On combinatorial structures and algorithms common to digital fingerprinting and group testing

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04974
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: University of Tsukuba
• Principal Investigator: Miao Ying 筑波大学, システム情報系, 教授 (10302382)
• Co-Investigator(Kenkyū-buntansha): 藤原 良叔 筑波大学, システム情報系(名誉教授), 名誉教授 (30165443)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: デジタル指紋 / グループ検査 / 組合せ構造 / アルゴリズム / 構成法 / 最適 / ゼロ差均衡関数

Outline of Final Research Achievements

We have investigated properties and construction of combinatorial structures common to digital fingerprinting and group testing, and developed tracing/ identification algorithms based on these structures. We have introduced strongly separable codes and multimedia IPP codes, and developed tracing algorithms based on these codes. We have derived tight upper and lower bounds on the sizes of separable codes, frameproof codes, multimedia IPP codes, and traceability schemes. We have constructed infinite series of perfect hash families, optimal separable codes, optimal strongly separable codes, and optimal multimedial IPP codes. We have used generalized cyclotomy to construct infinite series of zero-difference balanced functions, and then constructed many sequences used in communication.

Free Research Field

組合せ論