Bit-decomposition, which is proposed by Damgård et al., is a powerful tool for multi-party computation (MPC). Given a sharing of secret a, it allows the parties to compute the sharings of the bits of a in constant rounds. With the help of bit-decomposition, constant-rounds protocols for various MPC problems can be constructed. However, bit-decomposition is relatively expensive, so constructing protocols for MPC problems without relying on bit-decomposition is a meaningful work. In multi-party computation, it remains an open problem whether the modulo reduction problem can be solved in constant rounds without bit-decomposition. In this paper, we propose a protocol for (public) modulo reduction without relying on bit-decomposition. This protocol achieves constant round complexity and linear communication complexity. Moreover, we show a generalized bit-decomposition protocol which can, in constant rounds, convert the sharing of secret a into the sharings of the digits of a, along with the sharings of the bits of every digit. The digits can be base-m for any m ≥ 2. © 2010 International Association for Cryptologic Research.
CITATION STYLE
Ning, C., & Xu, Q. (2010). Multiparty computation for modulo reduction without bit-decomposition and a generalization to bit-decomposition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6477 LNCS, pp. 483–500). Springer Verlag. https://doi.org/10.1007/978-3-642-17373-8_28
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