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Journal of Inforamtion Science and Engineering, Vol.7 No.1, pp.13-23 (March 1991)
Dynamic Threshold Scheme Based on the Definition of
Cross-Product in an N-Dimensional Linear Space*

Chi-Sung Laih, Lein Harn+, Jau-Yien Lee and Tzonlih Hwang#
Department of Electrical Engineering
National Cheng Kung University
Tainan, Taiwan, Republic of China
+Computer Science Program,
University of Missouri-Kansas City
Kansas City, MO 64110, U.S.A.
# Institute of Information Engineering
National Cheng Kung University
Tainan, Taiwan, Republic of China

This paper investigates the characterizations of threshold/ramp schemes which give rise to time-dependent threshold schemes. These schemes are called "dynamic threshold schemes" as compared to the conventional time-independent threshold cheme. In a (d, m, n, T) dynamic threshold scheme, there are n secret shadows and a public shadow, pj, at time t=tj 1tjT. After determining any m shadows, mn, and the public shadow, pj, we can easily recover d master keys, Kj1,Kj2,..., and Kjd. Furthermore, if the d master keys have to be changed to K1j-1,K2j-1,..., and Kdj-1 for some security reasons, only the public shadow, pj, has to be changed to pj+1. All the n secret shadows issued initially remain unchanged. Compared to the conventional threshold/ramp schemes, at least one of the previously issued n shadows needs to be changed whenever the master keys need to be updated for security reasons. A (1, m, n, T) dynamic threshold scheme based on the definition of cross-product in an N-dimensional linear space is proposed to illustrate the characterizations of the dynamic threshold schemes.

Keywords: threshold scheme, key safeguarding scheme, secret sharing scheme, cross product, conference key distribution system, cryptography

Received December 15, 1989; revised July 19, 1990.
Communicated by Lin-Shan Lee.
*Parts of this paper has been presented in CRYPTO'89, August 20-24, 1989, UCSB, USA, sponsored by the International Association for Cryptologic Research (IACR) and IEEE Computer Society Technical Committee on Security and Privacy.
This work was supported by the National Science Council, R.O.C., under contract NSC79-0408-E-006-02.