Cryptanalysis of substitution type ciphers 
  


 
  
  Hill Cipher  
  
          cryptanalysis for known plain text
          size of the matrix is assumed known, say k by k.

                note for a block of cipher text c (column vector)

                    c = Kp   where p is corresponding plaintext
                             arranged as a column vector

            so for a sequence of cipher text blocks c1,c2,....,ck


                 C  = K*P

            where C is the k by k matrix whose columns are c1,...,ck
            and P is a similar matrix formed from p1,....,pk which are
            columns of plaintext. C and P are known for known plaintext.
            If P is invertible then

                        K = C*P^{-1}    , C times the inverse of P
            If P is not invertible then the process must be repeated until
            an invertible P is found. 



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