# Gold functions and switched cube functions are not 0-extendable in dimension n > 5

@article{Beierle2022GoldFA, title={Gold functions and switched cube functions are not 0-extendable in dimension n > 5}, author={Christof Beierle and Claude Carlet}, journal={Designs, Codes and Cryptography}, year={2022} }

<jats:p>In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {F}_{2^5}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>F</mml:mi>
<mml:msup>
<mml:mn>2</mml:mn>
<mml:mn>5</mml:mn>
</mml:msup…

## References

SHOWING 1-10 OF 13 REFERENCES

### Recovering or Testing Extended-Affine Equivalence

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2022

A new algorithm that efficiently solves the EA-recovery problem for quadratic functions, based on the Jacobian matrix of the functions, is presented, which supersedes, in terms of performance, all previously known algorithms for solving this problem.

### Trims and extensions of quadratic APN functions

- Computer ScienceDesigns, Codes and Cryptography
- 2022

An EA-invariant for vectorial Boolean functions on F2n is defined and 6368 new quadratic APN functions in dimension eight are constructed up to EA-equivalence by extending a quadratics APN function in dimension seven.

### New Instances of Quadratic APN Functions

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2022

The recursive tree search for finding APN permutations with linear self-equivalences in small dimensions can be adapted to find many new instances of quadratic APN functions, including the highest possible non-trivial linearity for quadratics functions in dimension eight.

### On bent functions associated to AB functions

- Mathematics2011 IEEE Information Theory Workshop
- 2011

This paper determines γf for most of the known families of APN and AB functions, which leads to potentially new bent functions associated to the known AB functions.

### The classification of quadratic APN functions in 7 variables

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2020

It is proved that the updated list of quadratic APN functions in dimension 7 is complete up to CCZ-equivalence.

### A new almost perfect nonlinear function which is not quadratic

- Mathematics, Computer ScienceAdv. Math. Commun.
- 2009

It is shown that the approach shown can be used to construct a ''non-quadratic'' APN function, which is in remarkable contrast to all recently constructed functions which have all been quadratic.

### Boolean Functions for Cryptography and Coding Theory

- Computer Science, Mathematics
- 2020

This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results.

### Differentially Uniform Mappings for Cryptography

- Mathematics, Computer ScienceEUROCRYPT
- 1993

The examples of differentially uniform mappings provided in this paper have also other desirable cryptographic properties: large distance from affine functions, high nonlinear order and efficient computability.

### Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems

- Computer Science, MathematicsDes. Codes Cryptogr.
- 1998

The "coding theory" point of view for studying the existence of almost bent functions is developed, showing explicitly the links with cyclic codes and new characterizations are given by means of associated Boolean functions.

### Vectorial Boolean Functions for Cryptography

- MathematicsBoolean Models and Methods
- 2010

To appear as a chapter of the volume " Boolean Methods and Models " , this chapter describes the construction of Boolean models and some examples show how to model Boolean functions using LaSalle's inequality.