       Q. Simultaneous Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg2567] Q. Simultaneous Equations
• From: "Enrico C. Walker" <ewalke1 at gl.umbc.edu>
• Date: Tue, 21 Nov 1995 09:24:38 -0500
• Organization: University of Maryland, Baltimore County

```I'm working on a cipher problem where a plaintext {a,b,c,...,z is mapped to
0,1,2,...,25, respectively} is initially encrypted in a three blocks
raised to power of 26. For example,

DOG --> 3(26^2)+14(26)+6 = 2398    --> (a 656+ b 26 + c == k)
CAT --> 2(26^2)+0(26)+19 = 1371    --> (d 656+ e 26 + f == l)
ZZZ --> 25(26^2)+25(26)+25 = 17575 --> (g 656+ h 26 + i == m)

(2398,1371,17575) are then encrypted in some formulae which resulted
to some corresponding integers. Well, I've finally decrypted the given
cipher and now facing with lots of integers (like 2398,1371,17575). I
need to find the corresponding a,b,c = 2398 (as shown above). I'm not really
sure if this is a simultaneous linear equations or perhaps can be solved
in some other way. I guess the main question is that:

How can I find the variables (a,b,c) that will satisfy an integer k where
(a,b,c) are integers between 0,1,2,...,25 .

a 656 + b 26 + c = 2398