S-box is one of the core components of symmetric cryptographic algorithms, but differential distribution table (DDT) is an important tool to research some properties of S-boxes to resist differential attacks. In this paper, we give a relationship between the sum-of-squares of DDT and the sum-of-squares indicator of (n, m)-functions based on the autocorrelation coefficients. We also get some upper and lower bounds on the sum-of-squares of DDT of balanced (n, m)-functions, and prove that the sum-of-squares of DDT of (n, m)-functions is affine invariant under affine affine equivalent. Furthermore, we obtain a relationship between the sum-of-squares of DDT and the signal-to-noise ratio of (n, m)-functions. In addition, we calculate the distributions of the sum-of-squares of DDT for all 3-bit S-boxes, the 4-bit optimal S-boxes and all 302 balanced S-boxes (up to affine equivalence), data experiments verify our results.

Owing to the large amount of speckle noise and ill-defined edges present in echocardiographic images, computer-based boundary detection of the left ventricle has proved to be a challenging problem. In this paper, a Markovian level set method for boundary detection in long-axis echocardiographic images is proposed. It combines Markov random field (MRF) model, which makes use of local statistics with level set method that handles topological changes, to detect a continuous and smooth boundary. Experimental results show that higher accuracy can be achieved with the proposed method compared with two related MRF-based methods.