[cryptography] Duplicate primes in lots of RSA moduli

Adam Back adam at cypherspace.org
Sat Feb 18 04:40:48 EST 2012

I also was pondering as to how the implementers could have arrived at
this situation towards evaluating Stephen Farrell's draft idea to have
a service that double checks at key gen time (that none of the p, q
values are reused).  http://www.ietf.org/id/draft-farrell-kc-00.txt

(Which I dont think is nearly robust enough for relying on, but doesnt
hurt as a sanity check that will catch a small percentage of entropy

So then what *could* have gone wrong?

1. (most generous) they had a rng that accounted for entropy
estimation, waited until it had the target amount (eg 128-bits
minimum) and then generated p, q BUT there was an overestimate of the
entropy, it was MUCH worse than estimated

2. they didnt bother estimating entropy, the system clock was not set
or it didnt have one and/or they didnt use it or used memory state
after boot from rom or something predictable enough to show the
collision rate.  (aka incompetence)

3. your idea -- maybe -- more incompetent things have happened :)

Occam's razor suggests cryptographic incompetence.. number one reason
deployed systems have crypto fails.  Who needs to hire crypto people,
the developer can hack it together, how hard can it be etc.  There's a
psychological theory of why this kind of thing happens in general -
the Dunning-Kruger effect.  But maybe 1 happened.


[1] http://en.wikipedia.org/wiki/Dunning–Kruger_effect

On 18 February 2012 07:57, Peter Gutmann <pgut001 at cs.auckland.ac.nz> wrote:
> Adam Back <adam at cypherspace.org> writes:
>>Further the fact that the entropy seeding is so bad that some implementations
>>are generating literally the same p value (but seemingly different q values)
>>I would think you could view the fact that this can be detected and
>>efficiently exploited via batch GCD as an indication of an even bigger
> Do we know that this is accidental rather than deliberate?  A cute
> "optimisation" for keygen would be to only randomly generate one half of the
> {p,q} pair.  It's plenty of randomness after all, surely you don't really need
> both to be generated randomly, only one will do, and it'll halve the keygen
> time...
> Peter.

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