Bounds on Traceability Schemes

Yujie Gu, Ying Miao

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

The Stinson-Wei traceability scheme (known as traceability scheme) was proposed for broadcast encryption as a generalization of the Chor-Fiat-Naor traceability scheme (known as traceability code). Cover-free family was introduced by Kautz and Singleton in the context of binary superimposed code. In this paper, we find a new relationship between a traceability scheme and a cover-free family, which strengthens the anti-collusion strength from t to t2, i.e., a t-traceability scheme is a t2-cover-free family. Based on this interesting discovery, we derive new upper bounds for traceability schemes. By using combinatorial structures, we construct several infinite families of optimal traceability schemes, which attain our new upper bounds. We also provide a constructive lower bound for traceability schemes, the size of which has the same order of magnitude as our general upper bound. Meanwhile, we consider parent-identifying set systems, an anti-collusion key-distributing scheme requiring weaker conditions than traceability scheme but stronger conditions than cover-free family. A new upper bound is also given for parent-identifying set systems.

Original languageEnglish
Pages (from-to)3450-3460
Number of pages11
JournalIEEE Transactions on Information Theory
Volume64
Issue number5
DOIs
Publication statusPublished - May 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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