International Association for Cryptologic Research

International Association
for Cryptologic Research


Multiparty Generation of an RSA Modulus

Megan Chen
Jack Doerner
Yashvanth Kondi
Eysa Lee
Schuyler Rosefield
Abhi Shelat
Ran Cohen
DOI: 10.1007/s00145-021-09395-y
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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.
  title={Multiparty Generation of an RSA Modulus},
  journal={Journal of Cryptology},
  author={Megan Chen and Jack Doerner and Yashvanth Kondi and Eysa Lee and Schuyler Rosefield and Abhi Shelat and Ran Cohen},