Euclidean Algorithm for Sound Generation

Euclidean algorithm is known by humanity for more than two thousand years. During this period many applications for it were found, covering different disciplines and music is one of those. Such algorithm application in music first appeared in 2005 when researchers found a correlation between world music rhythm and the Euclidean algorithm result, defining Euclidean rhythms as the concept.In the modern world, music could be created using many approaches. The first one being the simple analogue, the analogue signal is just a sound wave that emitted due to vibration of a certain medium, the one that is being recorded onto a computer hard drive or other digital storage called digital and has methods of digital signal processing applied. Having the ability to convert the analogue signal or create and modulate digital sounds creates a lot of possibilities for sound design and production, where sonic characteristics were never accessible because of limitations in sound development by the analogue devices or instruments, nowadays become true. Sound generation process, which usually consists of modulating waveform and frequency and can be influenced by many factors like oscillation, FX pipeline and so on. The programs that influence synthesised or recorded signal called VST plugins and they are utilising the concepts of digital signal processing.This paper aims to research the possible application of Euclidean rhythms and integrate those in the sound generation process by creating a VST plugin that oscillates incoming signal with one of the four basic wave shapes in order to achieve unique sonic qualities. The varying function allows modulation with one out of four basic wave shapes such as sine, triangle, square and sawtooth, depending on the value received from the Euclidean rhythm generator, switching modulating functions introduces subharmonics, with the resulting richer and tighter sound which could be seen on the spectrograms provided in the publication.

Separating Phages From Other Virus Families and Classifying the Different Phage Families By GI-Clusters

Background: Phages are the most abundant biological entities, but the commonly used clustering techniques are difficult to separate them from other virus families and classify the different phage families together.Results: This work uses GI-clusters to separate phages from other virus families and classify the different phage families, where GI-clusters are constructed by GI-features, GI-features are constructed by the togetherness with F-features, training data, MG-Euclidean and Icc-cluster algorithms, F-features are the frequencies of multiple-nucleotides that are generated from genomes of viruses, MG-Euclidean algorithm is able to put the nearest neighbors in the same mini-groups, and Icc-cluster algorithm put the distant samples to the different mini-clusters. For these viruses that the maximum element of their GI-features are in the same locations, they are put to the same GI-clusters, where the families of viruses in test data are identified by GI-clusters, and the families of GI-clusters are defined by viruses of training data.Conclusions: From analysis of 4 data sets that are constructed by the different family viruses, we demonstrate that GI-clusters are able to separate phages from other virus families, correctly classify the different phage families, and correctly predict the families of these unknown phages also.

Profiling Attack against RSA Key Generation Based on a Euclidean Algorithm

A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended Euclidean algorithm for modular inverse and GCD computations. To date, this algorithm has only been exploited by simple power analysis; therefore, the countermeasures described in the literature are focused on mitigating only this kind of attack. We demonstrate that one of those countermeasures is not effective in preventing profiling attacks. The feasibility of our approach relies on the extraction of several leakage vectors from a single power trace. Moreover, because there are known relationships between the secrets and the public modulo in RSA, the uncertainty in some of the guessed secrets can be reduced by simple tests. This increases the effectiveness of the proposed attack.

GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm

Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing some cryptographic architectures that could be used in design of strong encryption schemes.

Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field

We analyse the behaviour of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field $\mathbb{F}_{q}$ of q elements when the highest degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f that are relatively prime with g and for the average degree of $\gcd(g,f)$ . We also exhibit asymptotically optimal bounds for the average-case complexity of the Euclidean algorithm applied to pairs (g,f) as above.

A Note on the Computation of the Modular Inverse for Cryptography

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a<n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a<<n (e.g., a<lnn).

Current situation and development direction of sports industry in colleges and universities based on euclidean algorithm

With the development of sports in colleges and universities, the research on innovation reform of sports industry has been deepened. Therefore, based on the above situation, a study of the status quo and development direction of sports industry in colleges and universities based on the Euclid algorithm is proposed. In the research here, according to the traditional sports industry concept to sum up, and then according to the advantages of computer technology to deal with the relevant data. In order to realize good overlap between data, an application of Euclidean algorithm is proposed. In the test of Euclidean algorithm, the efficiency and function of the algorithm are tested comprehensively, and the test results show that the research is feasible.

Improvement of RSA Algorithm Using Euclidean Technique

Information Security has become an essential concern in the modern world. Encryption is an effective way to prevent an unofficial person from viewing the digital information with the secret key. RSA encryption is often used for digital signatures which can prove the authenticity and reliability of a message. As RSA encryption is less competent and resource-heavy, it is not used to encrypt the entire message. If a message is encrypted with a symmetric-key RSA encryption it will be more efficient. Under this process, only the RSA private key will be able to decrypt the symmetric key. The Euclidean algorithm is attainably one of the most extensively known algorithms. The Euclidean algorithm is used for finding the greatest common divisor of two numbers. The algorithm can also be defined for more general rings than just the integers. This work is very useful to improve the data security in Smart card and Aadhaar card. In this paper, the RSA algorithm is modified using the Euclidean technique to improve its performance. The proposed algorithm shows its better performance in terms of speed, throughput, power consumption, and the avalanche effect. Experimental results and mathematical justification supporting the proposed method are reported.