1,720,987 research outputs found
On Homomorphic Encryption Using Abelian Groups:Classical Security Analysis
No full textLeonardi and Ruiz-Lopez recently proposed an additively homomorphic public key encryption scheme based on combining group homomorphisms with noise. Choosing parameters for their primitive requires choosing three groups G, H, and K. In their paper, Leonardi and Ruiz-Lopez claim that when G, H, and K are abelian, then their public key cryptosystem is not quantum secure. In this chapter, we study security for finite abelian groups G, H, and K in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups
Power Values of Power Sums:A Survey
No full textResearch on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) number theory in recent years. In this survey, we present the key tools and techniques employed thus far in the (explicit) resolution of Diophantine problems, as well as an overview of existing results. We also state some open problems that naturally arise in the process.</p
Multiradical isogenies
Get PDFWe argue that for all integers and there exist multiradical isogeny formulae, that can be iteratively applied to compute -isogenies between principally polarized -dimensional abelian varieties, for any value of . The formulae are complete: each iteration involves the extraction of different th roots, whence the epithet multiradical, and by varying which roots are chosen one computes all extensions to an -isogeny of the incoming -isogeny. Our group-theoretic argumentation is heuristic, but it is supported by concrete formulae for several prominent families. As our main application, we illustrate the use of multiradical isogenies by implementing a hash function from -isogenies between Jacobians of superspecial genus- curves, showing that it outperforms its -counterpart by an asymptotic factor in terms of speed
Hecke algebras for GL n over local fields
No full textWe study the local Hecke algebra HG(K) for G= GL n and K a non-archimedean local field of characteristic zero. We show that for G= GL 2 and any two such fields K and L, there is a Morita equivalence HG(K) ∼ MHG(L) , by using the Bernstein decomposition of the Hecke algebra and determining the intertwining algebras that yield the Bernstein blocks up to Morita equivalence. By contrast, we prove that for G= GL n, there is an algebra isomorphism HG(K) ≅ HG(L) which is an isometry for the induced L1-norm if and only if there is a field isomorphism K≅ L
Numerical reconstruction of curves from their Jacobians
No full textConference Name:18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021Date of Conference: May 31– June 4, 2021We approach the Torelli problem of recostructing a curve from its Jacobian from a
computational point of view. Following Dubrovin, we design a machinery to solve this
problem effectively, which builds on methods in numerical algebraic geometry. We
verify this methods via numerical experiments with curves up to genus 7
Rational approximations, multidimensional continued fractions and lattice reduction
Get PDFWe first survey the current state of the art concerning the dynamical
properties of multidimensional continued fraction algorithms defined
dynamically as piecewise fractional maps and compare them with algorithms based
on lattice reduction. We discuss their convergence properties and the quality
of the rational approximation, and stress the interest for these algorithms to
be obtained by iterating dynamical systems. We then focus on an algorithm based
on the classical Jacobi--Perron algorithm involving the nearest integer part.
We describe its Markov properties and we suggest a possible procedure for
proving the existence of a finite ergodic invariant measure absolutely
continuous with respect to Lebesgue measure.Comment: 30 pages, 4 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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