Journal ArticleDOI
Orderly enumeration of nonsingular binary matrices applied to text encryption
W. H. Payne,K. L. McMillen +1 more
TLDR
Examples of complete enumeration of all 2 × 2 and 3 × 3 nonsingular binary matrices were produced by mapping the intermediate vectors to the matrices, which has application to the Vernam encipherment method using pseudorandom number sequences.Abstract:
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 × 2 and 3 × 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 from 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.read more
Citations
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The k.Distribution of Generalized Feedback Shift Register
M. Fushimi,S. Tezuka +1 more
TL;DR: A necessary and sufficient condition for the generalized feedback shift regis- ter (GFSR) sequence introduced by Lewis and Payne to be k-distributed was established in this paper.
Journal ArticleDOI
The k-distribution of generalized feedback shift register pseudorandom numbers
M. Fushimi,Shu Tezuka +1 more
TL;DR: A necessary and sufficient condition is established for the generalized feedback shift register (GFSR) sequence introduced by Lewis and Payne to be k-distributed and a theoretical test for k- Distributivity is proposed and performed in a reasonable amount of computer time.
Journal ArticleDOI
A comparative study of some pseudorandom number generators
TL;DR: In this article, the authors present results of a test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations.
Journal ArticleDOI
Initializing generalized feedback shift register pseudorandom number generators
TL;DR: This paper considers an alternative method of initialization based on a natural polynomial representation for the terms of a feedback shift register sequence that results in substantial improvements in the initialization process.
Journal ArticleDOI
Random number generation with the recursion X t =X t-3p ⊕X t-3q
TL;DR: A similar algorithm is proposed which uses a primitive polynomial with many nonzero terms, but generates a number as fast as the original GFSR algorithm, which is guaranteed to be equidistributed in higher dimensions and to have a good autocorrelation property.
References
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Journal ArticleDOI
Communication theory of secrecy systems
TL;DR: A theory of secrecy systems is developed on a theoretical level and is intended to complement the treatment found in standard works on cryptography.
Journal ArticleDOI
Generalized Feedback Shift Register Pseudorandom Number Algorithm
Ted G. Lewis,W. H. Payne +1 more
TL;DR: The generalized feedback shift register pseudorandom number algorithm has several advantages over all other pseudor random number generators, including an arbitrarily long period independent of the word size of the computer on which it is implemented and the “same” floating-point pseudOrandom number sequence is obtained on any machine.