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Abstract. We present a new method for upper bounding the maximum differential probability and the maximum linear hull probability for 2 rounds of SPN structures. Our upper bound can be computed for any value of the branch number of the linear transformation and by incorporating the distribution of differential probability values and linear probability values for S-box. On application to AES, we obtain that the maximum differential probability and the maximum linear hull probability for 4 rounds of AES are bounded by 1.144 × 2 −111 and 1.075 × 2 −106 , respectively.

This paper presents a vibration-based damage detection method for shear buildings using the damage-induced deflections estimated by modal flexibility from ambient vibration measurements. This study intends to provide a basis for the damage detection problem of more complex building structures by investigating a rather idealized structure, a shear building. From analytical investigations on the damage-induced inter-story deflection (DI-ID) of shear buildings, it was shown that the DI-ID occurs only at damaged floors and not at intact floors as long as a proper load is applied to the building. To simplify the damage detection procedure a new load concept, the positive shear inspection load (PSIL), was proposed, defined as a load producing positive shear forces at all floors. It was shown that an excessive DI-ID under a PSIL indicates the existence of damage to the building and that the floors with excessive DI-ID are the damaged floors. A simple damage index Z i is proposed based on outlier analysis to account for measurement noise. Numerical and experimental studies on a 5-story shear building were carried out for two damage scenarios with 10% column E I reductions. The proposed method was found to identify the damage locations successfully for the multiple damage case as well as the single damage case, with no false-positive or false-negative detections. For the purpose of comparison, damage detection was also conducted using the damage index method and the mode shape curvature method. The mode shape curvature method was found to be the most sensitive metric, but it showed false-positive detections on an undamaged floor. The damage index method had no false-positive detections, but it was found to miss some damage in the multiple damage case.

Weighted sum, Strong convergence, Complete convergence, Negatively associated random variable, 60F15, 62G05,