Pseudorandom number generators - Revision history

Xkrep33 at 10:31, 19 January 2016

2016-01-19T10:31:20Z

Jakub: /* Required properties */

2012-12-30T19:02:34Z

‎Required properties

Jakub: /* Required properties */

2012-12-30T18:56:57Z

‎Required properties

Jakub: /* Required properties */

2012-12-30T18:49:34Z

‎Required properties

Jakub: /* Mersenne twister */

2012-12-30T18:34:30Z

‎Mersenne twister

Jakub: /* Lagged Fibonacci generator */

2012-12-30T18:34:16Z

‎Lagged Fibonacci generator

Jakub: /* Lagged Fibonacci generator */

2012-12-30T16:59:15Z

‎Lagged Fibonacci generator

Jakub: /* Mersenne twister */

2012-12-30T16:58:52Z

‎Mersenne twister

Jakub: /* Multiplicative Congruential Generator */

2012-12-30T16:56:15Z

‎Multiplicative Congruential Generator

Jakub: /* Linear Congruential Generator */

2012-12-30T16:48:36Z

‎Linear Congruential Generator

@@ Line 332: / Line 332: @@
 ==Testing==
-Very important contcept to ensure reliability and determine possible areas of use is testing PRGs. There are many tests for PRGs. First of all let's take a look at bacis catogories of tests.
+Very important concept to ensure reliability and determine possible areas of use is testing PRGs. There are many tests for PRGs. First of all let's take a look at bacis catogories of tests.
 === Theoretic tests ===

@@ Line 45: / Line 45: @@
 '''Security'''<br/>
-The generator should be secured
+The generator should be secured. Basically, security of the generator ensures that no one can break the generator in reasonable time either by the brute-force approach or by more clever ones. If there is no polynomial-time algorithm that on the first <math>m</math> output sequence can predict the <math>{m + 1}^{th}</math> bit with probability greater than 0.5 we consider the generator to be secured.
 == Construction of simple PRG ==

@@ Line 37: / Line 37: @@
 '''Long period'''<br/>
-The generator should be of long period
+The generator should be of long period because this property directly influences the randomness of generated outputs. This is crucial for example for simulations since they are conducted in order to simulate dynamic behavior and states of an environment not only the cyclic stages of an environment.
 '''Fast computation'''<br/>
-The generator should be reasonably fast
+The generator should be reasonably fast. It is always a good idea to take care about the users of the generator since they might be in a quite constrained environment either by hardware specifications or by expected time performance.

@@ Line 25: / Line 25: @@
 '''Unbiased - Uniform distribution'''<br/>
-By definition of the word unbiased this property states that PRG is showing no prejudice for or against something. In PRG language this means that all values of whatever sample size is collected are equiprobable.
+By definition of the word unbiased this property states that PRG is showing no prejudice for or against something. In PRG language this means that all values of whatever sample size is collected are equiprobable. This property ensures the independence of the generator and its stability against certain types of attacks.
 '''Unpredictable - Independence'''<br/>
-It is impossible to predict what the next output will be, given all the previous outputs, but not the internal state
+It is impossible to predict what the next output will be, given all the previous outputs, but not the internal state. If this is not guaranteed then basically anyone can pose as a generator. This is used for example in the man in the middle attack.
 '''Unreproducible'''<br/>
-Two of the same generators, given the same starting conditions, will produce different outputs
+Two of the same generators, given the same starting conditions, will produce different outputs. Certain types of spoofing attacks try to reproduce subset of real production environment in order to exploit the lack of security in respect with this condition.
 '''Long period'''<br/>
 The generator should be of long period
 '''Fast computation'''<br/>
 The generator should be reasonably fast
 '''Security'''<br/>
 The generator should be secured
 == Construction of simple PRG ==

@@ Line 278: / Line 278: @@
 [[File:LFG_example.gif]]
-=== Mersenne twister ===
+=== Mersenne Twister ===
 {| class=infobox width=250px
 |style="background:#33CC33;color:#FFFFFF"|<center>'''Advantages'''</center>

@@ Line 229: / Line 229: @@
 |}
-=== Lagged Fibonacci generator ===
+=== Lagged Fibonacci Generator ===
 {| class=infobox width=250px
 |style="background:#33CC33;color:#FFFFFF"|<center>'''Advantages'''</center>

← Older revision		Revision as of 16:59, 30 December 2012
Line 277:		Line 277:

	[[File:LFG_example.gif]]		[[File:LFG_example.gif]]
−
−	~~'''Example:'''<br/>~~
−	~~<todo>~~

	=== Mersenne twister ===		=== Mersenne twister ===

← Older revision		Revision as of 16:58, 30 December 2012
Line 308:		Line 308:

	[[File:MT_example.png]]		[[File:MT_example.png]]
−
−	~~'''Example:'''<br/>~~
−	~~<todo>~~

	==Nonlinear methods==		==Nonlinear methods==

@@ Line 210: / Line 210: @@
 '''Example:'''<br/>
-<todo>
+Following example shows how to compute first five output values for specified MCG:
 === Lagged Fibonacci generator ===

@@ Line 169: / Line 169: @@
 '''Example:'''<br/>
-<todo>
+Following example shows how to compute first five output values for specified LCG:
 === Multiplicative Congruential Generator ===