报告题目：An elementary construction of strongly multiplicative secret sharing
主讲人：邢朝平，上海交通大学教授
时间：2020年12月23日，14:00-15:00
地址：加入腾讯会议ID：890514233
摘要：Since the mid 2000s, asymptotically-good strongly-multiplicative linear (ramp) secret sharing schemes over a fixed finite field have turned out as a central theoretical primitive in numerous constant-communication-rate results in multi-party cryptographic scenarios, and, surprisingly, in two-party cryptography as well. Known constructions of this most powerful class of arithmetic secret sharing schemes all rely heavily on algebraic geometry (AG). It is a well-known open question since the first (explicit) constructions of such schemes appeared in CRYPTO 2006 whether the use of ``heavy machinery'' can be avoided here. i.e., the question is whether the mere existence of such schemes can also be proved by ``elementary'' techniques only (say, from classical algebraic coding theory), even disregarding effective construction. So far, there is no progress. In this talk we show the theoretical result that, no matter whether this open question has an affirmative answer or not, these schemes can be constructed explicitly by elementary algorithms defined in terms of basic algebraic coding theory. This pertains to all relevant operations associated to such schemes, including, notably, the generation of an instance for a given number of players n, as well as error correction in the presence of corrupt shares.
主讲人简介：邢朝平教授 1990 年在中国科学技术大学获得博士学位后留校工作，1993年获德国洪堡奖学金在Essen大学工作，其后在奥地利科学院从事研究。1998年加入新加坡国立大学，历任助教、tenured副教授、教授。2007年任职于新加坡南洋理工大学教授。2019年加入上海交通大学。长期从事密码、编码、安全多方、代数数论等方面的研究。曾获德国洪堡学者、新加坡国家科学奖、荷兰 Leiden 大学 Kloosterman 讲席教授等。受邀在欧洲数学家大会上作特邀报告。出版专著四本，由剑桥出版社出版的 Coding Theory -- A First Course一书已在世界多所大学作为教材使用。先后在美密会、欧密会、亚密会、TCC、PKC上发表文章10多篇，在计算机理论会议STOC、SODA、ICALP、CCC、RANDOM等发表论文10多篇。在信息论期刊IEEE Transactions on Information Theory Trans.发表编码论文60多篇，同时在数学期刊Advances in Mathematics、Trans. Of the Amer. Math. Soc.、Journal of Combinatorial Theory, Series A、Mathematics of Computation、Journal of Algebra、Journal of Number Theory等国际期刊上发表 SCI 期刊论文20多篇。承担过中国国家自然科学基金项目，新加坡国家科学技术基金，新加坡国防部基金，新加坡教育部基金等项目；特别是承担了新加坡国家研究基金局的重大项目，是新加坡第一个给基础理论研究的重大项目。目前任包括《IEEE Transactions on Information Theory》、《Finite Fields and Their Applications》在内的多个SCI期刊编委。
邀请人：文洁晶
