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.
McMillen, K.

Binary matrices, combinatorics, combinations, nonsingular
matrices, encryption, Vernam, pseudorandom 
numbers, feedback shiftregister sequences, random numbers.

3.7 5.3

CA780401 DH February 27, 1979  11:05 AM

2269	4	3115
2466	4	3115
2690	4	3115
2834	4	3115
2834	4	3115
2834	4	3115
2853	4	3115
2884	4	3115
2908	4	3115
3115	4	3115
3115	4	3115
3115	4	3115
3115	4	3115
3115	4	3115
3115	4	3115
3115	4	3115
907	5	3115
2045	5	3115
2417	5	3115
2466	5	3115
2884	5	3115
579	5	3115
3115	5	3115
3115	5	3115
3115	5	3115
785	5	3115