The Strict Avalanche Criterion (SAC) is a property of vectorial Boolean functions that is used in the construction of strong S-boxes. We show in this paper how to generalize the concept of SAC to address possible c-differential attacks, in the realm of finite fields. We define the concepts of c-Strict Avalanche Criterion (c-SAC) and c-Strict Avalanche Criterion of order m (c-SAC(m)), and generalize results of (Li and Cusick, 2005). We also show computationally how the new definition is not equivalent to the existing concepts of c-bent1-ness (Stanica et al., 2020), nor (for n = m) PcN-ness (Ellingsen et al., 2020)

In this paper we define a new (output) multiplicative differential, and the corresponding c-differential uniformity. With this new concept, even for characteristic 2, there are perfect c-nonlinear (PcN) functions. We first characterize the c-differential uniformity of a function in terms of its Walsh transform. We further look at some of the known perfect nonlinear (PN) functions and show that only one remains a PcN function, under a different condition on the parameters. In fact, the p-ary Gold PN function increases its c-differential uniformity significantly, under some conditions on the parameters. We then precisely characterize the c-differential uniformity of the inverse function (in any dimension and characteristic), relevant for the Rijndael (and Advanced Encryption Standard) block cipher.

The aim of this paper is to extend some basic concepts related to the Maximum Likelihood decoding of codes on the Z-channel, which is a particular, but very important, example of an asymmetric channel. We study distance properties of linear codes over the Z-channel, in order to define a suitable metric for the implementation of a Maximum Likelihood decoder on the channel. A combinatorial expression for an approximation on the probability of incorrect Maximum Likelihood decoding is also provided, and comparisons are given to evaluate the tightness of the estimation, when a Hamming code, a Turbo code and an LDPC code are used for communicating over the Z-channel.

We apply principles from digital image correction to enhance the correction of two-dimensionally correlated unidirectional errors on a two-dimensional grid system. A restoration technique presented in Neifield et al. (1996) based on Markov random fields, is used to find an estimate of the error pattern. This estimate then in turn provides a priori information for use in a soft decoder for the actual code (e.g. LDPC decoder).