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Applicability of Lightweight Stream Cipher in Crowd Computing: A Detailed Survey and Analysis
Published in Khan Pathan Al-Sakib, Crowd-Assisted Networking and Computing, 2018
Subhrajyoti Deb, Rohit Upadhya, Bubu Bhuyan
Algebraic normal form: Usually, every Boolean function has a unique representation as a multivariate over F2, which is known as the algebraic normal form (ANF). This function can be represented as f(x1,x2…xn)=c0⊕∑1≤i≤ncixi⊕∑1≤i≤j≤ncixixj⊕c(1…n)x1,…xn
The last chapter
Published in Jürgen Bierbrauer, Introduction to Coding Theory, 2016
23.12 Theorem. Let V = F2r. Each mapping f : V → F2can be written in a unique way as a polynomial in r variables x1,x2, ..., xrwith coefficients inF2such that in each monomial each variable occurs with exponent ≤ 1. This representation of f is known as thealgebraic normal form(ANF).
A Review on Evolution of Symmetric Key Block Ciphers and Their Applications
Published in IETE Journal of Education, 2020
A Boolean function f of n variables can be uniquely represented by a truth table (TT) for example consider a 3-input Boolean function f having eight values 0,1,0,1,1,1,0,0 corresponding to all eight input combinations 000,001,010,..111. This function can be obtained using a technique like Karnaugh map etc. However, the presentation may not be unique. Walsh transform is a second unique representation of a Boolean function that measures the similarity between f(x) and the linear function . Third unique representation of a Boolean function f on is by means of a polynomial which uses only AND operations and Exclusive OR functions. As an illustration, the Boolean function corresponding to the above example is as follows: This form is called algebraic normal form (ANF). The same function using truth table will be , Note that here + stands for OR logic function. Many other functions are possible in this representation. The student shall be taught how to get the sequence from the given ANF and vice-versa. Tools that can analyze the security properties of Boolean functions are: Boolfunpackage in R [67]: it is possible to load a package named boolfun that provides functionalities related to the cryptographic analysis of Boolean functions.Boolean functions in Sage [66]: In Sage, there is a module called BooleanFunctions that allows one to study cryptographic properties of Boolean functions.
A Simplistic and Novel Technique for ECG Signal Pre-Processing
Published in IETE Journal of Research, 2022
Varun Gupta, Monika Mittal, Vikas Mittal
Digital signal processing (DSP) improves ECG filtering to assist cardiologists in accurately and timely diagnosing heart related problems [22,23]. The primary goal is to preserve the essential clinical information of the ECG signals after performing the filtering operation [24,25]. Signal quality is measured by estimating the SNR of the sampled signals [26]. In the existing literature, fixed notch filter [27], low-pass, high-pass, band-pass and median filter [19], re-sampling, residual error signal, and principal component analysis (PCA) [28,29], adaptive filtering (AF) method, neural network (NN) [30–32], neighboring coefficients (NCs) [33], and wavelet transform (WT) [34–36] are some of the popular and widely used techniques that have been used for removing the undesired non-stationary trends from the ECG signals. Also, wavelet transforms have been used for various denoising and analysis related to responses of the complex systems to arbitrary inputs [37,38]. But all these methods did not get wide acceptance due to the time varying characteristics of an ECG signal. In some cases, they even failed to analyze micro potentials due to their overlap with the power line interference (PLI). Therefore in this paper, independent component analysis (ICA) and linear discriminant analysis (LDA) are proposed to be used combinedly for pre-processing and classification of an ECG signal, respectively. ICA is selected because it outperforms seven higher order filters (both analog and digital) with much less computational/ mathematical complexity and loss of information. It removes interferences by calculating independent components (ICs). LDA is selected to minimize the variance and maximize the distance between any two data-classes which results in a very less number of false detections. The performance of ICA is also compared with another benchmark technique for such purposes viz. ANF (adaptive notch filter). ANF has been selected due to its adaptive nature and the fact that it eliminates the need for higher filter-orders unlike that required in ordinary analog and digital filters. The performance of the proposed technique is assessed on the basis of sensitivity (Se) and detection error rate (DER) along with SNR [39].