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In this paper, the authors explain how an attacker can efficiently factor 184 distinct RSA keys out of more than two million 1024-bit RSA keys downloaded from Taiwan's national \"Citizen digital certificate\" database. These keys were generated by government-issued smart cards that have built-in hardware random-number generators and that are advertised as having passed FIPS 140-2 Level 2 certification. These 184 keys include 103 keys that share primes and that are efficiently factored by a batch-GCD computation.
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