Comparing Security Notions of Secret Sharing Schemes

Different security notions of secret sharing schemes have been proposed by different information measures. Entropies, such as Shannon entropy and min entropy, are frequently used in the setting security notions for secret sharing schemes. Different to the entropies, Kolmogorov complexity was also defined and used in study the security of individual instances for secret sharing schemes. This paper is concerned with these security notions for secret sharing schemes defined by the variational measures, including Shannon entropy, guessing probability, min entropy and Kolmogorov complexity.

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

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

[3]  Ehud D. Karnin,et al.  On secret sharing systems , 1983, IEEE Trans. Inf. Theory.

[4]  Luis Filipe Coelho Antunes,et al.  Entropy Measures vs. Kolmogorov Complexity , 2011, Entropy.

[5]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[6]  G. R. Blakley,et al.  Secret Sharing Schemes , 2011, Encyclopedia of Cryptography and Security.

[7]  Alfredo De Santis,et al.  On the size of shares for secret sharing schemes , 1991, Journal of Cryptology.

[8]  Junji Shikata,et al.  Information Theoretic Security for Encryption Based on Conditional Rényi Entropies , 2013, ICITS.

[9]  Junji Shikata,et al.  Secret sharing schemes based on min-entropies , 2014, 2014 IEEE International Symposium on Information Theory.

[10]  Douglas R. Stinson,et al.  Decomposition constructions for secret-sharing schemes , 1994, IEEE Trans. Inf. Theory.

[11]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

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

[13]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[14]  Alexandre Pinto,et al.  Comparing Notions of Computational Entropy , 2007, Theory of Computing Systems.

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

[16]  Tarik Kaced,et al.  Almost-perfect secret sharing , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[17]  Shaoquan Jiang.  On Unconditional ϵ-Security of Private Key Encryption , 2014, Comput. J..

[18]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences , 1966, JACM.

[19]  Mitsugu Iwamoto,et al.  Security notions for information theoretically secure encryptions , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[20]  Paul M. B. Vitányi,et al.  Shannon Information and Kolmogorov Complexity , 2004, ArXiv.

[21]  Luis Filipe Coelho Antunes,et al.  Cryptographic Security of Individual Instances , 2007, ICITS.

[22]  Reihaneh Safavi-Naini,et al.  Guessing Secrecy , 2012, ICITS.

[23]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..