Strongly separable codes

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 t-separable code (t-SSC) is introduced to improve such a scheme based on a binary t-FPC. A binary 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 t-SSCs from q-ary t-SSCs is described, which stimulates the research on q-ary t-SSCs with short length. Several infinite series of optimal q-ary 2-SSCs of length 2 are derived from the fact that a q-ary 2-SSC of length 2 is equivalent to a q-ary 2-separable code of length 2. Combinatorial properties of q-ary 2-SSCs of length 3 are investigated, and a construction for q-ary 2-SSCs of length 3 is provided. These 2-SSCs of length 3 have more than 12.5% codewords than 2-FPCs of length 3 could have.

Multimedia IPP codes with efficient tracing

“…The following theorem shows that a t-SMIPPC(n, M, 2) can be used to identify at least one colluder in the averaging attack with computational complexity O(nM ), which is more efficient than that of a t-MIPPC(n, M, 2). We in fact use Algorithm SSCTraceAlg(R) presented in [12]. For convenience, the detailed illustration is given below.…”

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

“…Jiang et al [13] established the following relationships among SC, SSC and FPC. The following example shows that the converse of Lemma 2.2 does not always hold.…”

“…Compared with frameproof codes, strongly separable codes have an advantage in copyright protection since a strongly t-separable code has the same traceability as a tframeproof code but has more codewords than a t-frameproof code, see [13]. Strongly separable codes can be also used to study the classic digital fingerprinting codes such as identifiable parent property (IPP) codes [12], frameproof codes [2,15], perfect hash families (PHFs) [3,16] and so on.…”

“…According to the relationship between strongly separable codes and separable codes, t-SSC(n, M, q) with parameters (t, n) = (2, 2), and (2, 3) were discussed in [13]. When t ≥ 3, the structure of t-SSCs becomes more complex so that little is known about t-SSCs.…”

Bounds and Constructions for $\overline{3}$-Strongly Separable Codes with Length $3$

“…However the anti-collusion codes constructed by t-separable codes have tracing complexity O(M t ), and those constructed by strongly t-separable codes and t-frameproof codes have tracing complexity O(M). Compared with frameproof codes, strongly separable codes have an advantage in copyright protection since a strongly t-separable code has the same traceability as a tframeproof code but has more codewords than a t-frameproof code, see [13]. Strongly separable codes can be also used to study the classic digital fingerprinting codes such as identifiable parent property (IPP) codes [12], frameproof codes [2,15], perfect hash families (PHFs) [3,16] and so on.…”