Slashdot Mirror
Factorable Keys: Twice As Many, But Half As Bad
J. Alex Halderman and Nadia Heninger write in with an update to yesterday's story on RSA key security: "Yesterday Slashdot posted that RSA keys are 99.8%
secure in the real world. We've been working on this
concurrently, and as it turns out, the story is a bit more
complicated. Those factorable keys are generated by your router and
VPN, not bankofamerica.com. The geeky details are pretty nifty: we
downloaded every SSL and SSH keys on the internet in a few days, did
some math on 100 million digit numbers, and ended up with 27,000
private keys. (That's 0.4% of SSL keys in current use.) We posted a
long
blog post summarizing our findings over at Freedom to Tinker."
So how do you go about matching one of the keys that you guessed and a specific users session? What's more, how do you do that before the key changes? I can guess a password is "fishmonkeywrinkles", but without a matching account that wont do much good.
"Have you ever thought about just turning off the TV, sitting down with your kids, and hitting them?"
Ah, I see. You regularly work with the product of all of the moduli gathered, which would be a fairly large number.
If you have a shit pseudo entropy generator, the keys you generate will be easy to factor because they will share one common prime factor (recall that key security depends on the computational intractability of factoring large numbers). This is called a related-key attack and has (so far) been responsible only for the demise of WEP.
As it turns out, OpenSSH/SSL has a shit PRNG which makes private keys generated with it recoverable using only the public keys, in some implementations and usage scenarios. Together, these amount to 0.4% of ALL public keys currently available on the open 'Net.
Something bad is coming when people are suddenly anxious to tell the truth.
As it turns out, OpenSSH/SSL has a shit PRNG
AFAIK, OpenSSL gets its entropy from the operating system. If the OS has no good source of entropy, like on the embedded devices mentioned in the article, it doesn't matter what library you use to generate your keys, they will alway be predictable and therefore weak.
The article makes no mention of keys generated on non-embedded devices being weak, so it's probably safe to assume that generating a key on a desktop or server with decent entropy sources using OpenSSL is secure.