著者

KSCHISCHANG F. R.

雑誌

IEEE Transactions on Information Theory

巻号頁・発行日

vol.47, pp.498-519, 2001

被引用文献数

104 4314

著者

SHOKROLLAHI A.

雑誌

IEEE Transactions On Information Theory

巻号頁・発行日

vol.52, no.6, 2006

被引用文献数

13 1992

著者

Iwamoto Mitsugu Koga Hiroki Yamamoto Hirosuke

出版者

IEEE

雑誌

IEEE transactions on information theory (ISSN:00189448)

巻号頁・発行日

vol.58, no.9, pp.6194-6206, 2012-09

被引用文献数

1

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Coding theorems on a $(2,2)$-threshold scheme with an opponent are discussed in an asymptotic setup, where the opponent tries to impersonate one of the two participants. A situation is considered where $n$ secrets $S^{n}$ from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to $S^{n}$ with permitting negligible decoding error. We introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a $(2, 2)$-threshold scheme that is secure against the impersonation attack by the opponent. It is shown that if the correlation level between the two shares equals to $ell geq 0$, the minimum attainable rates coincide with $H(S)+ell $, where $H(S)$ denotes the entropy of the source, and the maximum attainable exponent of the success probability of the impersonation attack equals to $ell $. It is also shown that a simple scheme using an ordinary $(2,2)$-threshold scheme attains all the bounds as well.