A security flaw in Infineon smart cards and TPMs allows an attacker to recover private keys from the public keys. Basically, the key generation algorithm sometimes creates public keys that are vulnerable to Coppersmith’s attack:
While all keys generated with the library are much weaker than they should be, it’s not currently practical to factorize all of them. For example, 3072-bit and 4096-bit keys aren’t practically factorable. But oddly enough, the theoretically stronger, longer 4096-bit key is much weaker than the 3072-bit key and may fall within the reach of a practical (although costly) factorization if the researchers’ method improves.
To spare time and cost, attackers can first test a public key to see if it’s vulnerable to the attack. The test is inexpensive, requires less than 1 millisecond, and its creators believe it produces practically zero false positives and zero false negatives. The fingerprinting allows attackers to expend effort only on keys that are practically factorizable.
This is the flaw in the Estonian national ID card we learned about last month.
The paper isn’t online yet. I’ll post it when it is.
Ouch. This is a bad vulnerability, and it’s in systems — like the Estonian national ID card — that are critical.
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