四川 成都 kaiyun開云官方網站2024年12月22日-2024年12月24日

本次會議主題包括(但不限于)：為了促進學術交流，加強學術合作，由kaiyun開云官方網站信息科學與技術學院、kaiyun開云官方網站主辦的“編碼與密碼學前沿研討會：后量子密碼及其相關問題”，將于2024年12月22日（周日）至12月24日（周二）在kaiyun開云官方網站召開。本次研討會將邀請編碼、密碼、組合數(shù)學與數(shù)論等領域的專家參加，共同研討相關方向的最新研究進展和發(fā)展趨勢，為相關學者提供一個學術平臺，交流最新發(fā)展動態(tài)及學術成果，促進信息學科、數(shù)學學科理論等相關領域的交叉、融合與發(fā)展，為該領域的老師、學生提供一個相互學習和交流的場所。

聯(lián)系人：

唐春明 ([email protected]; 18582182739)

羅榮 ([email protected]; 13882112127)

報告摘要

題目：超奇異橢圓曲線同源密碼

報告人：徐茂智教授

摘要：橢圓曲線是構造密碼算法的重要源泉，橢圓曲線密碼包括基于點的標量乘的密碼、基于雙線性配對的密碼和基于超奇異橢圓曲線同源的密碼。前兩者已經得到廣泛應用，而超奇異橢圓曲線同源密碼因為其抗量子攻擊的性質，成為密碼學界和應用數(shù)學界的一個研究熱點。 本報告介紹橢圓曲線概念、加法，并給出超奇異橢圓曲線及同源的概念，進而介紹使用超奇異橢圓曲線同源構造的密碼基礎和進展情況。涉及代數(shù)、數(shù)論、代數(shù)曲線知識和密碼學的概念。

報告題目：素數(shù)判定問題綜述

報告人：鄧映蒲教授

摘要：判定一個大整數(shù)是否是素數(shù)是計算數(shù)論的基本問題之－，在如密碼中有重要應用。我們綜述素數(shù)判定的一些重要算法，包括概率算法與確定性算法，如著名的AKS算法，還講述一些特殊數(shù)的素數(shù)判定方法

報告題目：后量子密碼學簡介

報告人：潘彥斌副研究員

摘要：隨著量子計算技術的快速發(fā)展，目前所廣泛使用的基于傳統(tǒng)數(shù)論問題的公鑰密碼體制受到了嚴重威脅。因此，抗量子密碼體制的研制近年來備受關注。本報告將簡要介紹主流后量子密碼體制的相關數(shù)學理論、發(fā)展現(xiàn)狀以及尚待解決的一些重要問題。

報告題目：ANALYSIS OF ROTH-LEMPEL CODES

報告人：周海燕教授

摘要：Near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities.This report focuses on Roth-Lempel codes and establishes necessary and sufficient conditions for them to be NMDS and further completely determine its weight distributions . Besides, we illustrate the linearly inequivalence of Roth-Lempel codes and NMDS codes of elliptic curve type when their corresponding code lenthts exceed $\frac{4(q+2\sqrt{q}+1)}{5}-1$. Finally we show that some special linear codes of elliptic-curve type are not equivalent to Roth-Lempel code C by Schur product.

報告題目：Weights of a class of projective geometry codes

報告人：麻常利教授

摘要：Linear codes are an important class of error-correcting codes and widely used in secret sharing schemes, combinational designs, authentication codes and so on. Let C(n-1,q) be the p-ary linear code generated by the rows of the incidence matrix of points and hyperplanes of PG(n-1,q), with q=ps, s\geq1 and p prime. This is a special class of projective geometry codes. The weights of C(n-1,q) have attracted a great many of research in recent years. Some previous results are as follows: the minimal weight of C(n-1,q) is θn-1, where θn=qn-1q-1; the second minimal weight of C(n-1,q) is 2qn-2; the third minimal weight of C(2,p) is 2p+1, with p prime and p≥11; the fourth minimum weight of C(2,p) is 3p-3, with p prime and p≥5. What are all the weights of C(n-1,q)? This is what we focus on in this paper. Our main results are as follows:

(i) We present that C(n-1,q) is a cyclic code, and give its generator polynomial and parity-check polynomial.

(ii) We give a formula to calculate some weights of C(n-1,q) by the weight distribution of CD, where CD is constructed from the defining set D.

(iii) When q>2 is even, we prove that the weight w of C(2,q) is w\equiv1(\mbox{or }0)~(\mbox{mod}~4). Furthermore, we give a method to calculate some weights of C(2,q) , and present a conjecture.

(iv) When q is even, we prove that each codeword of C2,q⊥ is a linear combination of the incidence vectors of some linear hyperovals, and every hyperoval is the sum of q+2 linear hyperovals, where 、C2,q⊥ is the dual code of C(2,q).

報告題目：Large-size families of Costas arrays with low cross-correlation

報告人：王琦教授

摘要：Costas arrays have been extensively investigated for decades due to their applications in Radar systems and their close connections to combinatorics. In this talk, I will introduce some new recent results on families of Costas arrays with low cross-correlation. More precisely, by employing some results on the number of roots of certain polynomials over finite fields, we are able to derive bounds on the cross-correlation of several large-size families of Costas arrays.

報告題目：子空間碼的消息認證碼的構造

報告人：張俊教授

摘要：子空間碼是線性網絡編碼的一類重要糾錯碼。由于網絡的復雜性，網絡中的替代攻擊/污染攻擊是常見的安全問題，消息認證碼是保證消息完整性、防止這兩類攻擊的有效手段。報告中，我們將利用經典糾錯碼對子空間碼設計一類消息認證碼。

報告題目：同源密碼及其計算

報告人：胡志副教授

報告內容：同源密碼是后量子密碼領域的一類重要研究對象，其優(yōu)勢是密鑰長度短，劣勢是安全基礎研究歷史短、底層理論復雜且實現(xiàn)效率低。2022年SIDH被攻破，以及后續(xù)SQIsign被遴選到NIST后量子密碼簽名算法標準征集中，相關事件使得同源密碼得到了眾多關注。本報告將介紹同源密碼的安全基礎、同源密碼方案以及相關同源計算，并探討同源密碼的發(fā)展前景。