Об аппаратной реализации одного класса байтовых подстановок
The paper studies the issues of implementation of one class of S-Boxes on FPGA and ASIC and compares them with the implementation of arbitrary mappings V8 → V8. The way of implementation of arbitrary S-Box is studied. It’s shown that any S-Box over V8 can be implemented using 40 LUTs (812 GE). For one class of S-Boxes over V8 with high cryptographic properties, the possibility of their implementation using 19 LUTs (147 GE) is shown.
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.
The article is concerned with the analysis of metapoetic statements of Genrikh Sapgir that were made by him in poetic form – in the shape of «programmatic» poems. In his work, the poet preferred to dispense with creative manifestos or forewords: there is extremely small number of them in Sapgir’s heritage. But at the same time he looked for ways to give a key to the meaning of his poetical quests and experiments, using his poetry, comprising of a new design concept: «poetics of semi-word» or particular method of «permutation».
We consider several procedures to number all outcomes of a permutation scheme, establish a one-to-one correspondence between the outcome and its number generated in the numbering procedure, and give some methods to simulate the outcomes.
"Designing" the complete works of his own is an important part of Aleksander Kondratov's creations, a neofuturist poet from Leningrad. One of the prospects of his future collection, "My Trinities" makes it possible to restore the poet's concept to create "The Concretions", a volume of concretist texts, which has not been fully implemented. These texts were obviously aimed at the demonstration of the whole paradigm of devices and forms of this trend of experimental poetry that Kondratov knew at the time. Keywords: Aleatory works, Aleksander Kondratov, dadaism, concretism, neofuturism, uncensored poetry, zero text, permutation, hollow text, found poetry.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.