The Mechanics of Compromising Low Entropy RSA Keys

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Presented at DEF CON 29 by

Over the past decade, there have been a number of research efforts (and DEFCON talks!) investigating the phenomenon of RSA keys on the Internet that share prime factors with other keys. This can occur when devices have poorly initialized sources of “randomness” when generating keys; making it trivial to factor the RSA modulus and recover the private key because, unlike large integer factorization, calculating the greatest common divisor (GCD) of two moduli can be fast and efficient. When describing their research, past hackers and researchers have attested that they “built a custom distributed implementation of Batch-GCD;” which seems like one hell of a detail to gloss over, right? This talk will detail a hacker's journey from understanding and implementing distributed batch GCD to analyzing findings from compromising RSA keys from network devices en masse.