Book ChapterDOI
Cumulative Arrays and Geometric Secret Sharing Schemes
Wen-Ai Jackson,Keith M. Martin +1 more
- pp 48-55
TLDR
It is shown that every non-degenerate geometric secret sharing scheme is ‘contained’ in the corresponding cumulative scheme.Abstract:
Cumulative secret sharing schemes were introduced by Simmons et al (1991) based on the generalised secret sharing scheme of Ito et al (1987). A given monotone access structure together with a security level is associated with a unique cumulative scheme. Geometric secret sharing schemes form a wide class of secret sharing schemes which have many desirable properties including good information rates. We show that every non-degenerate geometric secret sharing scheme is ‘contained’ in the corresponding cumulative scheme. As there is no known practical algorithm for constructing efficient secret sharing schemes, the significance of this result is that, at least theoretically, a geometric scheme can be constructed from the corresponding cumulative scheme.read more
Citations
More filters
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
Authenticated data structures for graph and geometric searching
TL;DR: It is demonstrated that the Micali-Sidney scheme is a special case of this general framework for shared generation of pseudo-random function using cumulative maps, and an upper and a lower bound for d are derived.
Journal Article
Secret Sharing Schemes with Applications in Security Protocols.
TL;DR: It is proved, using the concept of entropy, that in any perfect threshold secret sharing scheme the shares must be at least as long as the secret and, later on, Capocelli, De Santis, Gargano, and Vaccaro have extended this result to the …
Journal Article
Non-interactive deniable ring authentication
Willy Susilo,Yi Mu +1 more
TL;DR: In this paper, it is possible to convince a verifier that a member of an ad hoc collection of participants is authenticating a message m without revealing which one and the verifier V cannot convince any third party that the message m was indeed authenticated in a non-interactive way.
Book ChapterDOI
Attacks on the HKM/HFX Cryptosystem
Xuejia Lai,Rainer A. Rueppel +1 more
TL;DR: The HKM / HFX cryptosystem is proposed for standardization at the ITU Telecommunication Standardization Sector Study Group 8 and is designed to provide authenticity and confidentiality of FAX messages at a commercial level of security.
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.
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.
Book
Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
Journal ArticleDOI
Secret sharing scheme realizing general access structure
TL;DR: This paper shows that by providing the trustees with several information data concerning the distributed information of the (k, n) threshold method, any access structure can be realized.
Journal ArticleDOI
An explication of secret sharing schemes
TL;DR: This paper presents numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter, the vector space construction of Brickell, and the Simmons geometric construction, emphasizing combinatorial construction methods.