A Survey: Shamir Threshold Scheme and Its Enhancements

This paper serves as an introduction to secret sharing scheme, 12 and it provides the fundamental understandings to the scheme from various 13 aspects. We first review the basics of a Shamir threshold scheme, and discuss 14 various enhancements so that the scheme can be proactive and verifiable. 15 We then show how a Shamir scheme can be extended to realize any general 16 access structure. We also point out the relationship between a Shamir scheme 17 and other topics such as error correction code, ramp scheme, information 18 disposal algorithm and multiparty computation. Finally, we briefly discuss 19 other platforms for its implementation. 20

[1]  Mitsuru Ito,et al.  Secret sharing scheme realizing general access structure , 1989 .

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

[3]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .

[4]  Li Xi-mei.  Verifiable Multi-secret Sharing Scheme , 2009 .

[5]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

[6]  Wang Yu-min.  (t, n) threshold secret sharing scheme based on RSA cryptosystem , 2005 .

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

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

[9]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[10]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[11]  Douglas R. Stinson,et al.  An explication of secret sharing schemes , 1992, Des. Codes Cryptogr..

[12]  Lin Guo-shun.  Security research of secret sharing schemes based on Hash function , 2006 .

[13]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[14]  Fei Ru.  Cheat-Proof Secret Share Schemes Based on RSA and One-Way Function , 2003 .

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

[16]  Hugo Krawczyk,et al.  Secret Sharing Made Short , 1994, CRYPTO.

[17]  Ian Goldberg,et al.  Improving the Robustness of Private Information Retrieval , 2007 .

[18]  조위덕.  Cryptography , 1987, The Official (ISC)2 SSCP CBK Reference.

[19]  Alfredo De Santis,et al.  On the Size of Shares for Secret Sharing Schemes , 1991, CRYPTO.

[20]  Delaram Kahrobaei,et al.  A Secret Sharing Scheme Based on Group Presentations and the Word Problem , 2012, IACR Cryptol. ePrint Arch..

[21]  F. Moore,et al.  Polynomial Codes Over Certain Finite Fields , 2017 .

[22]  Yehuda Lindell,et al.  Introduction to Modern Cryptography , 2004 .

[23]  Eyal Kushilevitz,et al.  Private information retrieval , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[24]  R. Cramer,et al.  Multiparty Computation, an Introduction , 2005 .

[25]  Dongho Won,et al.  New On-Line Secret Sharing Scheme Using Hash Function , 2003 .

[26]  Hugo Krawczyk,et al.  Proactive Secret Sharing Or: How to Cope With Perpetual Leakage , 1995, CRYPTO.

[27]  Josef Pieprzyk,et al.  Remarks on the multiple assignment secret sharing scheme , 1997, ICICS.

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

[29]  Mitsuru Ito,et al.  Multiple assignment scheme for sharing secret , 1993, Journal of Cryptology.

[30]  Neil J. A. Sloane,et al.  The theory of error-correcting codes (north-holland , 1977 .

[31]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[32]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[33]  Liu Huan-ping.  A Dynamic Secret Sharing Scheme Based on One-Way Function , 2002 .