# 研究成果

#### 国際会議

• ##### Coding Theorems for a (2, 2)–Threshold Scheme Secure against Impersonation by an Opponent
著者
H. Koga, M. Iwamoto, and H. Yamamoto
会議名
IEEE ITW 2009
ページ
188–192
出版社
IEEE
発行年
2009
発表日
Oct. 11–16, 2009
###### Abstract

In this paper, we focus on a (2,2)-threshold scheme in the presence of an opponent who impersonates one of the two participants. We consider an asymptotic setting where two shares are generated by an encoder blockwisely from an n-tuple of secrets generated from a stationary memoryless source and a uniform random number available only to the encoder. We introduce a notion of correlation level of the two shares and give coding theorems on the rates of the shares and the uniform random number. It is shown that, for any (2,2)-threshold scheme with correlation level r, none of the rates can be less than H(S) + r, where H(S) denotes the entropy of the source. We also show that the impersonation by the opponent is successful with probability at least 2-nr+o(n). In addition, we prove the existence of an encoder and a decoder of the (2, 2)-threshold scheme that asymptotically achieve all the bounds on the rates and the success probability of the impersonation.