Classification of ideal homomorphic threshold schemes over finite Abelian groups
Yair Frankel,Yvo Desmedt +1 more
- pp 25-34
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.read more
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
Qiushi Yang,Yvo Desmedt +1 more
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
Mulan Liu,Zhanfei Zhou +1 more
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
More filters
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.