1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity

Several factors (e.g., balancedness, good correlation immunity) are considered as important properties of Boolean functions for using in cryptographic primitives. A Boolean function is perfect algebraic immune if it is with perfect immunity against algebraic and fast algebraic attacks. There is an increasing interest in construction of Boolean function that is perfect algebraic immune combined with other characteristics, like resiliency. A resilient function is a balanced correlation-immune function. This paper uses bivariate representation of Boolean function and theory of finite field to construct a generalized and new class of Boolean functions on even variables by extending the Carlet-Feng functions. We show that the functions generated by this construction support cryptographic properties of 1-resiliency and (sub)optimal algebraic immunity and further propose the sufficient condition of achieving optimal algebraic immunity. Compared experimentally with Carlet-Feng functions and the functions constructed by the method of first-order concatenation existing in the literature on even (from 6 to 16) variables, these functions have better immunity against fast algebraic attacks. Implementation results also show that they are almost perfect algebraic immune functions.

ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH σf = 22n + 2n+3(n ≥ 3)

The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n ≥ 5). We conclude that there does not exist a m(m ≥ 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n ≥ 7.

Planning of Disaster Prevention Space System Based on Urban Morphology - Take Suzhou Old Urban Area as an Example

Urban morphology analysis is the basis of cognition of city and making plan of disaster prevention space system. According to urban morphology of Suzhou old urban area of the double chessboard of River Street parallel and a moat surround the city, explores the construction of prevention space system combined with urban morphology: disaster prevention units are based on neighborhood in the old area and all kinds of space are organized to form order disaster prevention space system. Exploiting new function of the moat waterfront outside the old area, enhance the capabilities to form a " Resilient function" waterfront space; strengthen the construction of land and water secure channel, ensure that evacuation channels are unblocked in disaster. Combine three different levels of disaster prevention space to construct disaster prevention space systems of Suzhou old urban area. It can strengthen the efficiency of Suzhou comprehensive urban disaster prevention.