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