions from Z q n to Z q was developed by Kumar, Scholtz and Welch .
KeywordsCombinatorial Theory Bend Function Nonlinear Order Bent Function Cyclotomic Field
- 1.J. F. Dillon, Elementary Hadamard difference sets, Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Florida (1975), 237–249; Congressus Numerantium No. XIV, Utilitas Math., Winnipeg, Manitoba (1975).Google Scholar
- 7.W. Meier and O. Staffelbach, Nonlinearity criteria for cryptographic functions, Advances in Cryptology, Proceedings of Eurocrypt’ 89 (to appear).Google Scholar
- 11.B. Preneel et al., Propagation characteristics of Boolean bent functions, Proceedings of Eurocrypt’ 90 (to appear).Google Scholar