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S. R. Tate, R. Vishwanathan, and S. Weeks. "Encrypted Secret Sharing and Analysis by Plaintext Randomization," Proceedings of the 16th Information Security Conference, 2013, pp. 49-65.
Abstract:
In this paper we consider the problem of secret sharing where shares are encrypted using a public-key encryption (PKE) scheme and ciphertexts are publicly available. While intuition tells us that the secret should be protected if the PKE is secure against chosen-ciphertext attacks (i.e., CCA-secure), formally proving this reveals some subtle and non-trivial challenges. We isolate the problems that this raises, and devise a new analysis technique called "plaintext randomization" that can successfully overcome these challenges, resulting in the desired proof. The encryption of different shares can use one key or multiple keys, with natural applications in both scenarios.
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