**Multiparty Computation for Modulo Reduction without Bit-Decomposition and A Generalization to Bit-Decomposition**

*Chao Ning and Qiuliang Xu*

**Abstract: **Bit-decomposition, which is proposed by Damgård \emph{et al.}, is a powerful tool for multi-party computation (MPC). Given a sharing of secret $x$, it allows the parties to compute the sharings of the bits of $x$ 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 \emph{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 $x$ into the sharings of the digits of $x$, along with the sharings of the bits of every digit. The digits can be base-\emph{m} for any $m\geq2$. Obviously, when \emph{m} is a power of 2, this generalized protocol is just the original bit-decomposition protocol.

**Category / Keywords: **Secure Computation / Multiparty Computation, Constant-Rounds, Modulo Reduction, Generalization to Bit-Decomposition.

**Publication Info: **AsiaCrypt 2010. LNCS, vol 6477, pp. 483-500. Springer, Heidelberg (2010)

**Date: **received 8 May 2010, last revised 8 Mar 2011

**Contact author: **ncnfl at mail sdu edu cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20110308:133510 (All versions of this report)

**Short URL: **ia.cr/2010/266

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