A Low Distortion Audio Self-Recovery Algorithm Robust to Discordant Size Content Replacement Attack

Although the development of watermarking techniques has enabled designers to tackle normal processing attacks (e.g., amplitude scaling, noise addition, re-compression), robustness against malicious attacks remains a challenge. The discordant size content replacement attack is an attack against watermarking schemes which performs content replacement that increases or reduces the number of samples in the signal. This attack modifies the content and length of the signal, as well as desynchronizes the position of the watermark and its removal. In this paper, a source-channel coding approach for protecting an audio signal against this attack was applied. Before applying the source-channel encoding, a decimation technique was performed to reduce by one-half the number of samples in the original signal. This technique allowed compressing at a bit rate of 64 kbps and obtaining a watermarked audio signal with an excellent quality scale. In the watermark restoration, an interpolation was applied after the source-channel decoding to recover the content and the length. The procedure of decimation–interpolation was taken because it is a linear and time-invariant operation and is useful in digital audio. A synchronization strategy was designed to detect the positions where the number of samples in the signal was increased or reduced. The restoration ability of the proposed scheme was tested with a mathematical model of the discordant size content replacement attack. The attack model confirmed that it is necessary to design a synchronizing strategy to correctly extract the watermark and to recover the tampered signal. Experimental results show that the scheme has better restoration ability than state-of-the-art schemes. The scheme was able to restore a tampered area of around 20% with very good quality, and up to 58.3% with acceptable quality. The robustness against the discordant size content replacement attack was achieved with a transparency threshold above −2.

An improved spectral classification of Boolean functions based on an extended set of invariant operations

Boolean functions expressing some particular properties often appear in engineering practice. Therefore, a lot of research efforts are put into exploring different approaches towards classification of Boolean functions with respect to various criteria that are typically selected to serve some specific needs of the intended applications. A classification is considered to be strong if there is a reasonably small number of different classes for a given number of variables n and it it desir able that classification rules are simple. A classification with respect to Walsh spectral coefficients, introduced formerly for digital system design purposes, appears to be useful in the context of Boolean functions used in cryptography, since it is in a way compatible with characterization of cryptographically interesting functions through Walsh spectral coefficients. This classification is performed in terms of certain spectral invariant operations. We show by introducing a new spectral invariant operation in the Walsh domain, that by starting from n?5, some classes of Boolean functions can be merged which makes the classification stronger, and from the theoretical point of view resolves a problem raised already in seventies of the last century. Further, this new spectral invariant operation can be used in constructing bent functions from bent functions represented by quadratic forms.

GAUGE-INVARIANT FORMULATION OF QUANTUM ELECTRODYNAMICS

Electrodynamics is formulated so as to be manifestly invariant under general gauge transformations, through being built up entirely in terms of gauge-invariant dynamical variables. The quantization of the theory can be carried out by the usual rules and meets with the usual difficulties.It is found that the gauge-invariant operation of creation of an electron involves the simultaneous creation of an electron and of the Coulomb field around it. The requirement of manifest gauge invariance prevents one from using the concept of an electron separated from its Coulomb field.