2013 Fiscal Year Final Research Report

A Study on Cheating Prevention in Secret Sharing Schemes

Research Project

Project/Area Number	24800064
Research Category	Grant-in-Aid for Research Activity Start-up
Allocation Type	Single-year Grants
Research Field	Fundamental theory of informatics
Research Institution	Hosei University
Principal Investigator	OBANA Satoshi 法政大学, 情報科学部, 教授 (70633600)
Project Period (FY)	2012-08-31 – 2014-03-31
Keywords	効率の良い方式提案 / 理論的実現可能性の証明
Research Abstract	With respect to secret sharing schemes secure against rushing adversaries who determine their forged shares after observing shares of honest users, we construct four type of schemes secure against rushing adversaries. The sizes of shares of each proposed scheme achieves smallest bit length compared to those of existing schemes with the same security level. Further, we construct a scheme which can detect the fact of cheating and which ensure security whatever an finite field the secret belongs to. We should note that no existing schemes guarantee such a security feature. With respect to d-multiplicative secret sharing schemes which enable each user to compute a share of a polynomial with degree less than d (where d is a predetermined constant), we clarify conditions with which a secure d-multiplicative scheme (in which no user can cheat the other users) exists. Furthermore, we construct secure and efficient schemes secure against threshold adversary and general adversary, respectively.

(4 results)