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I want to break square-free: The 4p-1 factorization method and its RSA backdoor viability [SeCrypt 2019]

Authors: Vladimir Sedlacek, Dusan Klinec, Marek Sys, Petr Svenda, Vashek Matyas

Primary contact: Vladimir Sedlacek vlada.sedlacek@mail.muni.cz

Abstract: In this paper, we analyze Cheng's $4p-1$ factorization method as the means of a potential backdoor for the RSA primes generated inside black-box devices like cryptographic smartcards and we devise three detection methods for such a backdoor. We also audit 44 millions of RSA keypairs generated by 18 different types of cryptographic devices. Finally, we offer an improved, simplified and asymptotically deterministic version of the method, together with a deeper analysis of its performance and we publish a Sage implementation.

TODO: Add bibtex, links to the paper and the preprint, add the datasets