会议日程

2018年12月29日上午

开幕式：8：30—8：40；主持人：李立斌

Section A 主持人：唐元生

Section B 主持人：邢朝平

12月29日下午

Section C 主持人：岳勤

Section D 主持人：廖群英

12月30日上午

Section E 主持人：曹永林

Section F 主持人：王丽萍

12月30日下午

自由讨论

报告摘要

1. 邢朝平，南洋理工大学

题目：Secure multi-party computations—A brief introduction

摘要：Secure multi-party computation (also known as secure computation, multi-party computation/MPC, or privacy-preserving computation) is a subfield of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private. Unlike traditional cryptographic tasks, where the adversary is outside the system of participants (an eavesdropper on the sender and receiver), the adversary in this model controls actual participants. These types of tasks started in the late 1970s with the work on mental poker, cryptographic work that simulates game playing over distances without requiring a trusted third party. In this talk, I will first introduce the problem and then discuss several common methods to realize secure multi-party computation.

2.王丽萍，中国科学院

题目：A new code-based IND-CCA secure public key scheme

摘要：We first propose a new code family—lattice codes. Based on the lattice codes, we construct a new IND-CCA secure public key scheme. We also make a comparison between our scheme and some other NISTschemes.

3.曹永林，山东理工大学

题目：On self-dual $(1+alpha u^2)$-constacyclic codes of length $2^k$ over the finite chain ring $mathbb{F}_{2^m}[u]/langle u^4 angle$

摘要：Let $mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $delta$ and $alpha$ be nonzero elements in $mathbb{F}_{2^m}$ and denote $R=mathbb{F}_{2^m}[u]/langle u^4 angle$. Then $delta+alpha u^2$ is an invertible element of the finite chain ring $R$. For any integer $kgeq 2$, we give an explicit representation and enumeration for all distinct $(delta+alpha u^2)$-constacyclic codes over $R$ of length $2^k$, and determine their dual codes precisely. On that basis, we provide a complete description for all self-dual $(1+alpha u^2)$-constacyclic codes over $R$ of length $2^k$ and obtain a clear formula to count this kind of self-dual codes.

4.金玲飞，复旦大学

题目：Explicit construction of optimal locally recoverable codes of distance 5 and 6

摘要：It was shown that the length $n$ of a $q$-ary linear locally recoverable code with distance $dge 5$ is upper bounded by $O(dq^3)$. Thus, it is a challenging problem to construct $q$-ary locally recoverable codes with distance $dge 5$ and length approaching the upper bound. We present an explicit construction of $q$-ary locally recoverable codes of distance $d= 5$ and $6$ via binary constant weight codes.

5.李成举

题目：A class of exponential sums and sequence families

摘要：Let $m_1$ and $m_2$ be two distinct positive integers with $d=gcd(m_1, m_2)$. Let $Bbb F_{2^m}$ be the finite field with $2^m$ elements, where $m=m_1m_2/d$. In this talk, we investigate the exponential sums$$S(a,b)=sum_{x in Bbb F_{2^m}^*}(-1)^{ ext{Tr}_{m_1}(ax^{rac {2^m-1}{2^{m_1}-1}})+ ext{Tr}_{m_2}(bx^{rac {2^m-1}{2^{m_2}-1}})},$$ where $a in Bbb F_{2^{m_1}}$, $b in Bbb F_{2^{m_2}}$, and $ ext{Tr}_{t}$ denotes the trace function from $Bbb F_{2^t}$ to $Bbb F_2$. When $d=1, 2,3, 4$, we present the value distribution of the exponential sums $S(a,b)$ explicitly. As an application, we construct three families of binary sequences with three-valued correlation.

6.刘姝

题目：List Decodability of Random Subcodes of Gabidulin Codes

摘要：Efficient list decoding of rank-metric codes seems more difficult compared with classical block codes although list decodability of random rank-metric codes is completely determined by Ding. For example, it was shown by Raviv and Wachter-Zeh that the list decoding radius of Gabidulin codes is the same as the unique decoding radius, i.e., half the minimum distance for some instances of parameters. On the other hand, Guruswami and Xing give an explicit construction of subcodes of Gabidulin codes, which can be list decoded up to the Singleton bound. This implies that subcodes of Gabidulin codes are good candidates for list decoding. In this paper, we confirm that, with overwhelming probability, a random subcode of a Gabidulin code can be list decoded with decoding radius far beyond half of the minimum distance.

7.徐小凡

题目：Explicit deep holes of generalized projective Reed-Solomon codes

摘要：Let ${f F}_q$ be a finite field of $q$ elements with the odd prime number $p$ as its characteristic. Let $D={alpha_1,cdots,alpha_n}subset{f F}_q$ and $k$ be an integer such that $2le k

Furthermore, we also show that if $rac{q-1}{2}leq k

8.方晓磊

题目：New MDS Self-dual Codes over Finite Fields of Odd Characteristic

摘要：In this talk, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many new parameters of MDS self-dual code which have never been reported. For large square $q$, we can produce more than approximately 50% times of new MDS self-dual codes with different lengths than the previous results.

9.陆玫

题目：A class of exponential sums and sequence families

摘要：A perfect r-code in a graph G is a subset of the vertex set of G with the property that each vertex in G is within distance r of exactly one vertex in the subset. In this talk, we will present some results about perfect r-code in product graph of simple graphs G.

10.施敏加

题目：Additive perfect codes in Doob graphs

摘要：The Doob graph $D(m,n)$ is the Cartesian product of $m>0$ copies of the Shrikhande graph and $n$ copies of the complete graph of order $4$. Naturally, $D(m,n)$ can be represented as a Cayley graph on the additive group $(Z_4^2)^m imes (Z_2^2)^{n'} imes Z_4^{n''}$, where $n'+n''=n$. A set of vertices of $D(m,n)$ is called an additive code if it forms a subgroup of this group. We construct a $3$-parameter class of additive perfect codes in Doob graphs and show that the known necessary conditions of the existence of additive $1$-perfect codes in $D(m,n'+n'')$ are sufficient. Additionally, two quasi-cyclic additive $1$-perfect codes are constructed in $D(155,0+31)$ and $D(2667,0+127)$.

11.林富春

题目：Secret Sharing with Binary Shares

摘要：Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $ell$ among any $N leq 2^ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not reveal any information about the secret and, (ii) any choice of $t+1$ shares fully reveals the secret. It is known that any such threshold secret sharing scheme necessarily requires shares of length $ell$, and in this sense Shamir's scheme is optimal. The more general notion of ramp schemes requires the reconstruction of secret from any $t+g$ shares, for a positive integer gap parameter $g$. Ramp secret sharing scheme necessarily requires shares of length $ell/g$. Other than the bound related to secret length $ell$, the share lengths of ramp schemes can not go below a quantity that depends only on the gap ratio $g/N$.

In this work, we study secret sharing in the extremal case of bit-long shares and arbitrarily small gap ratio $g/N$, where standard ramp secret sharing becomes impossible. We show, however, that a slightly relaxed but equally effective notion of semantic security for the secret, and negligible reconstruction error probability, eliminate the impossibility. Moreover, we provide explicit constructions of such schemes. One of the consequences of our relaxation is that, unlike standard ramp schemes with perfect secrecy, adaptive and non-adaptive adversaries need different analysis and construction. For non-adaptive adversaries, we explicitly construct secret sharing schemes that provide secrecy against any $ au$ fraction of observed shares, and reconstruction from any $ ho$ fraction of shares, for any choices of $0 leq au < ho leq 1$. our construction achieves secret length $n( ho- au-o(1))$, which we show to be optimal. for adaptive adversaries, we construct explicit schemes attaining a secret length $omega(n( ho- au))$. we discuss our results and open questions.

12.易宗向

题目：函数的零差分性质及其应用

摘要：零差分平衡函数是对完全非线性函数的推广,在编码、组合设计和序列中都有广泛的应用。本次报告首先介绍两种在环上构造零差分平衡函数的方法，然后给出零差分平衡函数构造常重复合码，集合差系统以及跳频序列的框架。在此之上，我们尝试推广零差分平衡函数，考虑利用函数的零差分性质在上述应用中面临的问题，最后给出一些具有“好”的零差分性质的函数。