A unified model for unconditionally secure key distribution

A key distribution scheme is a method by means of which a trusted party distributes pieces of information among a set of users in such a way that each group of them can compute a common key for secure communication. In this paper we present a model for unconditionally secure key distribution schemes, i.e., schemes whose security is independent of the power of the adversary. We prove lower bounds on the amount of information the trusted party has to generate and each user has to keep secret in such schemes, and we show that some previous unconditionally secure models for key distribution fall in our model. As a consequence, the lower bounds given in the literature for these models can be seen as corollaries of our results. Hence, the main contribution of the paper consists in pointing out a sort of common structure underlying some apparently different key distribution techniques.

[1]  Amos Beimel,et al.  Communication in key distribution schemes , 1996, IEEE Trans. Inf. Theory.

[2]  Douglas R. Stinson,et al.  Fault Tolerant and DistributedBroadcast Encryption , 2003, CT-RSA.

[3]  Reihaneh Safavi-Naini,et al.  A Secure Re-keying Scheme with Key Recovery Property , 2002, ACISP.

[4]  Andrew Chi-Chih Yao,et al.  The complexity of nonuniform random number generation , 1976 .

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

[6]  Avishai Wool,et al.  Long-Lived Broadcast Encryption , 2000, CRYPTO.

[7]  Jessica Staddon,et al.  Combinatorial properties of frameproof and traceability codes , 2001, IEEE Trans. Inf. Theory.

[8]  Li Gong,et al.  A matrix key-distribution scheme , 2005, Journal of Cryptology.

[9]  Amos Fiat,et al.  Dynamic Traitor Tracing , 2001, Journal of Cryptology.

[10]  Giovanni Di Crescenzo,et al.  Efficient Re-keying Protocols for Multicast Encryption , 2002, SCN.

[11]  Douglas R. Stinson,et al.  Multiple Key Distribution Maintaining User Anonymity via Broadcast Channels , 1995, J. Comput. Secur..

[12]  Jessica Staddon,et al.  Efficient Methods for Integrating Traceability and Broadcast Encryption , 1999, CRYPTO.

[13]  Moni Naor,et al.  Digital signets: self-enforcing protection of digital information (preliminary version) , 1996, STOC '96.

[14]  Wen-Tsuen Chen,et al.  Secure Broadcasting Using the Secure Lock , 1989, IEEE Trans. Software Eng..

[15]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[16]  Douglas R. Stinson,et al.  An Application of Ramp Schemes to Broadcast Encryption , 1999, Inf. Process. Lett..

[17]  Rolf Blom,et al.  An Optimal Class of Symmetric Key Generation Systems , 1985, EUROCRYPT.

[18]  Reihaneh Safavi-Naini,et al.  A Group Key Distribution Scheme with Decentralised User Join , 2002, SCN.

[19]  Amos Fiat,et al.  Broadcast Encryption , 1993, CRYPTO.

[20]  Carlo Blundo,et al.  The Key Establishment Problem , 2001, FOSAD.

[21]  Kaoru Kurosawa,et al.  Security of the Center in Key Distribution Schemes , 1994, ASIACRYPT.

[22]  Carles Padró,et al.  A Ramp Model for Distributed Key Distribution Schemes , 2001, Discret. Appl. Math..

[23]  Moni Naor,et al.  Multicast security: a taxonomy and some efficient constructions , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[24]  Amos Beimel,et al.  Interaction in Key Distribution Schemes (Extended Abstract) , 1993, CRYPTO.

[25]  Reihaneh Safavi-Naini,et al.  New constructions for multicast re-keying schemes using perfect hash families , 2000, CCS.

[26]  Matthew K. Franklin,et al.  Self-healing key distribution with revocation , 2002, Proceedings 2002 IEEE Symposium on Security and Privacy.

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

[28]  Chris J. Mitchell,et al.  Key storage in secure networks , 1988, Discret. Appl. Math..

[29]  Hideki Imai,et al.  On the Key Predistribution System: A Practical Solution to the Key Distribution Problem , 1987, CRYPTO.

[30]  Douglas R. Stinson,et al.  Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes , 1998, SIAM J. Discret. Math..

[31]  Paolo D'Arco.  On the Distribution of a Key Distribution Center , 2001, ICTCS.

[32]  Tsutomu Matsumoto,et al.  A Quick Group Key Distribution Scheme with "Entity Revocation" , 1999, ASIACRYPT.

[33]  Carlo Blundo,et al.  Space Requirements for Broadcast Encryption , 1994, EUROCRYPT.

[34]  Douglas R. Stinson,et al.  On Some Methods for Unconditionally Secure Key Distribution and Broadcast Encryption , 1997, Des. Codes Cryptogr..

[35]  Douglas R. Stinson,et al.  On Unconditionally Secure Robust Distributed Key Distribution Centers , 2002, ASIACRYPT.

[36]  Ran Canetti,et al.  Efficient Communication-Storage Tradeoffs for Multicast Encryption , 1999, EUROCRYPT.

[37]  Chin-Chen Chang,et al.  A conference key broadcasting system using sealed locks , 1992, Inf. Syst..

[38]  Amit Sahai,et al.  Coding Constructions for Blacklisting Problems without Computational Assumptions , 1999, CRYPTO.

[39]  Douglas R. Stinson,et al.  Trade-offs Between Communication and Storage in Unconditionally Secure Schemes for Broadcast Encryption and Interactive Key Distribution , 1996, CRYPTO.

[40]  John S. Baras,et al.  An Information Theoretic Analysis of Rooted-Tree Based Secure Multicast Key Distribution Schemes , 1999, CRYPTO.

[41]  Adi Shamir,et al.  The LSD Broadcast Encryption Scheme , 2002, CRYPTO.

[42]  Moni Naor,et al.  Revocation and Tracing Schemes for Stateless Receivers , 2001, CRYPTO.

[43]  Evangelos Kranakis,et al.  On key distribution via true broadcasting , 1994, CCS '94.

[44]  Douglas R. Stinson,et al.  Key Preassigned Traceability Schemes for Broadcast Encryption , 1998, Selected Areas in Cryptography.

[45]  Carles Padró,et al.  Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures , 2001, Theor. Comput. Sci..

[46]  Moni Naor,et al.  Distributed Pseudo-random Functions and KDCs , 1999, EUROCRYPT.

[47]  Douglas R. Stinson,et al.  Some New Results on Key Distribution Patterns and Broadcast Encryption , 1998, Des. Codes Cryptogr..

[48]  Shimshon Berkovits,et al.  How To Broadcast A Secret , 1991, EUROCRYPT.

[49]  Jirí Sgall,et al.  Efficient dynamic traitor tracing , 2000, SODA '00.

[50]  Jessica Staddon,et al.  Combinatorial Bounds for Broadcast Encryption , 1998, EUROCRYPT.

[51]  Matthew K. Franklin,et al.  An Efficient Public Key Traitor Tracing Scheme , 1999, CRYPTO.

[52]  Reihaneh Safavi-Naini,et al.  Sequential Traitor Tracing , 2000, CRYPTO.

[53]  Moti Yung,et al.  Perfectly Secure Key Distribution for Dynamic Conferences , 1992, Inf. Comput..

[54]  Moni Naor,et al.  Efficient Trace and Revoke Schemes , 2000, Financial Cryptography.

[55]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[56]  Dawn Xiaodong Song,et al.  ELK, a new protocol for efficient large-group key distribution , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[57]  Chi-Sung Laih,et al.  A new threshold scheme and its application in designing the conference key distribution cryptosystem , 1989, Inf. Process. Lett..

[58]  Birgit Pfitzmann,et al.  Trials of Traced Traitors , 1996, Information Hiding.

[59]  Douglas R. Stinson,et al.  Generalized Beimel-Chor Schemes for Broadcast Encryption and Interactive Key Distribution , 1998, Theor. Comput. Sci..

[60]  Aggelos Kiayias,et al.  Traitor Tracing with Constant Transmission Rate , 2002, EUROCRYPT.

[61]  Carlo Blundo,et al.  A tau-Restricted Key Agreement Scheme , 1999, Comput. J..

[62]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.