The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Lilya Budaghyan - One of the best experts on this subject based on the ideXlab platform.
-
Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
IEEE Transactions on Information Theory, 2008Co-Authors: Lilya Budaghyan, Claude Carlet, Gregor LeanderAbstract:This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to power functions (at least for some values of the number of variables). These are two classes of APN binomials from F2n to F2n (for n divisible by 3, resp., 4). We prove that these functions are extended affine (EA)-Inequivalent to any power function and that they are CCZ-Inequivalent to the Gold, Kasami, inverse, and Dobbertin functions when n ges 12. This means that for n even they are CCZ-Inequivalent to any known APN function. In particular, for n = 12,20,24, they are therefore CCZ-Inequivalent to any power function.
-
The simplest method for constructing APN polynomials EA-Inequivalent to power functions.
IACR Cryptology ePrint Archive, 2007Co-Authors: Lilya BudaghyanAbstract:The first APN polynomials EA-Inequivalent to power functions have been constructed in [7, 8] by applying CCZ-equivalence to the Gold APN functions. It is a natural question whether it is possible to construct APN polynomials EA-Inequivalent to power functions by using only EA-equivalence and inverse transformation on a power APN function: this would be the simplest method to construct APN polynomials EA-Inequivalent to power functions. In the present paper we prove that the answer to this question is positive. By this method we construct a class of APN polynomials EA-Inequivalent to power functions. On the other hand it is shown that the APN polynomials from [7, 8] cannot be obtained by the introduced method.
-
A class of quadratic APN binomials Inequivalent to power functions.
IACR Cryptology ePrint Archive, 2006Co-Authors: Lilya Budaghyan, Claude Carlet, Gregor LeanderAbstract:We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EA-Inequivalent to any power function and that they are CCZ-Inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-Inequivalent to any known APN function, and in particular for n = 12, 24, they are therefore CCZ-Inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZInequivalent to the Kasami and Welch functions.
-
New Classes of Almost Bent and Almost Perfect Nonlinear Polynomials
arXiv: Combinatorics, 2005Co-Authors: Lilya Budaghyan, Claude Carlet, Alexander PottAbstract:We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely Inequivalent to any sum of a power function and an affine function.
-
New Classes of Almost Bent and Almost Perfect
2005Co-Authors: Lilya Budaghyan, Claude Carlet, Alexander PottAbstract:We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely Inequivalent to any sum of a power function and an affine function.
Gregor Leander - One of the best experts on this subject based on the ideXlab platform.
-
Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
IEEE Transactions on Information Theory, 2008Co-Authors: Lilya Budaghyan, Claude Carlet, Gregor LeanderAbstract:This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to power functions (at least for some values of the number of variables). These are two classes of APN binomials from F2n to F2n (for n divisible by 3, resp., 4). We prove that these functions are extended affine (EA)-Inequivalent to any power function and that they are CCZ-Inequivalent to the Gold, Kasami, inverse, and Dobbertin functions when n ges 12. This means that for n even they are CCZ-Inequivalent to any known APN function. In particular, for n = 12,20,24, they are therefore CCZ-Inequivalent to any power function.
-
A class of quadratic APN binomials Inequivalent to power functions.
IACR Cryptology ePrint Archive, 2006Co-Authors: Lilya Budaghyan, Claude Carlet, Gregor LeanderAbstract:We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EA-Inequivalent to any power function and that they are CCZ-Inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-Inequivalent to any known APN function, and in particular for n = 12, 24, they are therefore CCZ-Inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZInequivalent to the Kasami and Welch functions.
David Mcmullan - One of the best experts on this subject based on the ideXlab platform.
-
Constrained quantisation, gauge fixing and the Gribov ambiguity
Communications in Mathematical Physics, 1994Co-Authors: David McmullanAbstract:The role played by gauge fixing in the description of superselection sectors for a simple quantum mechanical system is analysed. By viewing this as a theory with constraints, it is shown that the possibility of having Inequivalent gauge fixing conditions (Gribov's ambiguity) signals the existence of Inequivalent reductions to a physical quantum theory, and hence superselection sectors. This point of view is contrasted with the more traditional one that identifies superselection sectors with Inequivalent quantisations. It is argued that emphasising the role of gauge fixing (along with the Gribov problem) will allow for a more direct extension of these ideas to quantum field theory and, in particular, gauge theories.
-
BPST instanton and spin from Inequivalent quantizations
Physics Letters B, 1994Co-Authors: David Mcmullan, Izumi TsutsuiAbstract:Abstract We present a simple alternative to Mackey's account of the (infinite) Inequivalent quantizations possible on a coset space G/H. Our reformulation is based on the reduction G→G/H and employs a generalized form of Dirac's approach to the quantization of onstrained systems. When applied to the four-sphere S 4 ≌Spin(5)/Spin(4), the Inequivalent quantizations induce relativistic spin and a background BPST instanton; thus they might provide a natural account of both of these physical entities.
Noah Linden - One of the best experts on this subject based on the ideXlab platform.
-
Inequivalent quantisations of the Neumann model
Physics Letters B, 1992Co-Authors: Noah LindenAbstract:Abstract Using the algebraic approach to quantisation, it is shown that there are many Inequivalent quantum versions of the Neumann model, each of which is integrable.
-
The geometry of Inequivalent quantizations
Nuclear Physics B, 1991Co-Authors: Nicolaas P. Landsman, Noah LindenAbstract:We describe how Inequivalent quantizations (superselection sectors) arise within two related algebraic approaches to quantum mechanics (viz. quantization by canonical groups and by C∗-algebras). By construction of the quantum hamiltonian and the path integral of a particle moving on a coset space, we show that the Inequivalent quantizations manifest themselves as the particle coupling to a certain fictitious external gauge field, in a representation depending on the superselection sector; various well-known topologically non-trivial Yang-Mills field configurations emerge in this way. The general theory is illustrated by taking the coset space to be a circle and a sphere, which puts θ-angles (hence the Aharonov-Bohm effect) and the Dirac charge quantization condition, respectively, in a new light.
Hans Halvorson - One of the best experts on this subject based on the ideXlab platform.
-
Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory
The British Journal for the Philosophy of Science, 2001Co-Authors: Rob Clifton, Hans HalvorsonAbstract:Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of Inequivalent quantizations of a classical field theory, i.e., Inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between Inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field.