四川 成都 kaiyun開(kāi)云官方網(wǎng)站2024年12月22日-2024年12月24日

本次會(huì)議主題包括(但不限于)：為了促進(jìn)學(xué)術(shù)交流，加強(qiáng)學(xué)術(shù)合作，由kaiyun開(kāi)云官方網(wǎng)站信息科學(xué)與技術(shù)學(xué)院、kaiyun開(kāi)云官方網(wǎng)站主辦的“編碼與密碼學(xué)前沿研討會(huì)：后量子密碼及其相關(guān)問(wèn)題”，將于2024年12月22日（周日）至12月24日（周二）在kaiyun開(kāi)云官方網(wǎng)站召開(kāi)。本次研討會(huì)將邀請(qǐng)編碼、密碼、組合數(shù)學(xué)與數(shù)論等領(lǐng)域的專家參加，共同研討相關(guān)方向的最新研究進(jìn)展和發(fā)展趨勢(shì)，為相關(guān)學(xué)者提供一個(gè)學(xué)術(shù)平臺(tái)，交流最新發(fā)展動(dòng)態(tài)及學(xué)術(shù)成果，促進(jìn)信息學(xué)科、數(shù)學(xué)學(xué)科理論等相關(guān)領(lǐng)域的交叉、融合與發(fā)展，為該領(lǐng)域的老師、學(xué)生提供一個(gè)相互學(xué)習(xí)和交流的場(chǎng)所。

聯(lián)系人：

唐春明 ([email protected]; 18582182739)

羅榮 ([email protected]; 13882112127)

報(bào)告摘要

題目：超奇異橢圓曲線同源密碼

報(bào)告人：徐茂智教授

摘要：橢圓曲線是構(gòu)造密碼算法的重要源泉，橢圓曲線密碼包括基于點(diǎn)的標(biāo)量乘的密碼、基于雙線性配對(duì)的密碼和基于超奇異橢圓曲線同源的密碼。前兩者已經(jīng)得到廣泛應(yīng)用，而超奇異橢圓曲線同源密碼因?yàn)槠淇沽孔庸舻男再|(zhì)，成為密碼學(xué)界和應(yīng)用數(shù)學(xué)界的一個(gè)研究熱點(diǎn)。 本報(bào)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(jìn)而介紹使用超奇異橢圓曲線同源構(gòu)造的密碼基礎(chǔ)和進(jìn)展情況。涉及代數(shù)、數(shù)論、代數(shù)曲線知識(shí)和密碼學(xué)的概念。

報(bào)告題目：素?cái)?shù)判定問(wèn)題綜述

報(bào)告人：鄧映蒲教授

摘要：判定一個(gè)大整數(shù)是否是素?cái)?shù)是計(jì)算數(shù)論的基本問(wèn)題之－，在如密碼中有重要應(yīng)用。我們綜述素?cái)?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?cái)?shù)判定方法

報(bào)告題目：后量子密碼學(xué)簡(jiǎn)介

報(bào)告人：潘彥斌副研究員

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

報(bào)告題目：ANALYSIS OF ROTH-LEMPEL CODES

報(bào)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(bào)告題目：Weights of a class of projective geometry codes

報(bào)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(bào)告題目：Large-size families of Costas arrays with low cross-correlation

報(bào)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(bào)告題目：子空間碼的消息認(rèn)證碼的構(gòu)造

報(bào)告人：張俊教授

摘要：子空間碼是線性網(wǎng)絡(luò)編碼的一類重要糾錯(cuò)碼。由于網(wǎng)絡(luò)的復(fù)雜性，網(wǎng)絡(luò)中的替代攻擊/污染攻擊是常見(jiàn)的安全問(wèn)題，消息認(rèn)證碼是保證消息完整性、防止這兩類攻擊的有效手段。報(bào)告中，我們將利用經(jīng)典糾錯(cuò)碼對(duì)子空間碼設(shè)計(jì)一類消息認(rèn)證碼。

報(bào)告題目：同源密碼及其計(jì)算

報(bào)告人：胡志副教授

報(bào)告內(nèi)容：同源密碼是后量子密碼領(lǐng)域的一類重要研究對(duì)象，其優(yōu)勢(shì)是密鑰長(zhǎng)度短，劣勢(shì)是安全基礎(chǔ)研究歷史短、底層理論復(fù)雜且實(shí)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(biāo)準(zhǔn)征集中，相關(guān)事件使得同源密碼得到了眾多關(guān)注。本報(bào)告將介紹同源密碼的安全基礎(chǔ)、同源密碼方案以及相關(guān)同源計(jì)算，并探討同源密碼的發(fā)展前景。