Another Proof of Kasami‘s Theorem
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Maximally Nonlinear Functions and Bent Functions
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
On MISTY1 Higher Order Differential Cryptanalysis
ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
Improved Construction of Nonlinear Resilient S-Boxes
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A New Characterization of Almost Bent Functions
FSE '99 Proceedings of the 6th International Workshop on Fast Software Encryption
FSE '98 Proceedings of the 5th International Workshop on Fast Software Encryption
Cartesian authentication codes from functions with optimal nonlinearity
Theoretical Computer Science
APN functions in odd characteristic
Discrete Mathematics - Special issue: Combinatorics 2000
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Journal of Complexity - Special issue on coding and cryptography
On the Non-linearity of Power Functions
Designs, Codes and Cryptography
Construction of high degree resilient S-boxes with improved nonlinearity
Information Processing Letters
Affinity of permutations of F2n
Discrete Applied Mathematics - Special issue: Coding and cryptography
The only crooked power functions are x2k+2l
European Journal of Combinatorics
Bundles, presemifields and nonlinear functions
Designs, Codes and Cryptography
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
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
On Cryptographically Significant Mappings over GF(2n)
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Several Families of Sequences with Low Correlation and Large Linear Span
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
New Sequences with Low Correlation and Large Family Size
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A Generalization of the Bent-Function Sequence Construction
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Algebraic immunity of S-boxes based on power mappings: analysis and construction
IEEE Transactions on Information Theory
Quadratic Equations from a Kind of S-boxes
Information Security Applications
Triple-error-correcting BCH-like codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics
Construction of high degree resilient S-boxes with improved nonlinearity
Information Processing Letters
Some results concerning cryptographically significant mappings over GF(2n)
Designs, Codes and Cryptography
The solutions of the third power sum equation for niho type decimations
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On highly nonlinear s-boxes and their inability to thwart DPA attacks
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Efficient representation and software implementation of resilient maiorana-mcfarland s-boxes
WISA'04 Proceedings of the 5th international conference on Information Security Applications
On exact algebraic [non-]immunity of s-boxes based on power functions
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
On the triple-error-correcting cyclic codes with zero set {1, 2i + 1, 2i + 1}
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Results on rotation-symmetric S-boxes
Information Sciences: an International Journal
Reversed Dickson polynomials over finite fields
Finite Fields and Their Applications
On Niho type cross-correlation functions of m-sequences
Finite Fields and Their Applications
Finite Fields and Their Applications
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
On three weights in cyclic codes with two zeros
Finite Fields and Their Applications
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
A new public key signature scheme based on multivariate polynomials
WISM'12 Proceedings of the 2012 international conference on Web Information Systems and Mining
| Hi-index | 754.90 |
We summarize the state of the classification of almost perfect nonlinear (APN) power functions xd on GF(2n) and contribute two new cases. To prove these cases we derive new permutation polynomials. The first case supports a well-known conjecture of Welch stating that for odd n=2m+1, the power function x2m+3 is even maximally nonlinear or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequence of degree n and a decimation of that sequence by 2m+3 takes on precisely the three values -1, -1±2m+1