南京大学计算机软件新技术国家重点实验室

摘 要：

A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size n). At STOC 1976 Valiant presented a graph theoretic approach to the construction of UCs, where a UC is represented by an edge universal graph (EUG) and is recursively constructed using a dedicated graph object (referred to as supernode). As a main end result, Valiant constructed a 4-way supernode of size 19 and an EUG of size 4.75nlogn (omitting smaller terms), which remained the most size-efficient even to this day (after more than 4 decades).

Motivated by the emerging applications of UCs in various privacy preserving computation scenarios, we revisit Valiant's universal circuits, and propose a size-optimal 4-way supernode of size 18, and an EUG of size 4.5nlogn. As confirmed by implementations, we reduce the size of universal circuits (and the number of AND gates) by more than 5% in general (rather than just for small-size circuits in particular), and thus improve upon the efficiency of UC-based cryptographic applications accordingly. Our approach to the design of optimal supernodes is computer aided (rather than by hand as in previous works), which might be of independent interests. As a complement, we give lower bounds on the size of EUGs and UCs in Valiant's framework, which significantly improves upon the generic lower bound on UC size and therefore reduces the gap between theory and practice of universal circuits.

报告人简介:

Yu Yu is a professor in Department of Computer Science and Engineering, Shanghai Jiaotong University. He earned his BS degree from Fudan University and PhD degree from Nanyang Technological University in 2006. He was a postdoctoral fellow at University of Leuven, Belgium. His research interests include foundations of cryptography, post-quantum cryptography, privacy-preserving computing, etc. His research results mostly appear in top crypto/information security venues, such as CRYPTO, EUROCRYPT, ASIACRYPT, IEEE S&P (Oakland), CCS, TCC. He has served as a member of the program committee of EUROCRYPT, ASIACRYPT, CCS, etc., a member of the steering committee of ASIACRYPT and an observer of the International Cryptography Society Council..

时间：9月27日   9:30-10:30

地点：计算机科学技术楼225室