Some connections between self-dual codes, combinatorial designs and secret sharing schemes
نویسندگان
چکیده
Some connections between self-dual codes, combinatorial designs and secret-sharing schemes Stefka Bouyuklieva, Zlatko Varbanov Department of Mathematics and Informatics, University of Veliko Tarnovo, Bulgaria In the present work we study a class of singly even self-dual codes with the special property that the minimum weight of their shadow is 1. Some of these codes support 1 and 2-designs. Using them, we describe two types of schemes based on codes with one-part secret and with two-part secret. Similar schemes can be constructed from self-dual codes that support 3-designs.
منابع مشابه
New combinatorial designs and their applications to authentication codes and secret sharing schemes
This paper introduces three new types of combinatorial designs, which we call external difference families (EDF), external BIBDs (EBIBD) and splitting BIBDs. An EDF is a special type of EBIBD, so existence of an EDF implies existence of an EBIBD. We construct optimal splitting A-codes by using EDF. Then we give a new bound on the number of shares required in robust secret sharing schemes (i.e.,...
متن کاملSecurity Analysis of a Hash-Based Secret Sharing Scheme
Secret sharing schemes perform an important role in protecting se-cret by sharing it among multiple participants. In 1979, (t; n) threshold secret sharing schemes were proposed by Shamir and Blakley independently. In a (t; n) threshold secret sharing scheme a secret can be shared among n partic-ipants such that t or more participants can reconstruct the secret, but it can not be reconstructed b...
متن کاملAbstracts for talks to be presented in the CCCS 98 Workshop Instructional
s for talks to be presented in the CCCS 98 Workshop Instructional Lectures Cryptography and Combinatorial Designs Charles J. Colbourn, Dorothean Professor of Computer Science University of Vermont In this series of five lectures, we explore some of the many problems in cryptography where combinatorial designs have played a substantial role. To set the stage, we review some ideas from classical ...
متن کاملAn Explication of Secret Sharing Schemes
This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate. In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean...
متن کاملRepresenting Small Identically Self-Dual Matroids by Self-Dual Codes
The matroid associated to a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated to a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code. This open problem was proposed in [8], where it was proved to be equivalent to an ope...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Adv. in Math. of Comm.
دوره 5 شماره
صفحات -
تاریخ انتشار 2011