In this paper we unify several existing regularity conditions for graphs, including strong regularity, k-isoregularity, and the t-vertex condition. We develop an algebraic composition/decomposition theory of conditions. Using our theoretical results show that a family non rank 3 graphs known to satisfy 7-vertex condition fulfills even stronger condition, (3,7)-regularity (the notion is defined ...

Due to the success of diierential and linear attacks on a large number of encryption algorithms, it is important to investigate relationships among the various cryptographic, including diierential and linear, characteristics of an S-box (substitution box). After discussing a precise relationship among three tables, namely the diierence, auto-correlation and correlation immunity distribution tab...