The exponent of the RSA public key must be odd.??
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/... 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 itŽs an implementation/standard option??
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/...
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 itŽs 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 ==========================
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/...
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 itŽs 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 ==========================
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"]
participants (3)
-
Luis Saiz -
Sunder -
Xcott Craver