Strongly Separable Codes

TL;DR

This paper introduces binary strongly separable codes to enhance multimedia fingerprinting, providing new constructions and demonstrating they contain more codewords than traditional frameproof codes, with specific focus on length 2 and 3 codes.

Contribution

It proposes binary strongly separable codes, offers a composition construction from q-ary codes, and derives optimal and larger codes for lengths 2 and 3.

Findings

Binary strongly separable codes have the same traceability as t-FPCs.

Constructed q-ary -SSCs of length 2 are optimal and larger than t-FPCs.

Developed a construction for q-ary -SSCs of length 3 with over 12.5% more codewords.

Abstract

Binary $t$-frameproof codes ($t$-FPCs) are used in multimedia fingerprinting schemes where the identification of authorized users taking part in the averaging collusion attack is required. In this paper, a binary strongly $\bar{t}$-separable code ($\bar{t}$-SSC) is introduced to improve such a scheme based on a binary $t$-FPC. A binary $\bar{t}$-SSC has the same traceability as a binary $t$-FPC but has more codewords than a binary $t$-FPC. A composition construction for binary $\bar{t}$-SSCs from $q$-ary $\bar{t}$-SSCs is described, which stimulates the research on $q$-ary $\bar{t}$-SSCs with short length. Several infinite series of optimal $q$-ary $\bar{2}$-SSCs of length $2$ are derived from the fact that a $q$-ary $\bar{2}$-SSC of length $2$ is equivalent to a $q$-ary $\bar{2}$-separable code of length $2$. Combinatorial properties of $q$-ary $\bar{2}$-SSCs of length $3$ are investigated, and a construction for $q$-ary $\bar{2}$-SSCs of length $3$ is provided. These $\bar{2}$-SSCs of length $3$ have more than $12.5\%$ codewords than $2$-FPCs of length $3$ could have.