Factoring RSA keys from certified smart cards: Coppersmith in the wild

Abstract

This paper explains 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. This is the same type of computation that was used last year by two independent teams (USENIX Security 2012: Heninger, Durumeric, Wustrow, Halderman; Crypto 2012: Lenstra, Hughes, Augier, Bos, Kleinjung, Wachter) to factor tens of thousands of cryptographic keys on the Internet. The remaining 81 keys do not share primes. Factoring these 81 keys requires taking deeper advantage of randomness-generation failures: first using the shared primes as a springboard to characterize the failures, and then using Coppersmith-type partial-key-recovery attacks. This is the first successful public application of Coppersmith-type attacks to keys found in the wild.

DOI: 10.1007/978-3-642-42045-0_18
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@inproceedings{Bernstein2013FactoringRK, title={Factoring RSA keys from certified smart cards: Coppersmith in the wild}, author={Daniel J. Bernstein and Yun-An Chang and Chen-Mou Cheng and Li-Ping Chou and Nadia Heninger and Tanja Lange and Nicko van Someren}, booktitle={IACR Cryptology ePrint Archive}, year={2013} }