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**2009/263**

**Title:**

General Error Decodable Secret Sharing Scheme and Its Application

**Authors:**
Kaoru Kurosawa

**Abstract:**

Consider a model of secret sharing schemes with cheaters. We say that a secret sharing scheme is error decodable if we can still recover the secret s correctly from a noisy share vector ({\tt share}_1', \cdots, {\tt share}_n'). In this paper, we first prove that there exists an error decodable secret sharing scheme if and only if the adversary structure \Gamma satisfies a certain condition called Q^3. Next for any \Gamma which satisfies Q^3, we show an error decodable secret sharing scheme such that the decoding algorithm runs in polynomial-time in |S| and the size of a linear secret sharing scheme (monotone span program) which realzes \Gamma. We finally show an applicaiton to 1-round Perfectly Secure Message Transmission schemes (PSMT).

**ePrint:**
https://eprint.iacr.org/2009/263

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