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Lousy Random Numbers Cause Insecure Public Keys

There's some excellent research (paper, news articles) surveying public keys in the wild. Basically, the researchers found that a small fraction of them (27,000 out of 7.1 million, or 0.38%) share a common factor and are inherently weak. The researchers can break those public keys, and anyone who duplicates their research can as well. The cause of this is almost certainly a lousy random number generator used to create those public keys in the first place. This shouldn't come as a surprise. One of the hardest parts of cryptography is random number generation. It's really easy to write a lousy random number generator, and it's not at all obvious that it is lousy. Randomness is a non-functional requirement, and unless you specifically test for it -- and know how to test for it -- you're going to think your cryptosystem is working just fine. (One of the reporters who called me about this story said that the researchers told him about a real-world random number generator that produced just seven different random numbers.) So it's likely these weak keys are accidental. It's certainly possible, though, that some random number generators have been deliberately weakened. The obvious culprits are national intelligence services like the NSA. I have no evidence that this happened, but if I were in charge of weakening cryptosystems in the real world, the first thing I would target is random number generators. They're easy to weaken, and it's hard to detect that you've done anything. Much safer than tweaking the algorithms, which can be tested against known test vectors and alternate implementations. But again, I'm just speculating here. What is the security risk? There's some, but it's hard to know how much. We can assume that the bad guys can replicate this experiment and find the weak keys. But they're random, so it's hard to know how to monetize this attack. Maybe the bad guys will get lucky and one of the weak keys will lead to some obvious way to steal money, or trade secrets, or national intelligence....

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Source: Schneier on Security - Thursday, 16 February


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