From: charliemerritt@BIX.com
Date: Mon, 4 Oct 93 19:59:07 PDT
To: cypherpunks@toad.com
Subject: RSA EXAMPLE
Message-ID: <9310042253.memo.37458@BIX.com>
MIME-Version: 1.0
Content-Type: text/plain


cc:simons@peti.GUN.de (peter simons)

Dear Peter Simons,

In your example P=5 Q=7 you are indeed using small numbers.
Dont forget that D*E should equal 1 mod ( (p-1)*(q-1)/G).
G=gcd(p-1,q-1) so in your example D*E=1 mod 12.
D*E can not have common factors with 12 (2,3,4,6) etc.

If E=5  then D=5, a nonsense situation.
   E=7       D=7
   E=11      D=11
your key will not work
* * * * * * *

Try this:  P=5  Q=11  N=55   G=2  (gcd(4,10)=2)
           (p-1)*(q-1)=40  /G  = 20

	E=3  D=7  (D*E=21)        21 mod 20 = 1
Good key!
 Message = 31
    31^3=29791  mod 55=36 so cyphertext=36
    36^7=78364164096  mod 55 = 31 so recovered message is indeed 31.
I hope this helps.  Charlie Merritt  [charliemerritt@bix.com]