Password-Protected Secret-Sharing (PPSS) schemes (parameterized by t and n) are a type of cryptographic protocols executed by a user and n servers, where the user shares a secret key (which in turn protects some secret information) among the servers and can reconstruct the key by interacting with t + 1 servers later. Any efficient adversary who breaks into t servers learns no information about the user's key. In this work, we take an existing PPSS scheme and improve it in terms of computational costs. We analyze the security of the new scheme in detail.
The PPSS scheme uses a functionality called Oblivious PRF (OPRF) as a crucial block. In addition, OPRF itself might be of interest in other areas. We formalize this OPRF functionality in the Universal-Composability (UC) framework, and realize it efficiently. This forms an improvement of a previous realization. We reduce the computational costs significantly, without changing the basic functions of OPRF.