17 Dec
2003
17 Dec
'03
11:17 p.m.
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"]