Re: I don't know PAIN...

Jerrold Leichter <jerrold.leichter@xxxxxxxxxx> writes:

> | > "Note that there is no theoretical reason that it should be
> | > possible to figure out the public key given the private key,
> | > either, but it so happens that it is generally possible to
> | > do so"
> | >
> | > So what's this "generally possible" business about?
> |
> | Well, AFAIK its always possible, but I was hedging my bets :-) I can
> | imagine a system where both public and private keys are generated from
> | some other stuff which is then discarded.
> That's true of RSA!  The public and private keys are indistinguishable - you
> have a key *pair*, and designate one of the keys as public.  Computing either
> key from the other is as hard as factoring the modulus.  (Proof:  Given both
> keys in the pair, it's easy to factor.)

It's worth pointing out that this isn't how RSA is used in practice,
for two reasons:

(1) Most everyone uses one of 3 popular RSA public exponents
    (3, 17, 65535) and then computes the private key from p and q.
(2) PKCS-1 RSAPrivateKey structures contain the public key.

-Ekr

-- 
[Eric Rescorla                                   ekr@xxxxxxxx]
                http://www.rtfm.com/

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