منابع مشابه
Arithmetic of Generalized Jacobians
This paper aims at introducing generalized Jacobians as a new candidate for discrete logarithm (DL) based cryptography. The motivation for this work came from the observation that several practical DL-based cryptosystems, such as ElGamal, the Elliptic and Hyperelliptic Curve Cryptosystems, XTR, LUC as well as CEILIDH can all naturally be reinterpreted in terms of generalized Jacobians. However,...
متن کاملDiscrete Logarithms in Generalized Jacobians
Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of group...
متن کاملSimpson Jacobians of generalized tree-like curves
The compactified Jacobian of any projective curve X is defined as the Simpson moduli space of torsion free rank one degree d sheaves that are semistable with respect to a fixed polarization H on X. In this paper we give explicitly the structure of this compactified Simpson Jacobian in the case where X is a generalized tree-like curve, i.e., a projective, reduced and connected curve such that th...
متن کاملGeneralized Jacobians of spectral curves and completely integrable systems
M P = {A(x) ∈ M : det(A(x)− yIr) = P (x, y)}. The system (1) has an obvious symmetry group G = IPGLr(I C; J) which is the subgroup of the projective group IPGLr(I C) formed by matrices which commute with J . The group G acts on M by conjugation, the action is Poisson, and the reduced Hamiltonian system is completely integrable too. As the symmetry group G acts freely and properly on the general...
متن کاملAn Open Mapping Theorem using unbounded Generalized Jacobians∗
In this paper, three key theorems (the open mapping theorem, the inverse function theorem, and the implicit function theorem) for continuously differentiable maps are shown to hold for nonsmooth continuous maps which are not necessarily Lipschitz continuous. The significance of these extensions is that they are given using generalized Jacobians, called approximate Jacobians. The approximate Jac...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1950
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1950-0034827-8