Secret Sharing Schemes with Conversion Protocol to Achieve Short Share-Size and Extendibility to Multiparty Computation

Secret sharing scheme (SSS) has been extensively studied since SSSs are important not only for secure data storage but also as the fundamental building block for many cryptographic protocols such as multiparty computation (MPC). Although both code efficiency and application of MPC are important for SSSs, it is difficult to satisfy both. There have been many studies about MPC on Shamir’s and replicated SSS while their share size is large, and computationally secure SSS and a ramp scheme have a short share size while there have been few studies concerning their MPC. We propose a new computational SSS, and show how to convert shares of our SSS and a ramp SSS to those of multiparty-friendly SSS such as Shamir’s and replicated SSS. This enables one to secretly-share data compactly and extend secretly-shared data to MPC if needed.

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