1 research outputs found
On the Differential-Linear Connectivity Table of Vectorial Boolean Functions
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers.
Different known attacks on block ciphers have resulted in diverse cryptographic
criteria for vectorial Boolean functions, such as differential uniformity and
nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new
tool, called the differential-linear connectivity table (DLCT), which allows
for taking into account the dependency between the two subciphers and
involved in differential-linear attacks. This new notion leads to
significant improvements of differential-linear attacks on several ciphers.
This paper presents a theoretical characterization of the DLCT of vectorial
Boolean functions and also investigates this new criterion for some families of
functions with specific forms.
More precisely, we firstly reveal the connection between the DLCT and the
autocorrelation of vectorial Boolean functions, we characterize properties of
the DLCT by means of the Walsh transform of the function and of its
differential distribution table, and we present generic bounds on the highest
magnitude occurring in the DLCT of vectorial Boolean functions, which coincides
(up to a factor~) with the well-established notion of absolute indicator.
Next, we investigate the invariance property of the DLCT of vectorial Boolean
functions under the affine, extended-affine, and Carlet-Charpin-Zinoviev (CCZ)
equivalence and exhaust the DLCT spectra of optimal -bit S-boxes under
affine equivalence. Furthermore, we study the DLCT of APN, plateaued and AB
functions and establish its connection with other cryptographic criteria.
Finally, we investigate the DLCT and the absolute indicator of some specific
polynomials with optimal or low differential uniformity, including monomials,
cubic functions, quadratic functions and inverses of quadratic permutations.Comment: arXiv admin note: text overlap with arXiv:1907.0598