New upper bounds for parent-identifying codes and traceability codes

Chong Shangguan, Jingxue Ma, Gennian Ge*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the last two decades, parent-identifying codes and traceability codes are introduced to prevent copyrighted digital data from unauthorized use. They have important applications in the scenarios like digital fingerprinting and broadcast encryption schemes. A major open problem in this research area is to determine the upper bounds for the cardinalities of these codes. In this paper we will focus on this theme. Consider a code of length N which is defined over an alphabet of size q. Let MIPPC(N, q, t) and MTA(N, q, t) denote the maximal cardinalities of t-parent-identifying codes and t-traceability codes, respectively, where t is known as the strength of the codes. We show MIPPC(N, q, t) ≤ rqN/(v-1)+ (v- 1 - r) qN/(v-1), where v= ⌊ (t/ 2 + 1) 2⌋ , 0 ≤ r≤ v- 2 and N≡rmod(v-1). This new bound improves two previously known bounds of Blackburn, and Alon and Stav. On the other hand, MTA(N, q, t) is still not known for almost all t. In 2010, Blackburn, Etzion and Ng asked whether MTA(N,q,t)≤cq⌈N/t2⌉ or not, where c is a constant depending only on N, and they have shown the only known validity of this bound for t= 2. By using some complicated combinatorial counting arguments, we prove this bound for t= 3. This is the first non-trivial upper bound in the literature for traceability codes with strength three.

Original languageEnglish
Pages (from-to)1727-1737
Number of pages11
JournalDesigns, Codes, and Cryptography
Issue number8
StatePublished - 1 Aug 2018
Externally publishedYes


  • Parent-identifying codes
  • Traceability codes
  • Traitor tracing schemes


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