Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Finite fields
A construction of bent function
FFA '95 Proceedings of the third international conference on Finite fields and applications
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
Designs, Codes and Cryptography
Cubic Monomial Bent Functions: A Subclass of $\mathcal{M}$
SIAM Journal on Discrete Mathematics
The Simplest Method for Constructing APN Polynomials EA-Inequivalent to Power Functions
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
On a Class of Permutation Polynomials over $\mathbb{F}_{2^n}$
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Affinity of permutations of F2n
Discrete Applied Mathematics - Special issue: Coding and cryptography
A note on a class of quadratic permutations over F2n
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
New classes of almost bent and almost perfect nonlinear polynomials
IEEE Transactions on Information Theory
On Almost Perfect Nonlinear Functions Over
IEEE Transactions on Information Theory
Hyperbent Functions, Kloosterman Sums, and Dickson Polynomials
IEEE Transactions on Information Theory
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
On EA-equivalence of certain permutations to power mappings
Designs, Codes and Cryptography
Permutation polynomials EA-equivalent to the inverse function over GF (2n)
Cryptography and Communications
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In this paper we investigate the existence of permutation polynomials of the form F(x) = x d + L(x) over GF(2 n ), L being a linear polynomial. The results we derive have a certain impact on the long-term open problem on the nonexistence of APN permutations over GF(2 n ), when n is even. It is shown that certain choices of exponent d cannot yield APN permutations for even n. When n is odd, an infinite class of APN permutations may be derived from Gold mapping x 3 in a recursive manner, that is starting with a specific APN permutation on GF(2 k ), k odd, APN permutations are derived over GF(2 k+2i ) for any i 驴 1. But it is demonstrated that these classes of functions are simply affine permutations of the inverse coset of the Gold mapping x 3. This essentially excludes the possibility of deriving new EA-inequivalent classes of APN functions by applying the method of Berveglieri et al. (approach proposed at Asiacrypt 2004, see [3]) to arbitrary APN functions.