A Generalisation of Dillon's APN Permutation With the Best Known Differential and Nonlinear Properties for All Fields of Size
The existence of almost perfect nonlinear (APN) permutations operating on an even number
of variables was a long-standing open problem, until an example with six variables was …
of variables was a long-standing open problem, until an example with six variables was …
If a generalised butterfly is APN then it operates on 6 bits
A Canteaut, L Perrin, S Tian - Cryptography and Communications, 2019 - Springer
Abstract Whether there exist Almost Perfect Non-linear permutations (APN) operating on an
even number of bits is the so-called Big APN Problem. It has been solved in the 6-bit case by …
even number of bits is the so-called Big APN Problem. It has been solved in the 6-bit case by …
Cryptanalysis of a theorem: Decomposing the only known solution to the big APN problem
Abstract The existence of Almost Perfect Non-linear (APN) permutations operating on an
even number of bits has been a long standing open question until Dillon et al., who work for …
even number of bits has been a long standing open question until Dillon et al., who work for …
Some new results on permutation polynomials over finite fields
Permutation polynomials over finite fields constitute an active research area and have
applications in many areas of science and engineering. In this paper, four classes of …
applications in many areas of science and engineering. In this paper, four classes of …
The complete differential spectrum of a class of power permutations over odd characteristic finite fields
H Yan, S Mesnager, X Tan - IEEE Transactions on Information …, 2023 - ieeexplore.ieee.org
Permutation polynomials over finite fields are fundamental objects as they are used in
various theoretical and practical applications in cryptography, coding theory, combinatorial …
various theoretical and practical applications in cryptography, coding theory, combinatorial …
Almost perfect nonlinear power functions on gf (2/sup n/): the welch case
H Dobbertin - IEEE Transactions on Information Theory, 1999 - ieeexplore.ieee.org
We summarize the state of the classification of almost perfect nonlinear (APN) power
functions x/sup d/on GF (2/sup n/) and contribute two new cases. To prove these cases we …
functions x/sup d/on GF (2/sup n/) and contribute two new cases. To prove these cases we …
Differentially 4-uniform permutations with the best known nonlinearity from butterflies
S Fu, X Feng, B Wu - Cryptology ePrint Archive, 2017 - eprint.iacr.org
Many block ciphers use permutations defined over the finite field $\mathbb {F} _ {2^{2k}} $
with low differential uniformity, high nonlinearity, and high algebraic degree to provide …
with low differential uniformity, high nonlinearity, and high algebraic degree to provide …
A new family of APN quadrinomials
L Budaghyan, T Helleseth… - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
The binomial B (x)= x 3+ βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known
example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a …
example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a …
A new APN function which is not equivalent to a power mapping
Y Edel, G Kyureghyan, A Pott - IEEE Transactions on …, 2006 - ieeexplore.ieee.org
A new APN function which is not equivalent to a power mapping Page 1 744 IEEE
TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006 A New APN …
TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006 A New APN …
New families of differentially 4-uniform permutations over
Y Tan, L Qu, CH Tan, C Li - International Conference on Sequences and …, 2012 - Springer
Differentially 4-uniform permutations over \mathbbF_2^2k, especially those with high
nonlinearity and high algebraic degree, are cryptographically significant mappings as they …
nonlinearity and high algebraic degree, are cryptographically significant mappings as they …