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Open AccessBook ChapterDOI

Classification of ideal homomorphic threshold schemes over finite Abelian groups

TLDR
It is proved that there exist infinitely many Abelian groups over which there does not exist an ideal homomorphic threshold scheme.
Abstract
Threshold schemes allow any t out of l individuals to recompute a secret (key). General sharing schemes are a generalization. In homomorphic sharing schemes the "product" of shares of the keys gives a share of the product of the keys. We prove that there exist infinitely many Abelian groups over which there does not exist an ideal homomorphic threshold scheme. Additionally we classify ideal homomorphic general sharing schemes. We discuss the potential impact of our result on the construction of general sharing schemes.

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Citations
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Book ChapterDOI

Nonperfect secret sharing schemes and matroids

TL;DR: This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes.
Book ChapterDOI

Efficient multiplicative sharing schemes

TL;DR: A new recursive construction for multiplicative threshold schemes is described which makes it possible to extend the number of users of such schemes for a relatively small expansion of the share size.
Journal ArticleDOI

Mutually Trusted Authority-Free Secret Sharing Schemes

TL;DR: This paper addresses the problem of establishing secret sharing schemes for a given access structure without the use of a mutually trusted authority by discussing a general protocol and implementing several implementations of this protocol.
Book ChapterDOI

General Perfectly Secure Message Transmission Using Linear Codes

TL;DR: The result is the first, in the context of PSMT in the general adversary model, to have constant round complexity when using interaction, as all of the protocols are executed in either 3 or 2 rounds.
Journal ArticleDOI

Ideal homomorphic secret sharing schemes over cyclic groups

TL;DR: For a cyclic group G and an access structure A, the sufficient and necessary condition under which A is G-ideal homomorphic is given by using the fine-representation of the corresponding matroid over the ring as discussed by the authors.
References
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Journal ArticleDOI

How to share a secret

TL;DR: This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
Journal ArticleDOI

Communication theory of secrecy systems

TL;DR: A theory of secrecy systems is developed on a theoretical level and is intended to complement the treatment found in standard works on cryptography.
Book

Information Theory and Reliable Communication

TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Proceedings ArticleDOI

Safeguarding cryptographic keys

TL;DR: Certain cryptographic keys, such as a number which makes it possible to compute the secret decoding exponent in an RSA public key cryptosystem, 1 , 5 or the system master key and certain other keys in a DES cryptos system, 3 are so important that they present a dilemma.
Journal ArticleDOI

Efficient dispersal of information for security, load balancing, and fault tolerance

TL;DR: Information Dispersal Algorithm (IDA) has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to fault-tolerant and efficient transmission ofInformation in networks, and to communications between processors in parallel computers.