一种可检测假冒攻击的（2，2）-门限方案的编码定理
Coding Theorems for a (2,2)-Threshold Scheme with Detectability of Impersonation Attacks
摘要：
在本文中，我们讨论的编码定理的$(2, 2)$ -阈值计划的存在下，一个对手谁冒充的两个股东之一，在一个渐进的设置。我们考虑的情况下，$n$秘密$S^n$从一个无记忆的来源是分块编码到两个份额和两个份额被解码到$S^n$允许可忽略的解码错误。我们引入相关水平的两个份额和描述的最低可达率的份额和一个统一的随机数实现的$(2, 2)$ -门限方案，是安全的，对模仿攻击的对手。结果表明，当两个份额之间的相关性水平等于$\ell \ge 0$时，最小可达速率与$H(S)+\ell$一致，其中$H(S)$表示源的熵，模仿攻击成功概率的最大可达指数等于$\ell$ .我们还给出了一个简单的构造的编码器和解码器使用普通的$(2,2)$ -阈值方案，其中两个份额是相关的，并达到所有的界限。
英文摘要：
In this paper, we discuss coding theorems on a $(2, 2)$--threshold scheme in the presence of an opponent who impersonates one of the two shareholders in an asymptotic setup. We consider a situation 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 an opponent. It is shown that, if the correlation level between the two shares equals to an $\ell \ge 0$, 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 $\ell$. We also give a simple construction of an encoder and a decoder using an ordinary $(2,2)$--threshold scheme where the two shares are correlated and attains all the bounds.
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