scholarly journals A TRANSFORMATION SEQUENCING APPROACH TO PSEUDORANDOM NUMBER GENERATION

2007 ◽  
Vol 18 (08) ◽  
pp. 1293-1302
Author(s):  
SYN KIAT TAN ◽  
SHENG-UEI GUAN
Keyword(s):  
Cellular Automata ◽  
Uniform Distribution ◽  
Design Patterns ◽  
Maximum Length ◽  
Pseudorandom Number ◽  
New Approach ◽  
Balanced Distribution ◽  
Pseudorandom Number Generation ◽  
Important Design ◽  
Randomness Tests

This paper presents a new approach to designing pseudorandom number generators based on cellular automata. Current cellular automata designs either focus on (i) ensuring desirable sequence properties such as maximum length period, balanced distribution of bits and uniform distribution of n-bit tuples, etc. or (ii) ensuring the generated sequences pass stringent randomness tests. In this work, important design patterns are first identified from the latter approach and then incorporated into cellular automata such that the desirable sequence properties are preserved like in the former approach. Preliminary experiment results show that the new cellular automata designed have potential in passing all DIEHARD tests.

scholarly journals CONFIGURABLE CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

2005 ◽  
Vol 16 (07) ◽  
pp. 1051-1073 ◽  
Author(s):  
MARIE THERESE QUIETA ◽  
SHENG-UEI GUAN
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generation ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
New Approach ◽  
Suitable Candidate ◽  
Number Generation ◽  
A Cell ◽  
Pseudorandom Number Generation

This paper proposes a generalized structure of cellular automata (CA) — the configurable cellular automata (CoCA). With selected properties from programmable CA (PCA) and controllable CA (CCA), a new approach to cellular automata is developed. In CoCA, the cells are dynamically reconfigured at run-time via a control CA. Reconfiguration of a cell simply means varying the properties of that cell with time. Some examples of properties to be reconfigured are rule selection, boundary condition, and radius. While the objective of this paper is to propose CoCA as a new CA method, the main focus is to design a CoCA that can function as a good pseudorandom number generator (PRNG). As a PRNG, CoCA can be a suitable candidate as it can pass 17 out of 18 Diehard tests with 31 cells. CoCA PRNG's performance based on Diehard test is considered superior over other CA PRNG works. Moreover, CoCA opens new rooms for research not only in the field of random number generation, but in modeling complex systems as well.

scholarly journals A FAMILY OF CONTROLLABLE CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

2002 ◽  
Vol 13 (08) ◽  
pp. 1047-1073 ◽  
Author(s):  
SHENG-UEI GUAN ◽  
SHU ZHANG
Keyword(s):  
Genetic Algorithm ◽  
Cellular Automata ◽  
Pseudorandom Number ◽  
Test Results ◽  
Randomness Test ◽  
Different Types ◽  
Pseudorandom Number Generation ◽  
Test Suites ◽  
Better Than

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1D CA. Moreover, their randomness can be comparable to that of 2D CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved as compared with any individual CCA PRNG.

scholarly journals Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

2017 ◽  
Vol 27 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Sylvain Contassot-Vivier ◽  
Jean-François Couchot ◽  
Christophe Guyeux ◽  
Pierre-Cyrille Heam
Keyword(s):  
Uniform Distribution ◽  
Hamiltonian Cycle ◽  
Chaotic Behavior ◽  
Statistical Tests ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Expected Length ◽  
Obvious Consequence ◽  
Pseudorandom Number Generation

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a [Formula: see text]-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distribution is calculated. Finally practical experiments show that the generators successfully pass the classical statistical tests.

scholarly journals LAYERED CELLULAR AUTOMATA FOR PSEUDORANDOM NUMBER GENERATION

2007 ◽  
Vol 18 (02) ◽  
pp. 217-234
Author(s):  
SYN KIAT TAN ◽  
SHENG-UEI GUAN
Keyword(s):  
Cellular Automata ◽  
Linear Function ◽  
Phase Difference ◽  
Linear Complexity ◽  
Maximum Length ◽  
Operating Speed ◽  
Time Varying ◽  
Nonlinear Functions ◽  
Initial States ◽  
Pseudorandom Number Generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set {Af | f = 1, 2, …, 2n -1} formed by the transformation matrix A of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L = 1, 2, 3, 4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions f30 and f45 in place of the linear function f204 used in the L-LCA. Linear complexity is significantly increased when f30 or f45 is used.

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