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Affine Space

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Mingwu Zhang – One of the best experts on this subject based on the ideXlab platform.

• anonymous spatial encryption under AffineSpace delegation functionality with full security
Information Sciences, 2014
Co-Authors: Mingwu Zhang, Bo Yang, Tsuyoshi Takagi
Abstract:

Abstract Anonymous encryption provides the decrypter’s identity privacy preservation as well as plaintext confidentiality. Spatial encryption, which is a kind of functional encryption, provides a generalized framework for special property encryption schemes such as broadcast encryption, predicate encryption, forward secure encryption, (hierarchical) identity-based encryption, delegatable attribute-based encryption etc. In this paper, we propose an anonymous spatial encryption scheme that deploys an Affine subSpace delegation mechanism. Our proposed scheme captures the message confidentiality , recipient anonymity , adaptive security , partial-order delegation and short ciphertext , simultaneously. To the best of our knowledge, the proposed scheme is the first anonymous spatial encryption that provides the anonymity property in adaptive security model, whose construction is based on a dual system encryption mechanism in bilinear composite-order groups. We also give a conversion construction to move into a prime-order setting with canceling property , whose security is based on the Decision Linear Problem. Finally, we provide a transformation methodology to obtain a CCA-secure scheme that combines a one-time signature, delegation functionality and the CPA-secure scheme.

Tsuyoshi Takagi – One of the best experts on this subject based on the ideXlab platform.

• anonymous spatial encryption under AffineSpace delegation functionality with full security
Information Sciences, 2014
Co-Authors: Mingwu Zhang, Bo Yang, Tsuyoshi Takagi
Abstract:

Abstract Anonymous encryption provides the decrypter’s identity privacy preservation as well as plaintext confidentiality. Spatial encryption, which is a kind of functional encryption, provides a generalized framework for special property encryption schemes such as broadcast encryption, predicate encryption, forward secure encryption, (hierarchical) identity-based encryption, delegatable attribute-based encryption etc. In this paper, we propose an anonymous spatial encryption scheme that deploys an Affine subSpace delegation mechanism. Our proposed scheme captures the message confidentiality , recipient anonymity , adaptive security , partial-order delegation and short ciphertext , simultaneously. To the best of our knowledge, the proposed scheme is the first anonymous spatial encryption that provides the anonymity property in adaptive security model, whose construction is based on a dual system encryption mechanism in bilinear composite-order groups. We also give a conversion construction to move into a prime-order setting with canceling property , whose security is based on the Decision Linear Problem. Finally, we provide a transformation methodology to obtain a CCA-secure scheme that combines a one-time signature, delegation functionality and the CPA-secure scheme.

D. Kazhdan – One of the best experts on this subject based on the ideXlab platform.

• On the Schwartz Space of the basic AffineSpace
Selecta Mathematica, 1999
Co-Authors: Amy Braverman, D. Kazhdan
Abstract:

Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G / U where U is the group of k -points of a maximal unipotent subgroup of G . In this paper we construct a certain canonical G -invariant Space ${\cal S}(X)$ (called the Schwartz Space of X ) of functions on X , which is an extension of the Space of smooth compactly supported functions on X . We show that the Space of all elements of ${\cal S}(X)^I$ , which are invariant under the Iwahori subgroup I of G , coincides with the Space generated by the elements of the so called periodic Lusztig basis, introduced recently by G. Lusztig (cf. [10] and [11]). We also give an interpretation of this Space in terms of a certain equivariant K-group (this was also done by G. Lusztig — cf. [12]). Finally we present a global analogue of ${\cal S}(X)$ , which allows us to give a somewhat non-traditional treatment of the theory of the principal Eisenstein series.

Ragnar Sigurdsson – One of the best experts on this subject based on the ideXlab platform.

• SICIAK-ZAHARIUTA EXTREMAL FUNCTIONS, ANALYTIC DISCS AND POLYNOMIAL HULLS
Mathematische Annalen, 2009
Co-Authors: Finnur Larusson, Ragnar Sigurdsson
Abstract:

We prove two disc formulas for the Siciak–Zahariuta extremal function of an arbitrary open subset of complex Affine Space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex Affine Space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected.

• Siciak-Zahariuta extremal functions and polynomial hulls
arXiv: Complex Variables, 2007
Co-Authors: Finnur Larusson, Ragnar Sigurdsson
Abstract:

We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex Affine Space in terms of analytic discs.

• the siciak zahariuta extremal function as the envelope of disc functionals
arXiv: Complex Variables, 2005
Co-Authors: Finnur Larusson, Ragnar Sigurdsson
Abstract:

We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex Affine Space, generalizing Lempert’s formula for the convex case. This function is also known as the pluricomplex Green function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert’s formula for this function from the convex case to the connected case.

Finnur Larusson – One of the best experts on this subject based on the ideXlab platform.

• Oka properties of groups of holomorphic and algebraic automorphisms of complex AffineSpace
Mathematical Research Letters, 2014
Co-Authors: Franc Forstneric, Finnur Larusson
Abstract:

We show that the group of all holomorphic automorphisms of complex Affine Space C, n > 1, and several of its subgroups satisfy the parametric Oka property with approximation and with interpolation on discrete sets.

• SICIAK-ZAHARIUTA EXTREMAL FUNCTIONS, ANALYTIC DISCS AND POLYNOMIAL HULLS
Mathematische Annalen, 2009
Co-Authors: Finnur Larusson, Ragnar Sigurdsson
Abstract:

We prove two disc formulas for the Siciak–Zahariuta extremal function of an arbitrary open subset of complex Affine Space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex Affine Space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected.

• Siciak-Zahariuta extremal functions and polynomial hulls
arXiv: Complex Variables, 2007
Co-Authors: Finnur Larusson, Ragnar Sigurdsson
Abstract:

We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex Affine Space in terms of analytic discs.