From: Xcott Craver <caj@math.niu.edu>

To: Luis Saiz <LSaiz@atos-ods.com>

Message Hash: dac8f39f6fd7eb660f053ace54679a9108370758035113c7e059f5c26a492cfe

Message ID: <Pine.SUN.3.91.980528142154.15208A-100000@baker>

Reply To: <356D88D7.1D480241@atos-ods.com>

UTC Datetime: 1998-05-28 19:40:04 UTC

Raw Date: Thu, 28 May 1998 12:40:04 -0700 (PDT)

```
From: Xcott Craver <caj@math.niu.edu>
Date: Thu, 28 May 1998 12:40:04 -0700 (PDT)
To: Luis Saiz <LSaiz@atos-ods.com>
Subject: Re: The exponent of the RSA public key must be odd.??
In-Reply-To: <356D88D7.1D480241@atos-ods.com>
Message-ID: <Pine.SUN.3.91.980528142154.15208A-100000@baker>
MIME-Version: 1.0
Content-Type: text/plain
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"]
```

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- 1998-05-28 (Thu, 28 May 1998 01:21:02 -0700 (PDT)) - The exponent of the RSA public key must be odd.?? -
*Luis Saiz <LSaiz@atos-ods.com>*- 1998-05-28 (Thu, 28 May 1998 07:41:57 -0700 (PDT)) - Re: The exponent of the RSA public key must be odd.?? -
*Sunder <sunder@brainlink.com>* - 1998-05-28 (Thu, 28 May 1998 08:55:03 -0700 (PDT)) - Re: The exponent of the RSA public key must be odd.?? -
*Luis Saiz <LSaiz@atos-ods.com>*- 1998-05-28 (Thu, 28 May 1998 12:40:04 -0700 (PDT)) - Re: The exponent of the RSA public key must be odd.?? -
*Xcott Craver <caj@math.niu.edu>*

- 1998-05-28 (Thu, 28 May 1998 12:40:04 -0700 (PDT)) - Re: The exponent of the RSA public key must be odd.?? -

- 1998-05-28 (Thu, 28 May 1998 07:41:57 -0700 (PDT)) - Re: The exponent of the RSA public key must be odd.?? -