Linear Complexity Time

From DiceLock.org

Linear Complexity

Test performed with librandomtests.so.

This is a test to analyze the relation between stream length and test time for Linear Complexity Random Test.

Also, it allows us to set the relation between stream length, test time, randomness and errors.

The test has been performed in order to extract information for DiceLock project.

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Test performed

Test environment:

Hardware: Intel Pentium IV - 3,2 GHz, 1 GB RAM
OS:       Linux 2.6.18.2-34-default i686
System:   openSUSE 10.2 (i586)

NIST file input stream data:

File: data.e
Minimum stream length:        104 bits (    13 bytes)
Maximum stream length:    262.144 bits (32.768 bytes)
Number of streams tested:  32.755 streams
All streams starting from first bit of file
Each stream 8 multiple 

Test Time & Stream Length

The relation between Stream Length and Test Time.

Graphically:

X:Stream Length - Y:Test Time - Non random=0, Random=1

Times for:

    104 bits: 0,000049 seg.
262.144 bits: 7,340538 seg.

Regression with Weka (streams with no errors):

Parameters:

section:          functions
Classifier:       LinearRegression
Cross-validation: 10-fold
class.            Test Time

Results:

=== Run information ===
Scheme:       weka.classifiers.functions.LinearRegression -S 0 -R 1.0E-8
Relation:     QueryResult-weka.filters.unsupervised.attribute.Remove-R1-2,4-6,8
Instances:    32144
Attributes:   2
              String_Length
              Test_Time
Test mode:    10-fold cross-validation
=== Classifier model (full training set) ===
Linear Regression Model
Test_Time =
     (28.4378 * 10e-6) * String_Length +
 -(67153.7195 * 10e-6)
Time taken to build model: 0.2 seconds
=== Cross-validation ===
=== Summary ===
Correlation coefficient                  0.9992
Relative absolute error                  2.4328 %
Root relative squared error              3.9552 %
Total Number of Instances                 32144

Test Time, Stream Length, Random & Test Errors

Graphically:

X:Stream Length - Y:Test Time - Z:Random (Non random=0, Random=1) - Colour:Test Error

Streams checked above 104 are random.

Errors shown:

None

References

[NIST] National Institute of Standards and Technology.

[NIST RNGT] NIST Random Number Generation and Testing.

[Weka] Weka - collection of machine learning algorithms for data mining tasks.

[RapidMiner] Rapidminer - open-source data mining solution