Abstract: Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.
Abstract: Applications of reversible logic gates in the design of complex integrated circuits provide power optimization. This technique finds a great use in low power CMOS design, optical computing, quantum computing and nanotechnology. This paper proposes a reversible signed division circuit that can divide an n-bit signed dividend with an n-bit signed divisor using non-restoration division logic. The proposed design adequately addresses the ‘delay’ there by improving the efficiency of the circuit. An attempt is made to design a reversible signed division circuit. This paper provides a threshold to build more complex arithmetic systems using reversible logic, thus increasing the performance of computing systems.
Abstract: In this paper, we extend the concepts of primal and
weakly primal ideals for posets. Further, the diameter of the zero
divisor graph of a poset with respect to a non-primal ideal is
determined. The relation between primary and primal ideals in posets
is also studied.
Abstract: The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: the Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.
Abstract: Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.
Abstract: In the context of large volume Big Divisor (nearly)
SLagy D3/D7 μ-Split SUSY [1], after an explicit identification
of first generation of SM leptons and quarks with fermionic superpartners
of four Wilson line moduli, we discuss the identification of
gravitino as a potential dark matter candidate by explicitly calculating
the decay life times of gravitino (LSP) to be greater than age of
universe and lifetimes of decays of the co-NLSPs (the first generation
squark/slepton and a neutralino) to the LSP (the gravitino) to be
very small to respect BBN constraints. Interested in non-thermal
production mechanism of gravitino, we evaluate the relic abundance
of gravitino LSP in terms of that of the co-NLSP-s by evaluating
their (co-)annihilation cross sections and hence show that the former
satisfies the requirement for a potential Dark Matter candidate. We
also show that it is possible to obtain a 125 GeV light Higgs in our
setup.
Abstract: A given polynomial, possibly with multiple roots, is
factored into several lower-degree distinct-root polynomials with
natural-order-integer powers. All the roots, including multiplicities,
of the original polynomial may be obtained by solving these lowerdegree
distinct-root polynomials, instead of the original high-degree
multiple-root polynomial directly.
The approach requires polynomial Greatest Common Divisor
(GCD) computation. The very simple and effective process, “Monic
polynomial subtractions" converted trickily from “Longhand
polynomial divisions" of Euclidean algorithm is employed. It
requires only simple elementary arithmetic operations without any
advanced mathematics.
Amazingly, the derived routine gives the expected results for the
test polynomials of very high degree, such as p( x) =(x+1)1000.