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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,
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.