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Re: fyi-- [dns-operations] early key rollover for dlv.isc.org

  • From: Joseph S D Yao
  • Date: Fri Sep 22 19:35:02 2006

On Thu, Sep 21, 2006 at 01:37:40PM -0400, Steven M. Bellovin wrote:
> On 21 Sep 2006 17:01:45 +0000, Paul Vixie <vixie@vix.com> wrote:
> > > Paul, what exponent does the new key use?  (I clicked on the public key
> > > link, but I can't decode the base64 that easily...)
> > 
> > it was made with bind9's "dnssec-keygen" utility, using the -e option, so...
> > 
> >     -e use large exponent (RSAMD5/RSASHA1 only)
> > 
> > ...hopefully it's a good exponent.  (every few years someone tries to explain
> > to me what a key exponent is, i think you steve have tried, but it just doesn't
> > stick.)
> 
> It's pretty simple, if you don't want to understand why it works...


;-)

Not having committed the maths to heart, I might be able to explain it a
little differently.

Paul, I think you know the basic idea of what an exponent is.  If you're
raising one number to a certain power (say, 127 to the fifth power),
then the power (5 in this example) is the exponent.  127^5 or 127**5 are
ways in various of the thousands of computer languages in existence for
expressing this.  Many more languages just use functions.

This exponent is used to encrypt or sign, by taking numbers calculated
from what you want to encrypt, raising each one to the (exponent)th
power, and doing a number of other mathematical operations on them.  It
matters what exponent you use.  A bigger exponent isn't necessarily
better - remember, I haven't committed the maths to heart, but I do
recall Don Knuth's warning about choosing such numbers arbitrarily.  

Steve has pointed out that 3 is recommended for DNSSEC, and NIST likes
65537 [2^16 + 1].  I don't have the maths to say why, so I'll leave it
at that.

;-)


-- 
Joe Yao
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