Threshold changeable secret sharing with secure secret reconstruction

Abstract ( t , n ) threshold secret sharing (SS) is an important cryptographic primitive in which a secret is divided into n shares, and then any t or more shareholders can exchange shares to reconstruct the secret without help of any trusted third party. However, if an illegal participant, without any valid share, impersonates a shareholder to recover the secret with m ( m ≥ t ) legal shareholders in a traditional ( t , n ) threshold SS scheme, it may obtain the secret. Therefore, this paper utilizes a bivariate symmetry polynomial to propose a basic threshold changeable secret sharing (TCSS) scheme which is cheating immune and thwarts the above illegal participant attack. In the basic TCSS scheme, threshold is allowed to increase from t to the exact number of all participants during secret reconstruction. In this way, the secret can be recovered only if all the participants have valid shares. However, each shareholder has to keep t coefficients of its share. Then, an improved TCSS scheme based on both univariate polynomial and bivariate symmetry polynomial is proposed to reduce coefficients of shares for each shareholder.

[1]  Xiangyang Luo,et al.  A new threshold changeable secret sharing scheme based on the Chinese Remainder Theorem , 2019, Inf. Sci..

[2]  Reihaneh Safavi-Naini,et al.  Bounds and Techniques for Efficient Redistribution of Secret Shares to New Access Structures , 1999, Comput. J..

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

[5]  Tsuyoshi Takagi,et al.  Note on Some Recent Cheater Identifiable Secret Sharing Schemes , 2015, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[6]  Lein Harn,et al.  Dynamic threshold secret reconstruction and its application to the threshold cryptography , 2015, Inf. Process. Lett..

[7]  Xuezheng Liu,et al.  On the (In)Security of Recent Group Key Distribution Protocols , 2016, Comput. J..

[8]  Yi Mu,et al.  Attribute-Based Oblivious Access Control , 2012, Comput. J..

[9]  Josh Benaloh,et al.  Secret Sharing Homomorphisms: Keeping Shares of A Secret Sharing , 1986, CRYPTO.

[10]  Yanxiao Liu.  Linear (k, n) Secret Sharing Scheme with Cheating Detection , 2015, 2015 IEEE International Conference on Computer and Information Technology; Ubiquitous Computing and Communications; Dependable, Autonomic and Secure Computing; Pervasive Intelligence and Computing.

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

[12]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[13]  Douglas R. Stinson,et al.  On dealer-free dynamic threshold schemes , 2013, Adv. Math. Commun..

[14]  Keith M. Martin,et al.  Updating the parameters of a threshold scheme by minimal broadcast , 2005, IEEE Transactions on Information Theory.

[15]  Hideki Imai,et al.  A Hierarchical Non-interactive Key-Sharing Scheme with Low Memory Size and High Resistance against Collusion Attacks , 2002, Comput. J..

[16]  Mingxing He,et al.  Collusion Attack Resistance and Practice-Oriented Threshold Changeable Secret Sharing Schemes , 2010, 2010 24th IEEE International Conference on Advanced Information Networking and Applications.

[17]  Sorin Iftene,et al.  General Secret Sharing Based on the Chinese Remainder Theorem with Applications in E-Voting , 2007, ICS@SYNASC.

[18]  Joseph Y. Halpern,et al.  Ra-tional secret sharing and multiparty computation , 2004, STOC 2004.

[19]  Lein Harn,et al.  Group Authentication , 2013, IEEE Transactions on Computers.

[20]  Atsuko Miyaji,et al.  Efficient and Unconditionally Secure Verifiable Threshold Changeable Scheme , 2001, ACISP.

[21]  Maurice Mignotte,et al.  How to Share a Secret? , 1982, EUROCRYPT.

[22]  John Bloom,et al.  A modular approach to key safeguarding , 1983, IEEE Trans. Inf. Theory.

[23]  Saba Asaad,et al.  A lattice-based threshold secret sharing scheme , 2014, 2014 11th International ISC Conference on Information Security and Cryptology.

[24]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

[25]  Zahra Ahmadian,et al.  Security Analysis of a Dynamic Threshold Secret Sharing Scheme Using Linear Subspace Method , 2017, IACR Cryptol. ePrint Arch..

[26]  Paul Feldman,et al.  A practical scheme for non-interactive verifiable secret sharing , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[27]  R. J. McEliece,et al.  On sharing secrets and Reed-Solomon codes , 1981, CACM.

[28]  Alfredo De Santis,et al.  Size of Shares and Probability of Cheating in Threshold Schemes , 1994, EUROCRYPT.

[29]  Feng Wang,et al.  Simulatable and secure certificate-based threshold signature without pairings , 2014, Secur. Commun. Networks.

[30]  Ron Steinfeld,et al.  Lattice-Based Threshold Changeability for Standard Shamir Secret-Sharing Schemes , 2004, IEEE Transactions on Information Theory.

[31]  Zahra Ahmadian,et al.  Linear Subspace Cryptanalysis of Harn’s Secret Sharing-Based Group Authentication Scheme , 2018, IEEE Transactions on Information Forensics and Security.

[32]  Ron Steinfeld,et al.  Lattice-based threshold-changeability for standard CRT secret-sharing schemes , 2006, Finite Fields Their Appl..

[33]  Martin Tompa,et al.  How to share a secret with cheaters , 1988, Journal of Cryptology.

[34]  Josef Pieprzyk,et al.  Changing Thresholds in the Absence of Secure Channels , 1999, Aust. Comput. J..

[35]  C. Pandu Rangan,et al.  Efficient Statistical Asynchronous Verifiable Secret Sharing with Optimal Resilience , 2009, ICITS.