Efficient multisecret sharing scheme using new proposed computational security model

A multisecret sharing (MSS) is a method for sharing a set of secrets among some participants. They can recover each of these secrets without endangering the other secrets. Two kinds of security models have been proposed for MSS schemes. These models are categorized into 2 types. The first security model is unconditional security. This approach decreases the efficiency of MSS schemes. Therefore, the second type of security, which is more relaxed, appeared. This approach is called computational security. In this paper, with 2 examples, we will show that the current definition of computational security does not satisfy all of our expectations from a secure MSS scheme. In fact, in these examples, recovering a secret leaks information to the other secrets while these schemes are considered secure in view of the computational security. After determining the shortcomings of the current security definition, we propose a new definition for computational security and present an MSS scheme that enjoys rigorous proof of security in terms of the new definition. In addition, a complete comparison in terms of share size, number of public values, and required operations for recovering a secret between our scheme and previous schemes indicates that the presented scheme is efficient.

[1]  G. R. Blakley,et al.  Safeguarding cryptographic keys , 1899, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[2]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[3]  Baruch Awerbuch,et al.  Verifiable secret sharing and achieving simultaneity in the presence of faults , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[4]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[5]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[6]  Ed Dawson,et al.  Multistage secret sharing based on one-way function , 1994 .

[7]  J. He,et al.  Multisecret-sharing scheme based on one-way function , 1995 .

[8]  L. Harn,et al.  Comment on "Multistage secret sharing based on one-way function" , 1995 .

[9]  L. Harn.  Efficient sharing (broadcasting) of multiple secrets , 1995 .

[10]  Markus Stadler,et al.  Publicly Verifiable Secret Sharing , 1996, EUROCRYPT.

[11]  Moni Naor,et al.  Visual Cryptography II: Improving the Contrast Via the Cover Base , 1996, Security Protocols Workshop.

[12]  Ueli Maurer,et al.  General Secure Multi-party Computation from any Linear Secret-Sharing Scheme , 2000, EUROCRYPT.

[13]  Rosario Gennaro,et al.  Securing Threshold Cryptosystems against Chosen Ciphertext Attack , 1998, Journal of Cryptology.

[14]  Alexandra Boldyreva,et al.  Efficient threshold signature, multisignature and blind signature schemes based on the Gap-Diffie-Hellman-Group signature scheme , 2002 .

[15]  Wei-Pang Yang,et al.  A new multi-stage secret sharing scheme using one-way function , 2005, OPSR.

[16]  Barbara Masucci.  Sharing Multiple Secrets: Models, Schemes and Analysis , 2006, Des. Codes Cryptogr..

[17]  Y. Yeh,et al.  Dynamic Multi-Secret Sharing Scheme , 2008 .

[18]  Avishek Adhikari,et al.  An efficient multi-use multi-secret sharing scheme based on hash function , 2010, Appl. Math. Lett..

[19]  Mohammad Reza Aref,et al.  Efficient multistage secret sharing scheme using bilinear map , 2014, IET Inf. Secur..

[20]  Partha Sarathi Roy,et al.  Multi-Use Multi-Secret Sharing Scheme for General Access Structure , 2014, ArXiv.

[21]  Lein Harn,et al.  Secure secret reconstruction and multi-secret sharing schemes with unconditional security , 2014, Secur. Commun. Networks.

[22]  V. P. Binu,et al.  An effective private data storage and retrieval system using secret sharing scheme based on secure multi-party computation , 2014, 2014 International Conference on Data Science & Engineering (ICDSE).

[23]  Germán Sáez,et al.  New results and applications for multi-secret sharing schemes , 2014, Des. Codes Cryptogr..

[24]  Tian Zeng,et al.  Multilevel threshold multi-secret sharing scheme based on LUC public key encryption , 2014 .

[25]  Shu-guang Dai,et al.  The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures , 2014 .

[26]  Massoud Hadian Dehkordi,et al.  Two verifiable multi secret sharing schemes based on nonhomogeneous linear recursion and LFSR public-key cryptosystem , 2015, Inf. Sci..

[27]  Jérôme Darmont,et al.  A Novel Multi-Secret Sharing Approach for Secure Data Warehousing and On-Line Analysis Processing in the Cloud , 2015, Int. J. Data Warehous. Min..

[28]  Shyamalendu Kandar,et al.  A (k, n) Multi Secret Sharing Scheme Using Two Variable One Way Function with Less Public Values , 2015, ICISS.

[29]  Lixiang Li,et al.  A Lightweight ID Based Authentication and Key Agreement Protocol for Multiserver Architecture , 2015, Int. J. Distributed Sens. Networks.

[30]  Lixiang Li,et al.  A biometrics and smart cards-based authentication scheme for multi-server environments , 2015, Secur. Commun. Networks.

[31]  P. Dharani,et al.  Survey on secret sharing scheme with deduplication in cloud computing , 2015, 2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO).

[32]  Ying Xia,et al.  Lightweight Data Storage Based on Secret Sharing for Cloud Data , 2015, 2015 Ninth International Conference on Frontier of Computer Science and Technology.

[33]  Zhihui Li,et al.  A new multi-use multi-secret sharing scheme based on the duals of minimal linear codes , 2015, Secur. Commun. Networks.

[34]  Yanhong Liu,et al.  Attacks to some verifiable multi-secret sharing schemes and two improved schemes , 2016, Inf. Sci..