Welcome to the resource topic for 2022/1632
Title:
Cryptography with Weights: MPC, Encryption and Signatures
Authors: Sanjam Garg, Abhishek Jain, Pratyay Mukherjee, Rohit Sinha, Mingyuan Wang, Yinuo Zhang
Abstract:The security of several cryptosystems rests on the trust assumption that a certain fraction of the parties are honest. This trust assumption has enabled a diverse of cryptographic applications such as secure multiparty computation, threshold encryption, and threshold signatures. However, current and emerging practical use cases suggest that this paradigm of
one-person-one-vote is outdated.
In this work, we consider {\em 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. Specifically, our proposed schemes incur only an {\em additive} overhead in weights.
\begin{itemize}
\item We first present a weighted ramp secret-sharing scheme where the size of the secret share is as short as O(w) (where w corresponds to the weight). In comparison, Shamir’s secret sharing with virtualization requires secret shares of size w\cdot\lambda, where \lambda=\log |\mathbb{F}| is the security parameter.
\item Next, we use our weighted secret-sharing scheme to construct weighted versions of (semi-honest) secure multiparty computation (MPC), threshold encryption, and threshold signatures. All these schemes inherit the efficiency of our secret sharing scheme and incur only an additive overhead in the weights.
\end{itemize}
Our weighted secret-sharing scheme is based on the Chinese remainder theorem. Interestingly, this secret-sharing scheme is {\em 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.
ePrint: https://eprint.iacr.org/2022/1632
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