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
The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion ...The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion excitation function derived from SPACE2002 series. The geophysical excitation functions of the individual AAM, OAM, HAM, and two combined excitations of the AAM + OAM and AAM + OAM + HAM at 1d, 5d, 1m and 3m in- tervals are statistically tested for the hypothesis of the nor- mality, and then tested for the hypotheses of identical distri- bution between the geodetic and the geophysical excitations. The results show that, among the total 16 components of the two combined excitation functions at 1d, 5d, 1m and 3m in- tervals,most follow random normal processes, the hy- potheses of identical distribution between the geodetic exci- tation and the two combined excitation are acceptable, while most of the hypotheses of identical distribution between the geodetic excitation and the individual excitations of the AAM, OAM, and HAM are rejectable. These results elucidate from a new point of view, that the excitations from AAM, OAM, and HAM are the main sources of the Chandler wobble, and the Chandler wobble excitation function is of a random normal property.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.
文摘The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion excitation function derived from SPACE2002 series. The geophysical excitation functions of the individual AAM, OAM, HAM, and two combined excitations of the AAM + OAM and AAM + OAM + HAM at 1d, 5d, 1m and 3m in- tervals are statistically tested for the hypothesis of the nor- mality, and then tested for the hypotheses of identical distri- bution between the geodetic and the geophysical excitations. The results show that, among the total 16 components of the two combined excitation functions at 1d, 5d, 1m and 3m in- tervals,most follow random normal processes, the hy- potheses of identical distribution between the geodetic exci- tation and the two combined excitation are acceptable, while most of the hypotheses of identical distribution between the geodetic excitation and the individual excitations of the AAM, OAM, and HAM are rejectable. These results elucidate from a new point of view, that the excitations from AAM, OAM, and HAM are the main sources of the Chandler wobble, and the Chandler wobble excitation function is of a random normal property.
