The autocorrelation of a Boolean function possesses the capability to reflect such characteristics as linear structure, Strict Avalanche Criterion(SAC) and Propagation Criterion(PC)of degree k. But it can do nothing i...The autocorrelation of a Boolean function possesses the capability to reflect such characteristics as linear structure, Strict Avalanche Criterion(SAC) and Propagation Criterion(PC)of degree k. But it can do nothing in determining the order of SAC or PC. A calculating table for the autocorrelation is constructed in this paper so as to show what is beyond the autocorrelation and how the three cryptographic characteristics are exhibited. A deeper study on the calculating table in a similar way has helped us to develop a new concept, named as the general autocorrelation, to address efficiently the problem how to determine the orders of SAC and PC. The application on the Advanced Encryption Standard(AES) shows the SAC and PC characteristics of Boolean functions of AES S-box.展开更多
This paper considers the empirical Bayes （EB） estimation problem for the parameter β of the linear regression model y = Xβ＋ ε with ε- N（0, σ^2I） given β. Based on Pitman closeness （PC） criterion and mean ...This paper considers the empirical Bayes （EB） estimation problem for the parameter β of the linear regression model y = Xβ＋ ε with ε- N（0, σ^2I） given β. Based on Pitman closeness （PC） criterion and mean square error matrix （MSEM） criterion, we prove the superiority of the EB estimator over the ordinary least square estimator （OLSE）.展开更多
基金Partially supported by the National 973 Project(G1999035803)National 863 Project (2002AA143021)the National Cryptography Development Funds for the Tenth Fiveyear Project
文摘The autocorrelation of a Boolean function possesses the capability to reflect such characteristics as linear structure, Strict Avalanche Criterion(SAC) and Propagation Criterion(PC)of degree k. But it can do nothing in determining the order of SAC or PC. A calculating table for the autocorrelation is constructed in this paper so as to show what is beyond the autocorrelation and how the three cryptographic characteristics are exhibited. A deeper study on the calculating table in a similar way has helped us to develop a new concept, named as the general autocorrelation, to address efficiently the problem how to determine the orders of SAC and PC. The application on the Advanced Encryption Standard(AES) shows the SAC and PC characteristics of Boolean functions of AES S-box.
文摘This paper considers the empirical Bayes （EB） estimation problem for the parameter β of the linear regression model y = Xβ＋ ε with ε- N（0, σ^2I） given β. Based on Pitman closeness （PC） criterion and mean square error matrix （MSEM） criterion, we prove the superiority of the EB estimator over the ordinary least square estimator （OLSE）.
