Efficient integer span program for hierarchical threshold access structure

Authors:
Qi Chen;Dingyi Pei;Chunming Tang;Gansen Zhao
Affiliations:
GCI Science & Technology Co., Ltd., Guangzhou 510310, China and GCI Science & Technology Co., Ltd., South China Normal University, Services Computing Joint Laboratory, Guangzhou 510310, China;College of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;College of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;GCI Science & Technology Co., Ltd., South China Normal University, Services Computing Joint Laboratory, Guangzhou 510310, China and School of Computer Science, South China Normal University, Guang ...
Venue:
Information Processing Letters
Year:
2013

Citing 15
Cited 0

Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group

SIAM Journal on Discrete Mathematics
How to share a secret

Communications of the ACM
Secret Sharing in Multilevel and Compartmented Groups

ACISP '98 Proceedings of the Third Australasian Conference on Information Security and Privacy
Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups

CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
How to (Really) Share a Secret

CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Threshold Cryptosystems

CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Hierarchical Threshold Secret Sharing

Journal of Cryptology
Characterizing Ideal Weighted Threshold Secret Sharing

SIAM Journal on Discrete Mathematics
Non-interactive Proofs for Integer Multiplication

EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Multipartite Secret Sharing by Bivariate Interpolation

Journal of Cryptology
On the Amortized Complexity of Zero-Knowledge Protocols

CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Efficient multi-party computation over rings

EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Efficient, robust and constant-round distributed RSA key generation

TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Black-box secret sharing from primitive sets in algebraic number fields

CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Linear integer secret sharing and distributed exponentiation

PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography

Quantified Score

Hi-index	0.89

Visualization

Abstract

Integer span program (ISP) is a monotone span program (MSP) over Z, which is introduced by Cramer and Fehr in CRYPTO 2002. ISP can be used to construct black-box secret sharing scheme (BBSSS) and linear integer secret sharing scheme (LISSS). The efficiency of ISPs is a very important research objective, as efficient ISP can be used to construct efficient BBSSS and efficient LISSS. Until now, only efficient ISPs that realize threshold access structure have been constructed, but not efficient ISPs realizing other access structures. The main contribution of this paper is that we propose an efficient ISP that realizes the hierarchical threshold access structure, to the best knowledge of the authors, which is the first efficient one for non-threshold access structure. Accordingly, with the proposed construction of efficient ISP realizing hierarchical threshold access structure, the construction of efficient non-threshold BBSSSs and LISSSs for a useful family of access structures is presented.