Cryptography with Weights: MPC, Encryption and Signatures.

The security of many powerful cryptographic systems such as secure multiparty computation, threshold encryption, and threshold signatures rests on trust assumptions about the parties. The de-facto model treats all parties equally and requires that a certain fraction of the parties are honest. While this paradigm of one-person-one-vote has been very successful over the years, current and emerging practical use cases suggest that it is outdated. In this work, we consider weighted cryptosystems where every party is assigned a certain weight and the trust assumption is that a certain fraction of the total weight is honest. This setting can be translated to the standard setting (where each party has a unit weight) via virtualization. However, this method is quite expensive, incurring a multiplicative overhead in the weight. We present new weighted cryptosystems with significantly better efficiency: our proposed schemes incur only an additive overhead in weights. We first present a weighted ramp secret-sharing scheme (WRSS) where the size of a secret share is O ( w ) (where w corresponds to the weight). In comparison, Shamir’s secret sharing with virtualization requires secret shares of size w · λ , where λ = log | F | is the security parameter. Next, we use our WRSS to construct weighted versions of (semi-honest) secure multiparty computation (MPC), threshold encryption, and threshold signatures. All these schemes inherit the efficiency of our WRSS and incur only an additive overhead in weights. Our WRSS is based on the Chinese remainder theorem-based secret-sharing scheme. Interestingly, this secret-sharing scheme is non-linear and only achieves statistical privacy. These distinct features introduce several technical hurdles in applications to MPC and threshold cryptosystems. We resolve these challenges by developing several new ideas.