Problem Set 1: 

Course:		CS 407 -- Codes and Internet Security
Posting Date:   September 2, 1998
Due Date:       September 9, 1998
Builds On:

   The digital versions of this and all other project descriptions will be 
written in pseudo-TeX.  For example, a_1 is a with a subscript 1, a^1 is a with 
a superscript 1, \Sigma is the capital Greek letter sigma, \Cal M is a script 
(calligraphic) M, and \in is the set membership sign.

   Of course, all problem sets will be written out on the board in class.  Old 
fashioned, but much easier to read.

   There is only one problem in this problem set.

Problem 1:  \Sigma is a finite alphabet.  A message is a finite string (finite 
sequence) of symbols from \Sigma.  \Cal M is the set of messages. e is an 
encription function.  The domain of e is \Cal M.  Give a formal mathematical 
proof of the following:  A necessary and sufficient condition for a decryption 
function d to exist, satisfying the fundamental property

          d(e(M)) = M, for all M \in \Cal M,

is that e be 1 to 1 (injective).