Weighted Secret Sharing Based on the Chinese Remainder Theorem

In a ) , ( n t secret sharing scheme (SS), a dealer divides a secret into n shares in such a way that (a) the secret can be recovered successfully with t or more than t shares, and (b) the secret cannot be recovered with fewer than t shares. In a weighted secret sharing scheme (WSS), each share of a shareholder has a positive weight. The secret can be recovered if the overall weight of shares is equal to or larger than the threshold; but the secret cannot be recovered if the overall weight of shares is smaller than the threshold value. The ) , ( n t SS is a special type of WSSs in which the weight of all shares is the same. A shareholder having a higher weight needs to keep multiple shares if we adopt a standard ) , ( n t SS to implement a WSS. In this paper, we propose a WSS based on the Chinese Remainder Theorem (CRT) and the security of our scheme is the same as the ) , ( n t SS proposed by Asmuth and Bloom. In our proposed WSS, every shareholder including shareholders having higher weights keeps only one share. Furthermore, the modulus associated with shareholders in our proposed scheme is smaller than the modulus in all existing schemes.

[1]  Wenchao Huang,et al.  A Distributed ECC-DSS Authentication Scheme Based on CRT-VSS and Trusted Computing in MANET , 2012, 2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications.

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

[3]  Wang Zhifang,et al.  A non-interactive modular verifiable secret sharing scheme , 2005, Proceedings. 2005 International Conference on Communications, Circuits and Systems, 2005..

[4]  Ying Guo,et al.  High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis , 2012, Quantum Information Processing.

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

[6]  Chin-Chen Chang,et al.  An authenticated group key distribution mechanism using theory of numbers , 2014, Int. J. Commun. Syst..

[7]  Mohammad S. Obaidat,et al.  Chinese Remainder Theorem-Based RSA-Threshold Cryptography in MANET Using Verifiable Secret Sharing Scheme , 2009, 2009 IEEE International Conference on Wireless and Mobile Computing, Networking and Communications.

[8]  Elisa Bertino,et al.  A New Approach to Weighted Multi-Secret Sharing , 2011, 2011 Proceedings of 20th International Conference on Computer Communications and Networks (ICCCN).

[9]  Tamir Tassa,et al.  Characterizing Ideal Weighted Threshold Secret Sharing , 2008, SIAM J. Discret. Math..

[10]  Ioana Boureanu,et al.  Weighted Threshold Secret Sharing Based on the Chinese Remainder Theorem , 2005, Sci. Ann. Cuza Univ..

[11]  Lein Harn,et al.  Verifiable secret sharing based on the Chinese remainder theorem , 2014, Secur. Commun. Networks.

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

[13]  Dana Ron,et al.  Chinese remaindering with errors , 1999, STOC '99.

[14]  Sorin Iftene,et al.  Secret Sharing Schemes with Applications in Security Protocols , 2006, Sci. Ann. Cuza Univ..

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

[16]  Tamir Tassa,et al.  Characterizing Ideal Weighted Threshold Secret Sharing , 2005, TCC.

[17]  Weighted Threshold Secret Sharing Schemes , 1999, Inf. Process. Lett..

[18]  Ali Aydin Selçuk,et al.  A Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem , 2008, INDOCRYPT.

[19]  Henri Cohen,et al.  A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[20]  Bart Preneel,et al.  On the Security of the Threshold Scheme Based on the Chinese Remainder Theorem , 2002, Public Key Cryptography.