Name
Abstract | ||
|---|---|---|
We consider n-bit permutations with differential uniformity of 4 and null nonlinearity. We first show that the inverses of Gold functions have the interesting property that one component can be replaced by a linear function such that it still remains a permutation. This directly yields a construction of 4-uniform permutations with trivial nonlinearity in odd dimension. We further show their existence for all n = 3 and n = 5 based on a construction in Alsalami (Cryptogr. Commun. 10(4): 611-628, 2018). In this context, we also show that 4-uniform 2-1 functions obtained from admissible sequences, as defined by Idrisova in (Cryptogr. Commun. 11(1): 21-39, 2019), exist in every dimension n = 3 and n = 5. Such functions fulfill some necessary properties for being subfunctions of APN permutations. Finally, we use the 4-uniform permutations with null nonlinearity to construct some 4-uniform 2-1 functions from Fn2 to Fn-1 2 which are not obtained from admissible sequences. This disproves a conjecture raised by Idrisova. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s12095-020-00434-2 | CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES |
Keywords | DocType | Volume |
Boolean function, Cryptographic S-boxes, APN permutations, Gold functions | Journal | 12 |
Issue | ISSN | Citations |
6 | 1936-2447 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christof Beierle | 1 | 56 | 6.87 |
| Gregor Leander | 2 | 1287 | 77.03 |