The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower ...The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower bound on the sum- of-squares indicator for a balanced Boolean function satisfy- ing the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propaga- tion criterion with respect to some vectors, we give three nec- essary and sufficient conditions on the auto-correlation distri- bution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator.展开更多
基金This work was supported by Sichuan Provincial Youth Science Fund, the Science and Technology on Communication Security Laboratory Project （9140C110201110C1102）, the National Natural Science Foundations of China （Grant Nos. 61003299, 61202437）, the Natural Sci- ence Basic Research Plan in Shaanxi Province of China （2012JM8041）, the Fundamental Research Funds for the Central Universities （K5051201036） and the ＂l 1 l＂ Project （B08038）. Thanks are due to anonymous referees for a series of comment on this paper.
文摘The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower bound on the sum- of-squares indicator for a balanced Boolean function satisfy- ing the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propaga- tion criterion with respect to some vectors, we give three nec- essary and sufficient conditions on the auto-correlation distri- bution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator.
