Improved Constructions of Frameproof Codes

Frameproof codes are used to preserve the security in the context of coalition when fingerprinting digital data. Let $M_{c,l}(q)$ be the largest cardinality of a $q$-ary $c$-frameproof code of length $l$ and $R_{c,l}=\lim_{q\rightarrow \infty}M_{c,l}(q)/q^{\lceil l/c\rceil}$. It has been determined by Blackburn that $R_{c,l}=1$ when $l\equiv 1\ (\bmod\ c)$, $R_{c,l}=2$ when $c=2$ and $l$ is even, and $R_{3,5}=5/3$. In this paper, we give a recursive construction for $c$-frameproof codes of length $l$ with respect to the alphabet size $q$. As applications of this construction, we establish the existence results for $q$-ary $c$-frameproof codes of length $c+2$ and size $\frac{c+2}{c}(q-1)^2+1$ for all odd $q$ when $c=2$ and for all $q\equiv 4\pmod{6}$ when $c=3$. Furthermore, we show that $R_{c,c+2}=(c+2)/c$ meeting the upper bound given by Blackburn, for all integers $c$ such that $c+1$ is a prime power.Comment: 6 pages, to appear in Information Theory, IEEE Transactions o

Constructions of almost secure frameproof codes with applications to fingerprinting schemes

The final publication is available at Springer via http://dx.doi.org/10.1007/s10623-017-0359-zThis paper presents explicit constructions of fingerprinting codes. The proposed constructions use a class of codes called almost secure frameproof codes. An almost secure frameproof code is a relaxed version of a secure frameproof code, which in turn is the same as a separating code. This relaxed version is the object of our interest because it gives rise to fingerprinting codes of higher rate than fingerprinting codes derived from separating codes. The construction of almost secure frameproof codes discussed here is based on weakly biased arrays, a class of combinatorial objects tightly related to weakly dependent random variables.Peer ReviewedPostprint (author's final draft

On Anti-Collusion Codes and Detection Algorithms for Multimedia Fingerprinting

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. AND anti-collusion codes can be used to construct fingerprints resistant to collusion attacks on multimedia contents. In this paper, we first investigate AND anti-collusion codes and related detection algorithms from a combinatorial viewpoint, and then introduce a new concept of logical anti-collusion code to improve the traceability of multimedia fingerprinting. It reveals that frameproof codes have traceability for multimedia contents. Relationships among anti-collusion codes and other structures related to fingerprinting are discussed, and constructions for both AND anti-collusion codes and logical anti-collusion codes are provided

Almost separating and almost secure frameproof codes over q-ary alphabets

The final publication is available at Springer via http://dx.doi.org/10.1007/s10623-015-0060-zIn this paper we discuss some variations of the notion of separating code for alphabets of arbitrary size. We show how the original definition can be relaxed in two different ways, namely almost separating and almost secure frameproof codes, yielding two different concepts. The new definitions enable us to obtain codes of higher rate, at the expense of satisfying the separating property partially. These new definitions become useful when complete separation is only required with high probability, rather than unconditionally. We also show how the codes proposed can be used to improve the rate of existing constructions of families of fingerprinting codes.Peer ReviewedPostprint (author's final draft

Gossip Codes for Fingerprinting: Construction, Erasure Analysis and Pirate Tracing

This work presents two new construction techniques for q-ary Gossip codes from tdesigns and Traceability schemes. These Gossip codes achieve the shortest code length specified in terms of code parameters and can withstand erasures in digital fingerprinting applications. This work presents the construction of embedded Gossip codes for extending an existing Gossip code into a bigger code. It discusses the construction of concatenated codes and realisation of erasure model through concatenated codes.Comment: 28 page

Fingerprinting Codes and Related Combinatorial Structures

Fingerprinting codes were introduced by Boneh and Shaw in 1998 as a method of copyright control. The desired properties of a good fingerprinting code has been found to have deep connections to combinatorial structures such as error-correcting codes and cover-free families. The particular property that motivated our research is called "frameproof". This has been studied extensively when the alphabet size q is at least as large as the colluder size w. Much less is known about the case q < w, and we prove several interesting properties about the binary case q = 2 in this thesis. When the length of the code N is relatively small, we have shown that the number of codewords n cannot exceed N, which is a tight bound since the n = N case can be satisfied a trivial construction using permutation matrices. Furthermore, the only possible candidates are equivalent to this trivial construction. Generalization to a restricted parameter set of separating hash families is also given. As a consequence, the above result motivates the question of when a non-trivial construction can be found, and we give some definitive answers by considering combinatorial designs. In particular, we give a necessary and sufficient condition for a symmetric design to be a binary 3-frameproof code, and provide example classes of symmetric designs that satisfy or fail this condition. Finally, we apply our results to a problem of constructing short binary frameproof codes