The International Conference on Coding Theory, Cryptography and Related Topics Sponsored by YZU and NTU，April 9-11，2015

2015年编码理论与密码学及相关课题国际研讨会

（扬州大学与南洋理工大学联合举办）

组委会：林杉教授，南洋理工大学理学院院长

李刚教授，扬州大学数学科学学院院长

邢朝平教授，南洋理工大学数学系

唐元生教授，扬州大学数学科学学院

会务组：黄勇（15952787766），成晓燕（13218996696），陈文兵（15705279286），余丽荣（13816307075）

1．报到时间：4月8日全天

2．报到地点：扬州市汶河北路蓝天大厦玉蜻蜓酒店

3．开幕式：4月9日8:30-9:00，蓝天大厦玉蜻蜓酒店3楼第一会议室

4．报告安排：

时间：4月9日9:05-12:15；14:30-18:15

4月10日8:30-12:15

4月11日8:30-12:15；14:30-18:15

地点：玉蜻蜓酒店3楼第一会议室

l 每个报告35分钟

5．4月10日下午游览瘦西湖景区。

6．就餐安排：

a) 早餐：7:00-8:15，蓝天大厦玉玲珑酒店二楼永遇乐厅（酒店自助早餐）

b) 午餐：12:20-13:00，玉玲珑酒店二楼永遇乐厅

c) 晚餐：18:20

l 4月8、9日，玉玲珑酒店二楼永遇乐厅

l 4月10日，玉玲珑景湖餐厅二楼V8，餐后集体乘车回玉蜻蜓酒店

l 4月11日，京华大酒店，餐后步行回玉蜻蜓酒店

7．4月12日离会。

l 如果下午离会，可安排上午参观扬州双博馆或游览东关街。

2015年4月9日

开幕式：8:30-9:00；主持人：李刚

Session A主持人:林杉

Session C主持人:胡磊

2015年4月10日

Session E主持人:邢朝平

2015年4月11日

Session G主持人:王华雄

Session I主持人:曹喜望

报告摘要

1.冯克勤，清华大学数学系

题目：广义bent函数的不存在性

摘要：本报告讨论由n个Z2的直和到Zm的映射。首先通过介绍前人的结果加上简单的考查得到对哪些情形{m,n}存在bent函数。对于其余情形目前没有构作出bent函数。报告的主要部分是给出一些不存在性的结果。工具是经典代数数论（分园域中的素理想分解律和分解域，虚二次域的整基，素理想分解律和理想类群的结构）。

2.葛根年，首都师范大学数学系

Title: Permutation codes, secure codes and hash families related to ex-tremal and probabilistic combinatorics

Abstract: A code can be regarded as a subset of its underlying base set satisfying some restrictions. In this talk, we will discuss the bounds and constructions for several classes of combinatorial codes, which are closely related to extremal and probabilistic combinatorics. These codes include: permutation codes, separable codes, frameproof codes and some related hash

families for security protection. For the lower bounds, by regarding a code as an independent set of a graph or a hyper-graph, we are able to improve the known lower bounds for permutation codes, 3-perfect hash families, 2-frameproof codes and _2-separable codes. In addition, we extend the constructions for separable codes and frameproof codes by applying the probabilistic method. Particularly, we obtain asymptotically optimal _2-separable codes by the deletion method. For the upper bounds, by considering some typical con_gurations of codes and applying combinatorial counting skills, we are able to improve the known upper bounds for separable codes and frameproof codes. Furthermore, using a result of Erdos and Gallai on hypergraph matching, we approve partially a well-known conjecture on an old problem of the disjunctive code theory.

3.林东岱，中科院信息安全重点实验室

题目：有限几何与多项式同构问题

4.万大庆，University of California, Irvine

Title: Decoding Complexity in Coding Theory

Abstract: We explain how Reed-Solomon codes can be used to obtain complexity results in maximum likelihood decoding of linear codes over finite fields. In particular, we show that decoding primitive Reed-Solomon codes is at least as hard as certain difficult subset sum problem. This is a joint work with Qi Cheng.

5.胡磊，中科院信息安全重点实验室

题目：Differential Analysis of Block Cipher PRIDE

摘要： PRIDE is a 20-round iterative lightweight block cipher proposed in the CRYPTO 2014 conference which is based on a good linear layer for achieving a tradeoff between security and efficiency. In this talk we will review the recent results on this ciper and report our differential analysis on it. Our analysis is based on an automatic search for iterative differential characteristics of PRIDE and is a differential attack on the 19-round PRIDE with data, time and memory complexity of $2^{62}$, $2^{63}$ and $2^{71}$ respectively. This is a joint work with Q. Yang et al.

6.洪绍方，四川大学数学学院

题目：Necessary conditions for reversed Dickson polynomials of the second kind to be permutational。

摘要：In this talk, we present several necessary conditions for the reversed Dickson polynomial $E_{n}(1, x)$ of the second kind to be a permutation of $\mathbb{F}_{q}$. In particular, we give explicit evaluation of the sum $\sum_{a\in \mathbb{F}_{q}}E_{n}(1,a)$. This is a joint work with Dr. Qin and Zhao.

7.邓映蒲，中国科学院数学与系统科学研究院

题目：广义Fermat素数的判定

摘要：素数判定问题在2004年被三个印度学者Agrawal- Kayal- Saxena证明是P问题，但他们给出的AKS算法由于复杂性太高仅具理论意义而没有实际价值。另一方面，对于特殊数存在更快速的素数判定方法，这方面经典的例子有对于Mersenne素数的Lucas-Lehmer判别法和对于Fermat素数的Pepin判别法。我和我的学生们近几年在素数判定方面有一些工作，本报告汇报我们在广义Fermat素数判定方面的工作，其中使用了代数数论中的高次互反律。

8．吴国华，南洋理工大学数学系

Title: Nonexistence of Minimal Pairs in L[d]

Abstract: For a d.c.e. set $D$ with a d.c.e. approximation $\{D_s\}_{s\in\omega}$, the Lachlan set of $D$ is defined as $L(D)= \{ s: \exists x \in D_{s} - D_{s-1} \ \hbox{and} \ x \not\in D\}$. For a d.c.e. degree ${\mathbf d}$, $L[{\bf d}]$ is defined as the class of c.e. degrees of thoseLachlansets of d.c.e. sets in ${\bf d}$. We prove that for any proper d.c.e. degree ${\bf d}$, no two elements in $L[{\bf d}]$ can form a minimal pair. This result gives another solution to Ishmukhametov's problem, which asks whether for any proper d.c.e. degree ${\bf d}$, $L[{\bf d}]$ always has a minimal element. A negative answer to this question was first given by Fang, Wu and Yamaleev in 2013.

It is a joint work with Fang, Liu and Yamaleev.

9.向青，Department of Mathematics, University of Delaware, USA

Title: Cameron-Liebler Line Classes, Projective Two-Weight Codes, and Two-Intersection Sets

Abstract: Cameron-Liebler line classes are sets of lines in PG(3,q) having many interesting combinatorial properties. These line classes were first introduced by Cameron and Liebler [2] in their study of collineation groups of PG(3,q) having the same number of orbits on points and lines of PG(3,q). In the last few years, Cameron-Liebler line classes have received considerable attention from researchers in both finite geometry and algebraic combinatorics; see, for example, [3,10,11,14,6,7]. In [2], the authors gave several equivalent conditions for a set of lines of PG(3,q) to be a Cameron-Liebler line class; Penttila [12] gave a few more of such characterizations. We will use one of these characterizations as the definition of Cameron-Liebler line class. Let L be a set of lines of PG(3,q) with L=x(q^2+q+1), x a nonnegative integer. We say that L is a Cameron-Liebler line class with parameter x if every spread of PG(3,q) contains x lines of L. It turned out that Cameron-Liebler line classes are closely related to certain projective two-weight codes (equivalently, certain two-intersection sets in PG(5,q)). We will talk about a recent construction of a new infinite family of Cameron-Liebler line classes with parameter x=(q^2-1)/2 for q\equiv 5 or 9(mod 12). This family of Cameron-Liebler line classes generalizes the examples found by Rodgers in [14] through a computer search, and represents the second infinite family of Cameron-Liebler line classes. Furthermore, in the case where q is an even power of 3, we construct the first infinite family of affine two-intersection sets. We should remark that De Beule, Demeyer, Metsch and Rodgersm [4] also independently obtained the same result as ours on Cameron-Liebler line classes with parameter x=(q^2-1)/2 at almost the same time.

10.唐春明，广州大学数学与信息科学学院

题目：Privacy-Preserving Face Recognition with Outsourced Computation

摘要：Face recognition is one of the most important biometrics pattern recognitions, which has been widely applied in a variety of enterprise, civilian and law enforcement. The privacy of biometrics data raises important concerns, in particular if computations over biometric data is performed at untrusted servers. In previous work of privacy-preserving face recognition, in order to protect individuals’ privacy, face recognition is performed over encrypted face images. However, these results increase the computation cost of the client and the face database owners, which may enable face recognition cannot be efficiently executed. Consequently, it would be desirable to reduce computation over sensitive biometric data in such environments. Currently, no secure techniques for outsourcing face biometric recognition is readily available. In this paper, we propose a privacy-preserving face recognition protocol with outsourced computation for the first time, which efficiently protects individuals’ privacy. Our protocol substantially improves the previous works in terms of the online computation cost by outsourcing large computation task to a cloud server who has large computing power. In particular, the overall online computation cost of the client and the database owner in our protocol is at most 1/2 of the corresponding protocol in the state of the art algorithms. In addition, the client requires the decryption operations with only O(1) independent of M, where M is the size of the face database. Furthermore, the clientcan verify the correction of the recognition result.

11.罗元勋(Yuan-Hsun Lo),Department of Mathematics, National Taiwan Normal University

Title：Optimal (equi-difference) conflict-avoiding codes and weighted maximum matchings

Abstract：A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of Z_n such that Δ(x) ∩ Δ(y) =∅for any x, y∈C and x ≠ y, where Δ(x) = {a − b∶a, b∈x, a ≠ b}. Let CAC(n, k) denote the class of all CACs of length n and weight k. A CAC C∈CAC(n, k) is said to be equi-difference if any codeword x∈C has the form {0, i, 2i, … , (k−1)i}. A CAC with maximum size is called optimal. In this talk we propose a graphical characterization of an equi-difference CAC, and then provide an infinite number of optimal CACs and optimal equi-difference CACs for weight three and four.

12.樊恽，华中师范大学数学与统计学学院

Title: Quasi-cyclic codes of index 1.5

Abstract: We introduce a notion of quasi-cyclic codes of index 1.5 over a finite field, and prove that the quasi-cyclic codes of index 1.5 are asymptotically good.

13.符方伟，南开大学陈省身数学研究所

Title：The minimal polynomial of sequence obtained from componentwise linear transformation of linear recurring sequence

Abstract: Let S be a linear recurring sequence with terms in GF(q^n) and T be a linear transformation of GF(q^n) over GF(q). Denote T(S) the sequence obtained by componentwise linear transformation of S. In this paper, we determine the minimal polynomial of T(S) if the canonical factorization of the minimal polynomial of S without multiple roots is known. Particurly, we determine the minimal polynomial of T(S) if the minimal polynomial of S is primitive. Finally, we give an upper bound on the linear complexity of T(S) when T exhausts all possible linear transformations of GF(q^n) over GF(q). This bound is tight in some cases.

14.熊茂胜，香港科技大学数学系

Title: Optimal cyclic codes with generalized Niho type zeroes and the weight distribution.

Abstract: Extending previous works in two directions, we define two families of cyclic codes whose duals may have arbitrary number of Niho type zeroes over any finite field and compute the weight distribution. Numerical data shows that many of the cyclic codes in the family are optimal. This is joint work with Nian Li, Zheng-Chun Zhou and Cun-Sheng Ding.

15.骆源，上海交通大学计算机系

题目：Relative Generalized Hamming Weight on Distributed Storage

摘要：The dimension/length profile (DLP) and the generalized Hamming weight (GHW) hierarchy of a linear code play an important role in coding theory, especially in trellis complexity, secure communication, multiple access communication and puncturing codes. Here we study properties (maybe asymptotical) of RGHW, its equivalent concepts, its coding constructions, and then apply them to the (full or partial) recovery ability of linear coding data storage system combining with data security. For achieving the multiple requirements, we focus on not only the coding rate, the data security, but also on list decoding and their realization.

16.刘宏伟，华中师范大学数学与统计学学院

题目：Some Results on One Weight $Z_2Z_4$ Additive Codes

摘要：Additive codes were first introduced by Delsarte in 1973. Recently, Borges and other researchers studied $Z_2Z_4$ additive codes. In this talk, we will give some recent results on one-weight $Z_2Z_4$ additive codes and their dual codes. The binary images of one-weight $Z_2Z_4$ additive codes under the Gray map are also discussed.

17.曹永林，山东理工大学数学系

Title：Concatenated structure of cyclic codes over Z4 of length 4n

Abstract：Let N = 2kn where n is odd and k a positive integer. We present a canonical form decomposition for every cyclic code over Z4 of length N, where each subcode is concatenated by a basic irreducible cyclic code over Z4 of length n as the inner code and a constacyclic code over a Galois extension ring of Z4 for length 2k as the outer code. For the case of k = 2, by determining the outer code, we give a precise description for each cyclic code over Z4, present precisely dual codes and investigate self-duality for cyclic codes over Z4 of length 4n. We end by listing all 339 distinct self-dual cyclic codes over Z4 of length 28 and all 9315 distinct self-dual cyclic codes over Z4 of length 60, respectively.

18.曹珍富，上海交通大学计算机系

Batch Cryptography

19．岳勤，南京航空航天大学数学系

Title: Weight distributions of cyclic codes of length $tl^m$

Abstract: In this talk, we mainly introduce our recent work on the weight distributions of cyclic codes of length $tl^m$ over $\Bbb F_q$. Assume that $l$ is a prime, $l^v\|(q-1)$, and $m=s+v$. $t$ is considered in three cases:\\ (1) $t=1$, \\ (3) $t|(q-1)$, \\ (2) $t= 4, 8$ and $q\equiv 3\pmod 8$.

20.吴佃华，广西师范大学数学系

Title：Optimal Variable-Weight OOCs with Unequal Correlation Constraints

Abstract：In 1996, Yang introduced variable-weight optical orthogonal code for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Let $W=\{w_1,\ldots, w_r\}$ be an ordering of a set of $r$ integers greater than $1$, $\lambda$ be a positive integer ({\it auto- and cross-correlation parameter}), and $Q=(q_1,\ldots, q_r)$ be an $r$-tuple ({\it weight distribution sequence}) of positive rational numbers whose sum is $1$. A $(v,W,\lambda,Q)$ variable-weight optical orthogonal code ($(v,W,\Lambda_a,\lambda_c,Q)$-OOC) is a collection of $(0, 1)$ sequences with weights in $W$, auto- and cross-correlation parameter $\lambda$. Some works had been done on the construction of optimal $(v,W,1,Q)$-OOCs, while little is known on the construction of $(v,W,\Lambda_a,\lambda_c,Q)$-OOCs with unequal correlation constraints. In this talk, new upper bounds on the number of codewords of $(v,\{3,4\},\Lambda_a,1,Q)$-OOCs are given, where $\Lambda_a\in \{(1,2), (2,1), (2,2)\}$, and infinite classes of optimal $(v, \{3,4\}, 2,Q)$-OOCs are constructed.

21．王明生，中科院信息安全重点实验室

题目：密码非线性函数的构造；

摘要：主要报告密码算法设计中的非线性函数的研究，包括它应该满足的准则。一些新的构造方法，和工程实践中通常关心的问题。

22．曹喜望，南京航空航天大学数学系

题目：Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method

摘要：The so-called switching method is a very powerful method to construct new APN functions and differentially 4-uniform permutations over finite fields of even characteristic. In this talk, we will introduce how to use this method to construct infinite classes of non-power APN functions and bent functions in finite fields of odd characteristic.

23.张志芳，中科院数学与系统科学研究院

Title：Optimal Locally Repairable Code

Abstract：Recently, locally repairable codes (LRC) have attracted much attention from people working on coding for distributed storage systems. An (n,k) code is called locally repairable if each of its coordinates can be recovered by accessing at most r other coordinates. When r<

24.曾光，数学工程与先进计算国家重点实验室

题目：SHA-1最优扰动向量分类

摘要：该研究内容是Hash函数SHA-1攻击的中的扰动向量构造环节的研究，我们的研究改进了Manuel提出的EEM扰动向量搜索算法，

给出了最优扰动向量分类定理，完成了2512空间中对最优扰动向量的搜索和证明，对SHA-1的随机碰撞研究具有理论指导意义。

25．夏永波，中南民族大学数学与统计学学院

Title: Some results on cross-correlation between decimated sequences and their applications

Abstract: Some recent results on cross-correlation between m-sequences and their decimated sequences will be introduced. Their applications in sequence construction will be also given.

26.李成举，Department of Mathematics，Korea Advanced Institute of Science and Technology

题目：On the complete weight enumerators of some reducible cyclic codes

摘要：In this talk, we use Gauss sums to investigate the complete weight enumerators of two classes of reducible cyclic codes. Moreover, we present their explicitly complete weight enumerators of some cyclic codes.

27.潘彦斌，中国科学院数学与系统科学研究院

题目：Solving Random Subset Sum Problem by l_p-norm SVP Oracle

摘要：It is well known that almost all random subset sum instances with density less than 0.9408... can be solved with an l_2-norm SVP oracle. In this talk, we generalize this classical result to l_p-norm. Interestingly, it seems that an l_p-norm SVP oracle with bigger p can solve more subset sum instances. Moreover, an l_p-norm SVP oracle with p>2 can help solve almost all random subset sum instances with density one, which are thought to be the most difficult instances.

28.马立明，扬州大学数学科学学院

Title:On automorphism groups of global function fields

Abstract: In this talk, we will introduce the application of automorphism groups in the constructions of global function fields with many rational places. In particular, we study the decomposition groups of the infinity places which are maximal subgroups of the automorphism groups of the Deligne--Lusztig function fields. By considering the fixed subfields corresponding to the subgroups of the decomposition groups, we can obtain new function fields with many rational places and even maximal function fields. Also, we will introduce how to determine the automorphism groups of the cyclotomic function fields over finite fields.

29.王华雄，南洋理工大学数学系

Title: Secure Multiparty Computation – Past and Present

Abstract: We give a survey of the state-of-the-art in secure multiparty computation.