Wavelets and recursive filter banks

It is shown that infinite impulse response (IIR) filters lead to more general wavelets of infinite support than finite impulse response (FIR) filters. A complete constructive method that yields all orthogonal two channel filter banks, where the filters have rational transfer functions, is given, and it is shown how these can be used to generate orthonormal wavelet bases. A family of orthonormal wavelets that have a maximum number of disappearing moments is shown to be generated by the halfband Butterworth filters. When there is an odd number of zeros at π it is shown that closed forms for the filters are available without need for factorization. A still larger class of orthonormal wavelet bases having the same moment properties and containing the Daubechies and Butterworth filters as the limiting cases is presented. It is shown that it is possible to have both linear phase and orthogonality in the infinite impulse response case, and a constructive method is given. It is also shown how compactly supported bases may be orthogonalized, and bases for the spline function spaces are constructe

Wavelets and Filter Banks: Theory and Design

The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetrie

Orthogonal time-varying filter banks and wavelet packets

Considers the construction of orthogonal time-varying filter banks. By examining the time domain description of the two-channel orthogonal filter bank the authors find it possible to construct a set of orthogonal boundary filters, which allows to apply the filter bank to one-sided or finite-length signals, without redundancy or distortion. The method is constructive and complete. There is a whole space of orthogonal boundary solutions, and there is considerable freedom for optimization. This may be used to generate subband tree structures where the tree varies over time, and to change between different filter sets. The authors also show that the iteration of discrete-time time-varying filter banks gives continuous-time bases, just as in the stationary case. This gives rise to wavelet, or wavelet packet, bases for half-line and interval region

Markets for Zero-Day Exploits: Ethics and Implications

A New Security Paradigms Workshop (2013) panel discussed the topic of ethical issues and implications related to markets for zero-day exploits, i.e., markets facilitating the sale of previously unknown details on how to exploit software vulnerabilities in target applications or systems. The related topic of vulnerability rewards programs (“bug bounties ” offered by software vendors) was also discussed. This note provides selected background material submitted prior to the panel presentation, and summarizes discussion resulting from the input of both the panelists and NSPW participants

Painless migration from passwords to two factor authentication

Abstract-In spite of growing frequency and sophistication of attacks two factor authentication schemes have seen very limited adoption in the US, and passwords remain the single factor of authentication for most bank and brokerage accounts. Clearly the cost benefit analysis is not as strongly in favor of two factor as we might imagine. Upgrading from passwords to a two factor authentication system usually involves a large engineering effort, a discontinuity of user experience and a hard key management problem. In this paper we describe a system to convert a legacy password authentication server into a two factor system. The existing password system is untouched, but is cascaded with a new server that verifies possession of a smartphone device. No alteration, patching or updates to the legacy system is necessary. There are now two alternative authentication paths: one using passwords alone, and a second using passwords and possession of the trusted device. The bank can leave the password authentication path available while users migrate to the two factor scheme. Once migration is complete the passwordonly path can be severed. We have implemented the system and carried out two factor authentication against real accounts at several major banks