Cryptology ePrint Archive: Report 2019/334

Practically Efficient Secure Distributed Exponentiation without Bit-Decomposition

Abdelrahaman Aly and Aysajan Abidin and Svetla Nikova

Abstract: Bit-decomposition is a powerful tool which can be used to design constant round protocols for bit-oriented multiparty computation (MPC) problems, such as comparison and Hamming weight computation. However, protocols that involve bit-decomposition are expensive in terms of performance. In this paper, we introduce a set of protocols for distributed exponentiation without bit-decomposition. We build upon the current state-of-the-art by Ning and Xu [ASIACRYPT 2010 & ASIACRYPT 2011], in terms of round and multiplicative complexity. We consider different cases where the inputs are either private or public and present privacy-preserving protocols for each case. Our protocols offer perfect security against passive and active adversaries and have constant multiplicative and round complexity, for any fixed number of parties. Furthermore, we showcase how these primitives can be used, for instance, to perform secure distributed decryption for some public key schemes, that are based on modular exponentiation.

Category / Keywords: applications / applied secure multiparty computation, distributed exponentiation, applied cryptography

Original Publication (with minor differences): Financial Cryptography 2018

Date: received 27 Mar 2019

Contact author: abdelrahaman aly at esat kuleuven be

Available format(s): PDF | BibTeX Citation

Note: We have added some small adaptations for the case where both the exponent and the base are secret shared on the same Z_q. And we want to make this version of our paper available for the community.

Version: 20190403:015753 (All versions of this report)

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