A Linear Algebraic Approach to Metering Schemes

A metering scheme is a method by which an audit agency is able to measure the interaction between servers and clients during a certain number of time frames. Naor and Pinkas (Vol. 1403 of LNCS, pp. 576–590) proposed metering schemes where any server is able to compute a proof (i.e., a value to be shown to the audit agency at the end of each time frame), if and only if it has been visited by a number of clients larger than or equal to some threshold h during the time frame. Masucci and Stinson (Vol. 1895 of LNCS, pp. 72–87) showed how to construct a metering scheme realizing any access structure, where the access structure is the family of all subsets of clients which enable a server to compute its proof. They also provided lower bounds on the communication complexity of metering schemes. In this paper we describe a linear algebraic approach to design metering schemes realizing any access structure. Namely, given any access structure, we present a method to construct a metering scheme realizing it from any linear secret sharing scheme with the same access structure. Besides, we prove some properties about the relationship between metering schemes and secret sharing schemes. These properties provide some new bounds on the information distributed to clients and servers in a metering scheme. According to these bounds, the optimality of the metering schemes obtained by our method relies upon the optimality of the linear secret sharing schemes for the given access structure.

[1]  Annalisa De Bonis,et al.  Dynamic Multi-threshold Metering Schemes , 2000, Selected Areas in Cryptography.

[2]  Barbara Masucci,et al.  Efficient metering schemes with pricing , 2001, IEEE Trans. Inf. Theory.

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

[4]  B. Masucci,et al.  New bounds on the communication complexity of metering schemes , 2002, Proceedings IEEE International Symposium on Information Theory,.

[5]  Annalisa De Bonis,et al.  Bounds and constructions for metering schemes , 2002, Commun. Inf. Syst..

[6]  Gustavus J. Simmons,et al.  How to (Really) Share a Secret , 1988, CRYPTO.

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

[8]  Barbara Masucci,et al.  Metering Schemes for General Access Structures , 2000, ESORICS.

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

[10]  Moni Naor,et al.  Secure and Efficient Metering , 1998, EUROCRYPT.

[11]  Matthew K. Franklin,et al.  Auditable Metering with Lightweight Security , 1997, J. Comput. Secur..

[12]  Josh Benaloh,et al.  Generalized Secret Sharing and Monotone Functions , 1990, CRYPTO.

[13]  Stelvio Cimato,et al.  A note on optimal metering schemes , 2002, Inf. Process. Lett..

[14]  Barbara Masucci,et al.  Eecient Metering Schemes with Pricing , 2000 .

[15]  Markus Jakobsson,et al.  Secure and Lightweight Advertising on the Web , 1999, Comput. Networks.

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

[17]  Dahlia Malkhi,et al.  Auditable metering with lighweight security , 1998 .

[18]  A. De Bonis,et al.  An information theoretic approach to metering schemes , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[19]  Moni Naor,et al.  Secure Accounting and Auditing on the Web , 1998, Comput. Networks.

[20]  Keith M. Martin,et al.  Geometric secret sharing schemes and their duals , 1994, Des. Codes Cryptogr..

[21]  Ernest F. Brickell,et al.  Some Ideal Secret Sharing Schemes , 1990, EUROCRYPT.

[22]  Benny Pinkas,et al.  Secure and Eecient Metering , 1998 .

[23]  Carles Padró,et al.  Secret sharing schemes with bipartite access structure , 2000, IEEE Trans. Inf. Theory.

[24]  Annalisa De Bonis,et al.  Metering Schemes with Pricing , 2000, DISC.

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

[26]  Avi Wigderson,et al.  On span programs , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[27]  Alfredo De Santis,et al.  Tight Bounds on the Information Rate of Secret Sharing Schemes , 1997, Des. Codes Cryptogr..