International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2010: Advances in Cryptology - ASIACRYPT 2010 pp 483-500

# Multiparty Computation for Modulo Reduction without Bit-Decomposition and a Generalization to Bit-Decomposition

• Chao Ning
• Qiuliang Xu
Conference paper

DOI: 10.1007/978-3-642-17373-8_28

Volume 6477 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Ning C., Xu Q. (2010) Multiparty Computation for Modulo Reduction without Bit-Decomposition and a Generalization to Bit-Decomposition. In: Abe M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg

## Abstract

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.

### Keywords

Multiparty ComputationConstant-RoundsModulo ReductionGeneralization to Bit-Decomposition