Cross-correlations of geometric sequences in characteristic two
Designs, Codes and Cryptography
Differentially uniform mappings for cryptography
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Finite fields
Almost perfect nonlinear power functions on GF (2n): the Niho case
Information and Computation
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
Designs, Codes and Cryptography
Uniformly Packed Codes and More Distance Regular Graphs from Crooked Functions
Journal of Algebraic Combinatorics: An International Journal
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
Codes, graphs, and schemes from nonlinear functions
European Journal of Combinatorics
On the Non-linearity of Power Functions
Designs, Codes and Cryptography
The only crooked power functions are x2k+2l
European Journal of Combinatorics
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
IEEE Transactions on Information Theory
Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A new APN function which is not equivalent to a power mapping
IEEE Transactions on Information Theory
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
Designs, Codes and Cryptography
Bundles, presemifields and nonlinear functions
Designs, Codes and Cryptography
On a Class of Permutation Polynomials over $\mathbb{F}_{2^n}$
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On Designs and Multiplier Groups Constructed from Almost Perfect Nonlinear Functions
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
New semifields, PN and APN functions
Designs, Codes and Cryptography
Notes on APN functions, semibiplanes and dimensional dual hyperovals
Designs, Codes and Cryptography
On the duals of certain d-dimensional dual hyperovals in PG(2d+1,2)
Finite Fields and Their Applications
When does G(x )+γTr(H(x)) permute Fpn?
Finite Fields and Their Applications
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A map f:F"2"^"n-F"2"^"n is called crooked if the set {f(x+a)+f(x):x@?F"2"^"n} is an affine hyperplane for every fixed a@?F"2"^"n^* (where F"2"^"n is considered as a vector space over F"2). We prove that the only crooked power maps are the quadratic maps x^2^^^i^+^2^^^j with gcd(n,i-j)=1. This is a consequence of the following result of independent interest: for any prime p and almost all exponents 0=0 are arbitrary elements from F"p"^"n.