Attacks to some verifiable multi-secret sharing schemes and two improved schemes

Secret sharing plays an important role in protecting confidential information from being lost, destroyed, or falling into wrong hands. Verifiable multi-secret sharing enables a dealer to share multiple secrets among a group of participants such that the deceptive behaviors of the dealer and the participants can be detected. In this paper, we analyze the security of several recently proposed verifiable multi-secret sharing schemes. We show that these schemes cannot withstand some deceptive behaviors of the dealer, and hence fails to satisfy the basic requirement of secure verifiable secret sharing schemes. After that, we present two improved verifiable multi-secret sharing schemes. Our new schemes can not only resist cheating by the dealer or participants, but also remove the use of private channels.

[1]  Wei-Pang Yang,et al.  An improvement on the Lin-Wu (t, n) threshold verifiable multi-secret sharing scheme , 2005, Appl. Math. Comput..

[2]  Zheng Ming-hui,et al.  Improved Multi-secret Sharing Scheme Based on One-Way Function , 2014 .

[3]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[4]  Massoud Hadian Dehkordi,et al.  New efficient and practical verifiable multi-secret sharing schemes , 2008, Inf. Sci..

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

[6]  M. Stadler.  Publicly Veriiable Secret Sharing , 1996 .

[7]  N. J. Meyler.  To a T , 2013 .

[8]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[9]  Lein Harn,et al.  Strong (n, t, n) verifiable secret sharing scheme , 2010, Inf. Sci..

[10]  Rong Zhao,et al.  A practical verifiable multi-secret sharing scheme , 2007, Comput. Stand. Interfaces.

[11]  Hung-Yu Chien,et al.  A Practical ( t , n ) Multi-Secret Sharing Scheme , 2000 .

[12]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[13]  Kaijun Tan,et al.  Cheater identification in (t, n) threshold scheme , 1999, Comput. Commun..

[14]  G. Winskel.  What Is Discrete Mathematics , 2007 .

[15]  Jianzhong Zhang,et al.  A Secure and Efficient (t, n) Threshold Verifiable Multi-secret Sharing Scheme , 2005, CIS.

[16]  Chuntian Cheng,et al.  A New (t, n)-Threshold Multi-secret Sharing Scheme , 2005, CIS.

[17]  Nithin Nagaraj,et al.  How not to share a set of secrets , 2010, ArXiv.

[18]  Dieter Gollmann,et al.  Secret Sharing with Reusable Polynomials , 1997, ACISP.

[19]  Keith M. Martin,et al.  On Sharing Many Secrets (Extended Abstract) , 1994, ASIACRYPT.

[20]  Xian-Mo Zhang,et al.  Constructions of Cheating Immune Secret Sharing , 2001, ICISC.

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

[22]  Zhenfu Cao,et al.  A new efficient (t, n) verifiable multi-secret sharing (VMSS) based on YCH scheme , 2005, Appl. Math. Comput..

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

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

[25]  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).

[26]  Whitfield Diffie,et al.  Multiuser cryptographic techniques , 1976, AFIPS '76.

[27]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[28]  Massoud Hadian Dehkordi,et al.  An efficient threshold verifiable multi-secret sharing , 2008, Comput. Stand. Interfaces.

[29]  Josef Pieprzyk,et al.  On Cheating Immune Secret Sharing , 2004, Discret. Math. Theor. Comput. Sci..

[30]  Giovanni Di Crescenzo.  Sharing one secret vs. sharing many secrets: tight bounds on the average improvement ratio , 2000, SODA.

[31]  Wei-Hua He,et al.  Comment on Lin-Wu (t, n)-threshold verifiable multisecret sharing scheme , 2001 .

[32]  Giovanni Di Crescenzo.  Sharing one secret vs. sharing many secrets , 2003, Theor. Comput. Sci..

[33]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice , 1995 .

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

[35]  Min-Shiang Hwang,et al.  A (t, n) multi-secret sharing scheme , 2004, Appl. Math. Comput..

[36]  Yu-Min Wang,et al.  A New (t, n) Multi-Secret Sharing Scheme , 2005, 2008 International Conference on Computer and Electrical Engineering.

[37]  Chin-Chen Chang,et al.  An on-line secret sharing scheme for multi-secrets , 1998, Comput. Commun..

[38]  Tan Kai.  CHEATER IDENTIFICATION IN ( t,n ) THRESHOLD SCHEME , 1999 .

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

[40]  T.-C. Wu,et al.  (t,n) threshold verifiable multisecret sharing scheme based on factorisation intractability and discrete logarithm modulo a composite problems , 1999 .