Processes for producing secure software

Summarizes work initiated at the National Cybersecurity Summit, held 2-3 December 2003 in Santa Clara, California. Attendees representing industry, academia, and the US Department of Homeland Security (DHS) formed five task forces to focus on specific topic areas. This report describes, the key problems and recommendations identified by the Software Process subgroup of the "Security Across the Software Development Lifecycle" task force. Producing secure software is a multifaceted problem of software engineering, security engineering, and management. Thus, producing secure software starts with outstanding software engineering practices, augmented with sound technical practices, and supported by management practices that promote secure software development. We discuss these practices.     

Oversampling in the Gabor scheme

A method for calculating the coefficients of the Gabor expansion in the case of oversampling is presented. The method is based on the concept of frames and utilizes the Zak transform. As such, the Zak transform highlights the meaning and importance of frames in the context of oversampling, and other aspects of signal representation by means of nonorthogonal bases     

Frame analysis of the discrete Gabor-scheme

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this function. The frame bounds are calculated by means of the eigenvalues of the matrix-valued function, and the dual frame, which is used in calculation of the expansion coefficients, is expressed by means of the inverse matrix. DFT-based algorithms for computation of the expansion coefficients, and for the reconstruction of signals from these coefficients, are generalized for the case of oversampling of the Gabor space. The algorithms are implemented in an example of representation of a nonstationary signal     

Discrete multiwindow Gabor-type transforms

The discrete (finite) Gabor scheme is generalized by incorporating multiwindows. Two approaches are presented for the analysis of the multiwindow scheme: the signal domain approach and the Zak transform domain approach. Issues related to undersampling, critical sampling, and oversampling are considered. The analysis is based on the concept of frames and on generalized (Moore-Penrose) inverses. The approach based on representing the frame operator as a matrix-valued function is far less demanding from a computational complexity viewpoint than a straightforward matrix algebra in various operations such as the computation of the dual frame. DFT-based algorithms, including complexity analysis, are presented for the calculation of the expansion coefficients and for the reconstruction of the signal in both signal and transform domains. The scheme is further generalized and incorporates kernels other than the complex exponential. Representations other than those based on the dual frame and nonrectangular sampling of the combined space are considered as well. An example that illustrates the advantages of the multiwindow scheme over the single-window scheme is presented