Secret sharing schemes which are secure under the presence of malicious participants who forge their shares have been investigated by many researchers so far. In this paper we consider a secret sharing scheme with a key at an encoder and a decoder and analyze its security against the substitution attack by malicious participants. We first give conditions that the secret snaring scheme with a key must satisfy. Next, we construct a simple secret sharing scheme with a key that generates n shares and detects forged shares with high probability. We can prove that, if at most n - 1 malicious participants collude and try to deceive the other participants by forged shares optimally, the success probability of such an attack is upper-bounded by |S|-1/(|x|-1), where |S| and |X| denote the sizes of the secret and the n shares, respectively. In addition, we investigate basic properties of the scheme especially for the case of n = 2.
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机译：秘密共享计划根据许多研究人员调查了伪造股票的恶意参与者的存在。在本文中，我们考虑了一个秘密共享方案，在编码器和解码器处具有密钥，并通过恶意参与者对其对替代攻击的安全性进行分析。我们首先给出一个带有关键的秘密咆哮方案必须满足的条件。接下来，我们构建一个简单的秘密共享方案，一个键生成n个共享，并检测具有高概率的伪符。我们可以证明，如果最多的N - 1恶意参与者最佳地通过伪造的股票拼凑而成，那么这种攻击的成功概率是上限的| s | -1 /（| x | -1 ），其中o | s |和| x |表示秘密和n股的规模。此外，我们研究了该方案的基本性质，特别是对于n = 2的情况。
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