scholarly journals Algorithms and complexity evaluation of 3- and 5-isogeny calculation of super singular Edwards curves

Radiotekhnika ◽  
2020 ◽  
Vol 1 (200) ◽  
pp. 37-50
Author(s):  
А.В. Бессалов
Keyword(s):  
Edwards Curves ◽  
Algorithms And Complexity

Binary decompositions of probability densities and random-bit simulation

2020 ◽  
Vol 26 (2) ◽  
pp. 163-169
Author(s):  
Vladimir Nekrutkin
Keyword(s):  
New York ◽  
Distribution Function ◽  
Random Number ◽  
Discrete Distribution ◽  
Random Number Generation ◽  
Academic Press ◽  
Bernoulli Trials ◽  
Algorithms And Complexity ◽  
Binary Decomposition ◽  
Probability Densities

AbstractThis paper is devoted to random-bit simulation of probability densities, supported on {[0,1]}. The term “random-bit” means that the source of randomness for simulation is a sequence of symmetrical Bernoulli trials. In contrast to the pioneer paper [D. E. Knuth and A. C. Yao, The complexity of nonuniform random number generation, Algorithms and Complexity, Academic Press, New York 1976, 357–428], the proposed method demands the knowledge of the probability density under simulation, and not the values of the corresponding distribution function. The method is based on the so-called binary decomposition of the density and comes down to simulation of a special discrete distribution to get several principal bits of output, while further bits of output are produced by “flipping a coin”. The complexity of the method is studied and several examples are presented.

scholarly journals Identification, Location-Domination and Metric Dimension on Interval and Permutation Graphs. II. Algorithms and Complexity

Algorithmica ◽  
2016 ◽  
Vol 78 (3) ◽  
pp. 914-944 ◽  
Author(s):  
Florent Foucaud ◽  
George B. Mertzios ◽  
Reza Naserasr ◽  
Aline Parreau ◽  
Petru Valicov
Keyword(s):  
Metric Dimension ◽  
Permutation Graphs ◽  
Algorithms And Complexity

scholarly journals The Pairing Computation on Edwards Curves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfeng Wu ◽  
Liangze Li ◽  
Fan Zhang
Keyword(s):  
Geometric Interpretation ◽  
Tate Pairing ◽  
Quadric Surfaces ◽  
Edwards Curves ◽  
Explicit Formulae ◽  
Pairing Computation ◽  
Twisted Edwards Curves ◽  
Group Law

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.

scholarly journals Angle Covers: Algorithms and Complexity

2020 ◽  
pp. 94-106
Author(s):  
William Evans ◽  
Ellen Gethner ◽  
Jack Spalding-Jamieson ◽  
Alexander Wolff
Keyword(s):  
Algorithms And Complexity
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