Cryptology ePrint Archive: Report 2020/370

Multiparty Generation of an RSA Modulus

Megan Chen and Ran Cohen and Jack Doerner and Yashvanth Kondi and Eysa Lee and Schuyler Rosefield and abhi shelat

Abstract: We present a new multiparty protocol for the distributed generation of biprime RSA moduli, with security against any subset of maliciously colluding parties assuming oblivious transfer and the hardness of factoring.

Our protocol is highly modular, and its uppermost layer can be viewed as a template that generalizes the structure of prior works and leads to a simpler security proof. We introduce a combined sampling-and-sieving technique that eliminates both the inherent leakage in the approach of Frederiksen et al. (Crypto'18), and the dependence upon additively homomorphic encryption in the approach of Hazay et al. (JCrypt'19). We combine this technique with an efficient, privacy-free check to detect malicious behavior retroactively when a sampled candidate is not a biprime, and thereby overcome covert rejection-sampling attacks and achieve both asymptotic and concrete efficiency improvements over the previous state of the art.

Category / Keywords: cryptographic protocols / threshold cryptography, multi-party computation, RSA, biprime sampling, concrete efficiency

Date: received 30 Mar 2020, last revised 26 Apr 2020

Contact author: j at ckdoerner net

Available format(s): PDF | BibTeX Citation

Version: 20200426:184958 (All versions of this report)

Short URL: ia.cr/2020/370


[ Cryptology ePrint archive ]