NODE 6bd5ebbfThe exponent of the RSA public key must be odd.??
Luis Saiz <LSaiz@atos-ods.com>Thu, 28 May 1998 01:21:02 -0700 (PDT)
OS/390 Integrated Cryptographic Service Facility Application
Programmer's Guide Version 2 Release 5 Publication No. SC23-3976-02 :
http://ppdbooks.pok.ibm.com:80/cgi-bin/bookmgr/bookmgr.cmd/DOCNUM/SC23-3976/CCONTENTS
In several parts of the document it's specified that, as a restriction:
> The exponent of the RSA public key must be odd.
>
It's there any (unknown to me) security reason to be this way, or its
an implementation/standard option??
NODE eeb6c255Re: The exponent of the RSA public key must be odd.??
Sunder <sunder@brainlink.com>Thu, 28 May 1998 07:41:57 -0700 (PDT)
How many prime numbers do you know of that are even?
Luis Saiz wrote:
>
> OS/390 Integrated Cryptographic Service Facility Application
> Programmer's Guide Version 2 Release 5 Publication No. SC23-3976-02 :
> http://ppdbooks.pok.ibm.com:80/cgi-bin/bookmgr/bookmgr.cmd/DOCNUM/SC23-3976/CCONTENTS
>
> In several parts of the document it's specified that, as a restriction:
>
> > The exponent of the RSA public key must be odd.
> >
> It's there any (unknown to me) security reason to be this way, or its
> an implementation/standard option??
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NODE b8e6121dRe: The exponent of the RSA public key must be odd.??
Luis Saiz <LSaiz@atos-ods.com>Thu, 28 May 1998 08:55:03 -0700 (PDT)
Sunder wrote:
> How many prime numbers do you know of that are even?
>
One: 2 ;-)
OK, I've never realized that e and d must both be co-prime with respect to (p-1)(q-1), only
that ed=1 mod((p-1)(q-1)), and I didn't saw the implication.
Sorry for this stupid question, next time I'll do more mathematics before.
> Luis Saiz wrote:
> >
> > OS/390 Integrated Cryptographic Service Facility Application
> > Programmer's Guide Version 2 Release 5 Publication No. SC23-3976-02 :
> > http://ppdbooks.pok.ibm.com:80/cgi-bin/bookmgr/bookmgr.cmd/DOCNUM/SC23-3976/CCONTENTS
> >
> > In several parts of the document it's specified that, as a restriction:
> >
> > > The exponent of the RSA public key must be odd.
> > >
> > It's there any (unknown to me) security reason to be this way, or its
> > an implementation/standard option??
>
> --
>
> =====================================Kaos=Keraunos=Kybernetos==============
> .+.^.+.| Ray Arachelian |Prying open my 3rd eye. So good to see |./|\.
> ..\|/..|sunder@sundernet.com|you once again. I thought you were |/\|/\
> <--*-->| ------------------ |hiding, and you thought that I had run |\/|\/
> ../|\..| "A toast to Odin, |away chasing the tail of dogma. I opened|.\|/.
> .+.v.+.|God of screwdrivers"|my eye and there we were.... |.....
> ======================= http://www.sundernet.com ==========================
NODE dac8f39fRe: The exponent of the RSA public key must be odd.??
Xcott Craver <caj@math.niu.edu>Thu, 28 May 1998 12:40:04 -0700 (PDT)
On Thu, 28 May 1998, Luis Saiz wrote:
> OK, I've never realized that e and d must both be co-prime with respect to (p-1)(q-1),
> only that ed=1 mod((p-1)(q-1)), and I didn't saw the implication.
Actually, that the exponent must be odd is much more immediate:
If ed = 1 mod(p-1)(q-1), then
ed = 1 + multiple*(p-1)(q-1)
= 1 + multiple*(even #)
= 1 + even # = odd #.
If either e or d were even, this couldn't be true.
-Xcott
[This same argument, by the way, is how you prove that
e and d must both be co-prime to phi(n). Just let
C be any divisor of phi(n), and replace "even" with
"divisible by C" and "odd" with "not divisible by C"]