Author
Robert L McFarland
Bio: Robert L McFarland is an academic researcher. The author has contributed to research in topics: Prime power & Cyclic group. The author has an hindex of 1, co-authored 1 publications receiving 296 citations.
Topics: Prime power, Cyclic group
Papers
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TL;DR: A construction is given for difference sets in certain non-cyclic groups with the parameters v, k, λ, n, which has minus one as a multiplier for every prime power q and every positive integer s.
324 citations
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TL;DR: The polynomial degree of a bent function P ( x ) is studied, as are the properties of the Fourier transform of (−1) P(x) , and a connection with Hadamard matrices.
1,211 citations
01 Dec 1976
TL;DR: A simple description of pseudo-random sequences, or maximal-length shift-register sequences, and two-dimensional arrays of area n = 2lm- 1 with the same property.
Abstract: Binary sequences of length n = 2m- 1 whose autocorrelation function is either 1 or -1/n have been known for a long time, and are called pseudo-random (or PN) sequences, or maximal-length shift-register sequences. Two-dimensional arrays of area n = 2lm- 1 with the same property have rcently been found by several authors. This paper gives a simple description of such sequences and arrays and their many nice properties.
774 citations
TL;DR: The nature of the Fourier coefficients of a bent function is examined and a proof for the non-existence of bent functions over Jqm, m odd, is given for many values of q of the form q = 2 (mod 4).
425 citations
08 Apr 1991
TL;DR: In this article, it was shown that for a perfect nonlinear S-box, the number of input variables is at least twice the size of output variables, and two different construction methods were given.
Abstract: A perfect nonlinear S-box is a substitution transformation with evenly distributed directional derivatives. Since the method of differential cryptanalysis presented by E. Biham and A. Shamir makes use of nonbalanced directional derivatives, the perfect nonlinear S-boxes are immune to this attack. The main result is that for a perfect nonlinear S-box the number of input variables is at least twice the number of output variables. Also two different construction methods are given. The first one is based on the Maiorana-McFarland construction of bent functions and is easy and efficient to implement. The second method generalizes Dillon's construction of difference sets.
369 citations
Journal Article•
TL;DR: A perfect nonlinear S-box is a substitution transformation with evenly distributed directional derivatives and the number of input variables is at least twice thenumber of output variables.
Abstract: A perfect nonlinear S-box is a substitution transformation with evenly distributed directional derivatives. Since the method of differential cryptanalysis presented by E. Biham and A. Shamir makes use of nonbalanced directional derivatives, the perfect nonlinear S-boxes are immune to this attack. The main result is that for a perfect nonlinear S-box the number of input variables is at least twice the number of output variables. Also two different construction methods are given. The first one is based on the Maiorana-McFarland construction of bent functions and is easy and efficient to implement. The second method generalizes Dillon's construction of difference sets.
349 citations