Why isn't the first factor just 3 then?
Why isn't the first factor just 3 then?
But any "primes" being used should have some serious factorisation algorithms run over them before being used, so this is really embarrassing.
EDIT
And to answer contravariant's question[0]:
Also, shouldn't it only
have 2 prime factors?
It's possible that one of the "primes" it found was in fact composite, and it's that "prime" that has these factors. So you generate two large primes and multiply them together, not realising that one of your "primes" wasn't.These primes could not have been generated by any reputable prime generation algos that I can imagine.
This signals to me that both the keys are corrupted/bad to have really small prime factors (3, 7 and 11).
I have taken courses on discrete math, cryptography and read a few prime generation algos. Its a standard first step to check numbers against primes upto a million or so (nowadays, a billion). No prime generation algo I can imagine generated these keys.
Unless, by some incredible fluke, they managed to find a carmichael number.
IIRC PKCS#1 even supports more than two modulus factors in it's private key format (not that it is particularly useful for anything).