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Kyungyong Lee

Publications and source records attributed to Kyungyong Lee.

63 records · Page 4Linked to original sources
arXiv2010

On the Design and Implementation of Structured P2P VPNs

Centralized Virtual Private Networks (VPNs) when used in distributed systems have performance constraints as all traffic must traverse through a central server. In recent years, there has been a paradigm shift towards the use of P2P in VPNs to alleviate pressure placed upon the central server by allowing participants to communicate directly with each other, relegating the server to handling session management and supporting NAT traversal using relays when necessary. Another, less common, approach uses unstructured P2P systems to remove all centralization from the VPN. These approaches currently lack the depth in security options provided by other VPN solutions, and their scalability constraints have not been well studied. In this paper, we propose and implement a novel VPN architecture, which uses a structured P2P system for peer discovery, session management, NAT traversal, and autonomic relay selection and a central server as a partially-automated public key infrastructure (PKI) via a user-friendly web interface. Our model also provides the first design and implementation of a P2P VPN with full tunneling support, whereby all non-P2P based Internet traffic routes through a trusted third party and does so in a way that is more secure than existing full tunnel techniques. To verify our model, we evaluate our reference implementation by comparing it quantitatively to other VPN technologies focusing on latency, bandwidth, and memory usage. We also discuss some of our experiences with developing, maintaining, and deploying a P2P VPN.

cs.NI↗
arXiv2009

$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$

Let $I$ be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of the graded vector space $M(=\bigoplus_{d_1,d_2}M_{d_1,d_2})$ spanned by a minimal set of generators for $I$. In this paper we give simple upper bounds on $\text{dim}M_{d_1, d_2}$ in terms of partition numbers, and find all bi-degrees $(d_1,d_2)$ such that $\dim M_{d_1, d_2}$ achieve the upper bounds. For such bi-degrees, we also find explicit bases for $M_{d_1, d_2}$. The main idea is to define and study a nontrivial linear map from $M$ to a polynomial ring $\C[ρ_1, ρ_2,...]$.

math.CO↗
arXiv2008

Syzygies of multiplier ideals on singular varieties

It was recently established by the first two authors that multiplier ideals on a smooth variety satisfy some special syzygetic properties. The purpose of this note is to show how some of these can be extended to the singular setting.

math.AG↗
arXiv2007

On the symmetric subscheme of Hilbert scheme of points

We consider the Hilbert scheme Hilb^{d+1}(C^d) of (d+1) points in affine d-space C^d (d > 2), which includes the square of any maximal ideal. We describe equations for the most symmetric affine open subscheme of Hilb^{d+1}(C^d), in terms of Schur modules. In addition we prove that Hilb^{d+1}(C^d) is reducible for n>d>11.

math.AG↗
arXiv2007

Characteristic 2 approach to bivariate interpolation problems

We investigate bivariate interpolation problems in characteristic 2. Given a nonnegative integer $t$, we describe all the sub-linear systems generated by monomials, in which there is no curve passing through a general point with multiplicity at least $2^t$. As an application, we show that a certain linear system of plane curves with 10 base points is non-special.

math.AG↗
arXiv2006

Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.

math.AG↗