4,937 research outputs found
Problems on q-Analogs in Coding Theory
The interest in -analogs of codes and designs has been increased in the
last few years as a consequence of their new application in error-correction
for random network coding. There are many interesting theoretical, algebraic,
and combinatorial coding problems concerning these q-analogs which remained
unsolved. The first goal of this paper is to make a short summary of the large
amount of research which was done in the area mainly in the last few years and
to provide most of the relevant references. The second goal of this paper is to
present one hundred open questions and problems for future research, whose
solution will advance the knowledge in this area. The third goal of this paper
is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author
An Epitome of Multi Secret Sharing Schemes for General Access Structure
Secret sharing schemes are widely used now a days in various applications,
which need more security, trust and reliability. In secret sharing scheme, the
secret is divided among the participants and only authorized set of
participants can recover the secret by combining their shares. The authorized
set of participants are called access structure of the scheme. In Multi-Secret
Sharing Scheme (MSSS), k different secrets are distributed among the
participants, each one according to an access structure. Multi-secret sharing
schemes have been studied extensively by the cryptographic community. Number of
schemes are proposed for the threshold multi-secret sharing and multi-secret
sharing according to generalized access structure with various features. In
this survey we explore the important constructions of multi-secret sharing for
the generalized access structure with their merits and demerits. The features
like whether shares can be reused, participants can be enrolled or dis-enrolled
efficiently, whether shares have to modified in the renewal phase etc., are
considered for the evaluation
A Smart Approach for GPT Cryptosystem Based on Rank Codes
The concept of Public- key cryptosystem was innovated by McEliece's
cryptosystem. The public key cryptosystem based on rank codes was presented in
1991 by Gabidulin -Paramonov-Trejtakov(GPT). The use of rank codes in
cryptographic applications is advantageous since it is practically impossible
to utilize combinatoric decoding. This has enabled using public keys of a
smaller size. Respective structural attacks against this system were proposed
by Gibson and recently by Overbeck. Overbeck's attacks break many versions of
the GPT cryptosystem and are turned out to be either polynomial or exponential
depending on parameters of the cryptosystem. In this paper, we introduce a new
approach, called the Smart approach, which is based on a proper choice of the
distortion matrix X. The Smart approach allows for withstanding all known
attacks even if the column scrambler matrix P over the base field Fq.Comment: 5 pages. to appear in Proceedings of IEEE ISIT201
The Visual Secret Sharing Scheme Based on the Rgb Color System
The visual secret sharing (VSS) scheme is a method to maintain the confidentiality of a se-cret image by sharing it to some number participants. A (k, n) VSS divides the secret images into n parts, that are called shadows ; to recover the secret back, k shadows should be stacked. Some methods have been developed to implement VSS for color images. However, the methods are only suitable for images with limited number of colors. When more colors are used, the resulted stacked shadow image becomes unclear. Besides that, the size of the shadows becomes bigger as more colors are used. We develop a new method implementing the VSS using the RGB color system. Using our method, the problem related to the unclear stacked shadow image can be overcome
Quantum authentication with key recycling
We show that a family of quantum authentication protocols introduced in
[Barnum et al., FOCS 2002] can be used to construct a secure quantum channel
and additionally recycle all of the secret key if the message is successfully
authenticated, and recycle part of the key if tampering is detected. We give a
full security proof that constructs the secure channel given only insecure
noisy channels and a shared secret key. We also prove that the number of
recycled key bits is optimal for this family of protocols, i.e., there exists
an adversarial strategy to obtain all non-recycled bits. Previous works
recycled less key and only gave partial security proofs, since they did not
consider all possible distinguishers (environments) that may be used to
distinguish the real setting from the ideal secure quantum channel and secret
key resource.Comment: 38+17 pages, 13 figures. v2: constructed ideal secure channel and
secret key resource have been slightly redefined; also added a proof in the
appendix for quantum authentication without key recycling that has better
parameters and only requires weak purity testing code
Steiner t-designs for large t
One of the most central and long-standing open questions in combinatorial
design theory concerns the existence of Steiner t-designs for large values of
t. Although in his classical 1987 paper, L. Teirlinck has shown that
non-trivial t-designs exist for all values of t, no non-trivial Steiner
t-design with t > 5 has been constructed until now. Understandingly, the case t
= 6 has received considerable attention. There has been recent progress
concerning the existence of highly symmetric Steiner 6-designs: It is shown in
[M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial
flag-transitive Steiner 6-design can exist. In this paper, we announce that
essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008,
ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in
Computer Scienc
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