题目：Blackbox Secret Sharing Revisited: A Coding-Theoretic Approach
主讲人：邢朝平，中国科学技术大学博士，上海交通大学教授
时间：2020年5月27日14:00-15:00
地址：加入ZOOM会议 https://zoom.com.cn/j/2936654514
摘要：A blackbox secret sharing (BBSS) scheme works in exactly the same way for all finite Abelian groups G; it can be instantiated for any such group G and only black-box access to its group operations and to random group elements is required. A secret is a single group element and each of the n players' shares is a vector of such elements. Share-computation and secret-reconstruction is by integer linear combinations. These do not depend on G, and neither do the privacy and reconstruction parameters t,r. The expansion factor is the total number of group elements in a full sharing divided by n.In this talk, we introduce a novel, nontrivial, effective construction of BBSS based on coding theory instead of number theory. For threshold-BBSS we also achieve minimal expansion factor O(\log n). Our method is more versatile. Namely, we show, for the first time, BBSS that is near-threshold, i.e.,r-t is an arbitrarily small constant fraction of n, and that has expansion factor O(1), i.e., individual share-vectors of constant length. We also show expansion is minimal for near-threshold and that such BBSS cannot be attained by previous methods.Our general construction is based on a well-known mathematical principle, the local-global principle. More precisely, we first construct BBSS over local rings through either Reed-Solomon or algebraic geometry codes. We then ``glue'' these schemes together in a dedicated manner to obtain a global secret sharing scheme, i.e., defined over the integers, which, as we finally prove using novel insights, has the desired BBSS properties.
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
