Name
Abstract | ||
|---|---|---|
Recently, Beierle and Leander found two new sporadic quadratic APN permutations in dimension 9. Up to EA-equivalence, we present a single trivariate representation of those two permutations as Cu:(F2m)3→(F2m)3,(x,y,z)↦(x3+uy2z,y3+uxz2,z3+ux2y), where m=3 and u∈F23∖{0,1} such that the two permutations correspond to different choices of u. We then analyze the differential uniformity and the nonlinearity of Cu in a more general case. For m≥3 being a multiple of 3 and u∈F2m not being a 7-th power, we show that the differential uniformity of Cu is bounded above by 8, and that the linearity of Cu is bounded above by 81+⌊m2⌋. Based on numerical experiments, we conjecture that Cu is not APN if m is greater than 3. We also analyze the CCZ-equivalence classes of the quadratic APN permutations in dimension 9 known so far and derive a lower bound on the number of their EA-equivalence classes. We further show that the two sporadic APN permutations share an interesting similarity with Gold APN permutations in odd dimension divisible by 3, namely that a permutation EA-inequivalent to those sporadic APN permutations and their inverses can be obtained by just applying EA transformations and inversion to the original permutations. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.ffa.2022.102049 | Finite Fields and Their Applications |
Keywords | DocType | Volume |
06E30,94A60 | Journal | 81 |
ISSN | Citations | PageRank |
1071-5797 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christof Beierle | 1 | 0 | 0.34 |
| Claude Carlet | 2 | 2925 | 226.81 |
| Gregor Leander | 3 | 1287 | 77.03 |
| Léo Perrin | 4 | 4 | 3.59 |