Orderly Enumeration of Nonsingular Binary
Matrices Applied to Text Encryption
Nonsingular binary matrices of order N, i.e.,
nonsingular over the field {0, 1}, and an initial 
segment of the natural numbers are placed in one-to-one
correspondence.  Each natural number corresponds 
to two intermediate vectors.  These vectors are mapped into
a nonsingular binary matrix.  Examples of 
complete enumeration of all 2 x 2 and 3 x 3 nonsingular
binary matrices were produced by mapping the 
intermediate vectors to the matrices.  The mapping
has application to the Vernam encipherment method 
using pseudorandom number sequences.  A bit string formed
form bytes of text of a data encryption key 
can be used as a representation of a natural number. 
This natural number is transformed to a nonsingular 
binary matrix.  key leverage is obtained by using the
matrix as a"seed" in a shift register sequence 
pseudorandom number generator.  
CACM April, 1978
Payne, W.H.
McMillen, K.L.
