1,323 research outputs found
Fingerprinting Codes and Separating Hash Families
The thesis examines two related combinatorial objects, namely fingerprinting codes and separating hash families. Fingerprinting codes are combinatorial objects that have been studied for more than 15 years due to their applications in digital data copyright protection and their combinatorial interest. Four well-known types of fingerprinting codes are studied in this thesis; traceability, identifiable parent property, secure frameproof and frameproof. Each type of code is named after the security properties it guarantees. However, the power of these four types of fingerprinting codes is limited by a certain condition. The first known attempt to go beyond that came out in the concept of two-level traceability codes, introduced by Anthapadmanabhan and Barg (2009). This thesis extends their work to the other three types of fingerprinting codes, so in this thesis four types of two-level fingerprinting codes are defined. In addition, the relationships between the different types of codes are studied. We propose some first explicit non-trivial constructions for two-level fingerprinting codes and provide some bounds on the size of these codes. Separating hash families were introduced by Stinson, van Trung, and Wei as a tool for creating an explicit construction for frameproof codes in 1998. In this thesis, we state a new definition of separating hash families, and mainly focus on improving previously known bounds for separating hash families in some special cases that related to fingerprinting codes. We improve upper bounds on the size of frameproof and secure frameproof codes under the language of separating hash families
Linear time Constructions of some -Restriction Problems
We give new linear time globally explicit constructions for perfect hash
families, cover-free families and separating hash functions
Improved Constructions of Frameproof Codes
Frameproof codes are used to preserve the security in the context of
coalition when fingerprinting digital data. Let be the largest
cardinality of a -ary -frameproof code of length and
. It has
been determined by Blackburn that when ,
when and is even, and . In this paper, we
give a recursive construction for -frameproof codes of length with
respect to the alphabet size . As applications of this construction, we
establish the existence results for -ary -frameproof codes of length
and size for all odd when and for all
when . Furthermore, we show that
meeting the upper bound given by Blackburn, for all integers such that
is a prime power.Comment: 6 pages, to appear in Information Theory, IEEE Transactions o
Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
In parameterized complexity, it is a natural idea to consider different
generalizations of classic problems. Usually, such generalization are obtained
by introducing a "relaxation" variable, where the original problem corresponds
to setting this variable to a constant value. For instance, the problem of
packing sets of size at most into a given universe generalizes the Maximum
Matching problem, which is recovered by taking . Most often, the
complexity of the problem increases with the relaxation variable, but very
recently Abasi et al. have given a surprising example of a problem ---
-Simple -Path --- that can be solved by a randomized algorithm with
running time . That is, the complexity of the
problem decreases with . In this paper we pursue further the direction
sketched by Abasi et al. Our main contribution is a derandomization tool that
provides a deterministic counterpart of the main technical result of Abasi et
al.: the algorithm for -Monomial
Detection, which is the problem of finding a monomial of total degree and
individual degrees at most in a polynomial given as an arithmetic circuit.
Our technique works for a large class of circuits, and in particular it can be
used to derandomize the result of Abasi et al. for -Simple -Path. On our
way to this result we introduce the notion of representative sets for
multisets, which may be of independent interest. Finally, we give two more
examples of problems that were already studied in the literature, where the
same relaxation phenomenon happens. The first one is a natural relaxation of
the Set Packing problem, where we allow the packed sets to overlap at each
element at most times. The second one is Degree Bounded Spanning Tree,
where we seek for a spanning tree of the graph with a small maximum degree
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