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MathGroup Archive 1995

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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

Again your advice is greatly appreciated. 
I can also be reached at 1-800-775-7094 ext 3105.

-ENRICO-



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