Abstracts

김진영

Title : A family of stationary subdivision schemes with the fourth-order accuracy, C2 smoothness and shape preserving properties

Time : 10:20 ~ 10:45

The 4-point interpolatory scheme and the cubic B-spline are examples of the most wellknown stationary subdivision procedures. They are based on the space of cubic polynomials and have their respective strengths and weaknesses. In this regard, the aim of this study is to present a new type of subdivision scheme that integrates the advantages of both the 4-point and the cubic B-spline schemes. The proposed scheme achieves approximation order ‘four’ and an improved smoothness C2, while keeping the same support of the basic limit function as the 4-point scheme. Moreover, the new scheme has the monotonicity and convexity preserving properties under some mild conditions. Whereas most of high-order shape preserving schemes are non-linear and rather computationally complicated, but the proposed scheme is linear and stationary. Several numerical examples are provided to illustrate the efficiency of our subdivision algorithm.

정지혜

Title : CONSTRUCTION OF CRYPTOGRAPHIC FUNCTIONS WITH GOOD PROPERTIES

Time : 10:45 ~ 11:10

Boolean functions having high nonlinearities, balancedness, and high algebraic degrees are used for preventing cryptographic attacks in cryptographic systems. In particular, a plateaued function is a special class of Boolean functions with nonlinearity. It is thus important to study constructions of plateaued functions with balancedness and high algebraic degrees. In this talk, we present construction methods for producing infinite families of balanced s-plateaued functions with maximal algebraic degrees for every positive integer s. We first show a general framework for secondary constructions of plateaued functions; as input, we use initial vectors and Boolean functions which give s-plateaued functions, and then as output, we produce an (s + 1)-plateaued function. We then derive two explicit construction methods from this general framework by controlling initial vectors. These two constructions produce a pair of (s + 1)-plateaued functions from a given bent function and a pair of s-plateaued functions in a recursive way; therefore, we obtain r-plateaued functions for every r > s. Finally, we find two concrete methods for constructing balanced plateaued functions with maximal algebraic degrees from these two explicit constructions.

김보연

Title : Modeling the impact of the COVID-19 related disruption on tuberculosis in the Republic of Korea

Time : 11:10 ~ 11:35

The incidence and death of tuberculosis in Korea are steadily decreasing due to various tuberculosis management projects, but the burden is still high  as it ranks first among OECD countries. The pandemic has been underway since COVID-19 first occurred in Korea in January 2020, and measures to control it are directly or indirectly affecting tuberculosis management.If the medical system is overloaded due to the COVID-19 response, diagnosis and treatment of tuberculosis patients may be delayed. On the other hand, social distancing and wearing masks can reduce tuberculosis transmission by reducing physical contact. The purpose of this study is to predict the impact of the COVID-19 response strategy implemented for one year in 2020 on tuberculosis incidence and death in Korea by 2025 through mathematical modeling of tuberculosis. As a result, the number of tuberculosis patients decreased as the social distancing stage increased. However, regardless of social distance, the number of tuberculosis deaths increased as the burden of medical services increased.In particular, most of the increased deaths were elderly people aged 65 or older. Therefore, it suggested the importance of monitoring tuberculosis death for the impact of COVID-19 in domestic epidemiological situations where the burden of tuberculosis among the elderly is high.

이유진

Title : Adaptively Leakage-Resilient Secret Sharing Scheme with Seedless Non-malleable Extractor

Time : 11:35 ~ 12:00

At Crypto 2021, Nishanth Chandran, Bhavana Kanukurthi, Sruthi Sekar Sai and Lakshmi Bhavana Obbattu introduced the concept called Adaptive Extractors in their paper[8] ‘Adaptive Extractors and their Application to Leakage Resilient Secret Sharing’. These extractors output the string that still looks uniform even in the case where the adversary gets some information on not only seeds but also sources. Also, they constructed Leakage-Resilient Secret Sharing (LRSS) for Leakage and Reveal Model for Adaptive Manner by using them. In that scheme, 2hn number of components (of shares of seeds and sources) are used to mask one message.

In this paper, we adopted another extractor, the Seedless Non-malleable Extractor which was introduced in [11], to the scheme of [8]. By doing so, we reduced the number of components used in the whole scheme from 2hn to hn which is the half. By using the Seedless Non-malleable Extractor, we could remove the entire parts of seeds in the scheme and let sources to cover the role of seeds. Also by using the non-malleable property of the extractor, there was no security loss generated. Therefore just by changing the extractor, we could build the LRSS scheme with half number of shares (of only sources) used.

김재현

Title : Some numbers on certain pencils of rational curves in del Pezzo surfaces

Time : 14:00 ~ 15:00

An open subset in a normal projective variety X is called a cylinder if it is isomorphic to A^1 × Z for some affine variety Z. With an effective condition on the boundary of the cylinder, this A^1-ruledness ensures that a nontrivial unipotent group action on the affine cone of the corresponding ample polarization (X, H). In particular, for del Pezzo surfaces, there are good properties to determine its ample polar cylindricity. Here we will remark on some results for del Pezzo surfaces known so far containing recent own research in progress. We consider smooth case only and work over an algebraically closed field of characteristic zero.

김영빈

Title : Beamer를 이용하여 시각적인 발표 자료 만드는 법

Time : 15:00 ~ 15:30

LaTex의 패키지인 beamer와 tikz에대한 기본적인 사용법과, 이를 이용한 간단한 다이어그램 및 그래프를 첨부하는 방법을 소개.

김동하

Title : Critical Thresholds in Pressureless Euler-Poisson Equations : A New Method based on Lyapunov Functions

Time : 16:30 ~ 16:55

We investigate the critical thresholds phenomena in a large class of pressureless Euler-Poisson equations in one dimension. We propose a new method based on Lyapunov functions to construct the supercritical region with finite-time breakdown and the supercritical region with global regularity of C1 solutions.

By employing our new method, we first provide the analysis of critical thresholds in the pressureless Euler-Poisson system with attractive forces and variable background.

We next identify for the first time critical threshold curves for the pressureless damped Euler-Poisson equations with repulsive forces and variable background.

For both cases of attractive and repulsive interactions, we obtain the long time behavior of solutions with the initial data in the subcritical region. The lower and upper bounds on the blow-up time are also analyzed.

김현빈

Title : Introduction to Symplectic Geometry, Floer Theory, and Mirror Symmetry

Time : 16:55 ~ 17:20

In this short lecture, we briefly take a look at symplectic geometry, Floer theory, and mirror symmetry.  In particular, we review several different types of homology (such as singular, Morse, and Floer)  and how they relate to one another. We further  explore how these invariants play a role in modern geometry, with an eye towards mirror symmetry. If time permits, we get a glimpse of some ongoing researches in mirror symmetry. 

전소현

Title : On Subgaussian Gadget Decompositon in Homomorphic Encryption

Time : 17:20 ~ 17:45

Gadget decomposition is widely used in lattice based cryptography, especially homomorphic encryption (HE) to keep the noise growth slow. If it is randomized, it is called subgaussian (gadget) decomposition which guarantees that we can bound the noise contained in ciphertexts by its variance. This gives tighter and cleaner noise bound in average case, instead of the use of its norm. Even though there are few attempts to build efficient such algorithms, most of them are still not practical enough to be applied to homomorphic encryption schemes due to somewhat high overhead. Furthermore, there has been no detailed analysis of existing works. Therefore, HE schemes use the deterministic decomposition algorithm and rely on a Heuristic assumption that every output element follows a subgaussian distribution independently. In this work, we introduce a new practical subgaussian gadget decomposition algorithm which has the least overhead (less than 14%) among existing works for certain parameter sets. When the modulus is large (over 100-bit), our algorithm is not always faster than the other similar work. Therefore, we give a detailed comparison, even for large modulus, with all the competitive algorithms for applications to choose the best algorithm for their choice of parameters.