<abstract xmlns="http://www.w3.org/1999/xhtml">This paper deals with an implementation of the elliptic curve primality proving (ECPP) algorithm of Atkin and Morain. As the ECPP algorithm is not deterministic, we are developing a strategy to avoid certain situations in which the original implementation could get stuck and to get closer to the situation where the probability that the algorithm terminates successfully is 1. We apply heuristics and tricks in order to test the strategy in our implementation in M<sc>agma</sc> on numbers of up to 7000 decimal digits and collect data to show the advantages over previous implementations in practice.</abstract>

A strategy for elliptic curve primality proving

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we consider the RSA variant based on the key equation <italic>ed ≡ 1</italic> (mod <italic>φ</italic>(<italic>N</italic>)) where <italic>N = prq, r ≥ 2</italic>. We show that if the secret exponent <italic>d</italic> is close to any multiple of the prime factor <italic>p</italic> or its powers, then it is possible to factor <italic>N</italic> in polynomial time in log <italic>N</italic>.</abstract>

Laboratory of Mathematics, Cryptography and Mechanics, Fstm, University Hassan II of Casablanca, Morocco

Factoring multi power RSA moduli with a class of secret exponents

<abstract xmlns="http://www.w3.org/1999/xhtml">With the advent of the new and continuously improving technologies, in a couple of years DNA sequencing can be as commonplace as a simple blood test. The growth of sequencing efficiency has a larger exponent than the Moore’s law of standard processors, hence alignment and further processing of sequenced data is the bottleneck. The usage of FPGA (Field Programmable Gate Arrays) technology may provide an efficient alternative. We propose a simple algorithm for DNA sequence alignment, which can be realized efficiently by nucleotic principal agents of Non.Neumann nature. The prototype FPGA implementation runs on a small Terasic DE1-SoC demo board with a Cyclone V chip. We present test results and furthermore analyse the theoretical scalability of this system, showing that the execution time is independent of the length of reference genome sequences. A special advantage of this parallel algorithm is that it performs exhaustive search producing all match variants up to a predetermined number of point (mutation) errors.</abstract>

Wigner Institute and Eötvös Loránd University

Simple scalable nucleotic FPGA based short read aligner for exhaustive search of substitution errors

<abstract xmlns="http://www.w3.org/1999/xhtml">In our ever-evolving world, the importance of social networks is bigger now than ever. The purpose of this paper is to develop a sentiment analyzer for the Hungarian language, which we can then use to analyze any text and conduct further experiments. One such experiment is an application which can interface with social networks, and run sentiment analysis on the logged-in users friends’ posts and comments, while the other experiment is the use of sentiment analysis in order to visualize the evolution of relationships between characters in a text.</abstract>

Sapientia Hungarian University of Transylvania, Dept. Mathematics and Informatics, Târgu-Mureş

Sapiness–sentiment analyser

<abstract xmlns="http://www.w3.org/1999/xhtml">A <italic>k</italic>-hypertournament <italic>H = (V, A)</italic>, where <italic>V</italic> is the vertex set and <italic>A</italic> is an arc set, is a complete <italic>k</italic>-hypergraph with each <italic>k</italic>-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a <italic>k</italic>-hypertournament, the score <italic>si</italic>(losing score <italic>ri</italic>) of a vertex is the number of edges containing <italic>vi</italic> in which <italic>vi</italic> is not the last element(in which <italic>vi</italic> is the last element) and the total score of a vertex <italic>vi</italic> is <italic>ti = si − ri</italic>. For <italic>v ∈ V</italic> we denote 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/ausi-2015-0019_i1.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>d</mi><mi>H</mi><mo>+</mo></msubsup><mo>=</mo><munder><mo>∑</mo><mrow><mi>a</mi><mo>∈</mo><mi>H</mi></mrow></munder><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>v</mi><mo>,</mo><mi>a</mi><mo stretchy="false">)</mo></mrow></mrow></math><tex-math>$d_H^ + = \sum\limits_{a \in H} {\rho (v,a)} $</tex-math></alternatives></inline-formula>
 (or simply <italic>d+</italic>(<italic>v</italic>)) the degree of a vertex where, <italic>ρ(v, a)</italic> is <italic>k − i</italic> if <italic>v ∈ a ∈ A</italic> and <italic>v</italic> is the ith entry in <italic>a</italic>, otherwise zero. In this paper, we obtain necessary and sufficient conditions for a <italic>k</italic>-hypertournament to be degree regular. We use the inequalities of Holder and Chebyshev from mathematical analysis to study the score and degree structure of the <italic>k</italic>-hypertournaments.</abstract>

Eötvös Loránd University, Faculty of Informatics, Budapest, Hungary

On the scores and degrees in hypertournaments

<abstract xmlns="http://www.w3.org/1999/xhtml">The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2) gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.</abstract>

Eötvös University, Faculty of Informatics

Chaotic behavior of the lattice Yang-Mills on CUDA

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