WO2000013367A1

WO2000013367A1 - Visual detection of a lack of random behavior of a string of numbers

Info

Publication number: WO2000013367A1
Application number: PCT/US1999/019832
Authority: WO
Inventors: Adam Shefi
Original assignee: Warcop Investment Ltd.; Ron, Binyamin; RRIEDMAN, Mark, M.
Priority date: 1998-08-31
Filing date: 1999-08-30
Publication date: 2000-03-09
Also published as: EP1110346A1; IL141605A0; AU5698299A; EP1110346A4

Abstract

A method for detecting a discernible pattern in a sequence of numbers with a display unit, the method comprising the steps of: (a) providing a window, the window including a plurality of numbers from the sequence of numbers; (b) determining a visual character according to the plurality of numbers in the window; (c) displaying the visual character on the display unit; and (d) repeating steps (b) and (c) for at least a portion of the sequence of numbers, such that if a pattern is discernible on the display unit, the discernible pattern is detected.

Description

VISUAL DETECTION OF A LACK OF RANDOM BEHAVIOR OF A STRING OF NUMBERS

FIELD AND BACKGROUND OF THE INVENTION The present invention relates to a device, a system and a method for detecting the quality of random behavior of a sequence of numbers.

Random numbers are those numbers, usually generated by a physical process, which are stochastically random, and which are not capable of being repeatedly regenerated at will. By contrast, pseudorandom numbers are produced according to a mathematical algorithm and can theoretically be repeatedly regenerated. The mathematical algorithm according to which a computer is able to generate a pseudorandom number is called a pseudorandom number generator. One characteristic of such a pseudorandom number generator is that a seed is used to generate the sequence of pseudorandom numbers. The seed is automatically changed every time a pseudorandom number is generated because the same seed will always cause the same sequence of pseudorandom numbers to be generated for a particular pseudorandom number generator.

Pseudorandom number generators are useful for many different applications, such as simulations of biological, engineering and other "real world" events, and for modeling various processes. However, such pseudorandom number generators are substantially only useful if they produce numbers which are apparently random. If the numbers produced have a hidden pattern, then the pseudorandom number generator is not useful since the numbers produced are not sufficiently random.

Currently, many different statistical tests exist to determine whether a pseudorandom number generator produces pseudorandom numbers which are sufficiently random. For example, these numbers can be analyzed with "goodness of fit" tests, such as those described in Simulation and the Monte Carlo Method (R. Rubinstein, John Wiley and Sons, New York, 1981, Chapter 2, Section 2.3 "Statistical Tests of Pseudorandom Numbers", pages 26-33) and A Million Random Digits with 100,000 Normal Deviates (Rand Corporation, California, 1955). These "goodness of fit" tests examine the distribution of the sequence of supposedly random numbers, which should theoretically be uniform and which should also be mutually independent. Typically, these tests are performed not only on the string of numbers generated by the pseudorandom number generator, but also on groups of these numbers which have been manipulated in various ways, for example by being raised to the power of 2. Even after such manipulations, the resulting generated numbers should still behave correctly according to the predictions of probability theory. The manipulation of the numbers is important to test since many simulations rely upon various manipulations and calculations performed with these generated numbers, such that the simulations will not be correct if the manipulated generated numbers fail to maintain their statistically randomness predicted by probability theory. Furthermore, beyond testing pseudorandom number generators, such tests can be used to detect any non-random behavior of the output of encryption algorithms. Such non-random behavior can potentially render these algorithms more susceptible to attack, and hence decrease the security of the encrypted text. However, often such tests are not sufficiently sensitive to determine whether a sequence of numbers is sufficiently random, or whether a discernible pattern exists within the string of such numbers, regardless of whether the string represents the output of a pseudorandom number generator or of an encryption algorithm. In particular, "goodness of fit" tests have the disadvantage of only being able to detect patterns or relationships between numbers in a sequence which are essentially linear, rather than complicated non-linear interdependencies. Indeed, these tests may provide misleading results, indicating that a sequence of numbers is random when in fact discernible patterns exist within the sequence. Furthermore, these tests require a knowledgeable individual to perform these statistical tests and to interpret the results. Thus, the currently available tests for detecting non-random behavior of a string of numbers require special knowledge to perform and may provide inaccurate or misleading results. There is therefore a need for, and it would be useful to have, a method and a system for determining whether a sequence of numbers, such as a sequence generated by a pseudorandom number generator or the output of an encryption algorithm, is sufficiently random, or whether there is a discernible pattern within the sequence of numbers, the method and the system being operable substantially without any special knowledge of statistics.

SUMMARY OF THE INVENTION

It is one object of the present invention to provide a method and a system for determining whether a sequence of numbers has a discernible pattern.

It is another object of the present invention to determine if the sequence of numbers is not random.

It is yet another object of the present invention to provide a simple yet robust system and method which relies upon a visual display for determining whether a sequence of numbers has a discernible pattern.

It is still another object of the present invention to provide such a visual display on a display screen.

The present invention is of a system and method for determining whether a sequence of numbers has a discernible pattern. The present invention features a software program for displaying a plurality of visual characters on a computer screen or other display unit, each visual character being chosen according to at least one of the sequence of numbers to be analyzed. As a window is moved along the sequence of numbers, a corresponding visual character is displayed on the screen. Thus, any visual pattern which may be present is substantially immediately visually discernible to the human eye.

According to the present invention, there is provided a method for detecting a discernible pattern in a sequence of numbers with a display unit, the method comprising the steps of: (a) providing a window, the window including a plurality of numbers from the sequence of numbers; (b) determining a visual character according to the plurality of numbers in the window; (c) displaying the visual character on the display unit; (d) advancing the window one step in the sequence of numbers; and (e) repeating steps (b), (c) and (d) for at least a portion of the sequence of numbers, such that if a pattern is discernible on the display unit, the discernible pattern is detected.

Preferably, step (e) is repeated for substantially the entirety of the sequence of numbers.

According to a preferred embodiment of the present invention, the plurality of numbers is two numbers. More preferably, the visual character is determined according to the two numbers, a first of the two numbers representing an "x" coordinate and a second of the two numbers representing a "y" coordinate, such that the visual character is a point in two-dimensional space on the display unit. According to another preferred embodiment of the present invention, the plurality of numbers is three numbers. More preferably, the visual character is determined according to the three numbers, a first of the two numbers representing an "x" coordinate, a second of the two numbers representing a "y" coordinate and a third of the numbers representing a color, such that the visual character is a point with a color in two-dimensional space on the display unit. According to yet another preferred embodiment of the present invention, the plurality of numbers is four numbers. More preferably, the visual character is determined according to the four numbers, a first of the two numbers representing an "x" coordinate, a second of the two numbers representing a "y" coordinate, a third of the numbers representing a "z" coordinate and a fourth of the numbers representing a color, such that the visual character is a point with a color in three-dimensional space on the display unit.

According to still another preferred embodiment of the present invention, the plurality of numbers is at least four numbers. More preferably, the visual character is determined according to the at least four numbers, a first of the two numbers representing an "x" coordinate, a second of the two numbers representing a "y" coordinate and a third of the numbers representing a color, the fourth number determining a display of the visual character, such that a plurality of the displays are displayed on the display screen and such that the visual character is a point with a color in an interchanging plurality of displays on the display unit.

Preferably, the display unit is a display screen. Alternatively and preferably, the display unit is a printer. Preferably, the sequence of numbers is produced by a pseudorandom number generator, such that a usefulness of the pseudorandom number generator is determined according to whether the discernible pattern was detected.

Alternatively and preferably, the sequence of numbers is produced according to an encryption method, such that a usefulness of the encryption method is determined according to whether the discernible pattern was detected. Also alternatively and preferably, the sequence of numbers is produced according to an access control method, such that a usefulness of the access control method is determined according to whether the discernible pattern was detected.

According to another embodiment of the present invention, there is provided a system for detecting a discernible pattern in a sequence of numbers, the system comprising: (a) a number receiver for receiving the sequence of numbers; (b) a window for receiving a plurality of numbers from the number receiver; (c) a visual character for being determined according to the plurality of numbers in the window; and (d) a display unit for displaying the visual character, such that if a plurality of visual characters are determined according to at least a portion of the sequence of numbers, a discernible pattern is detected on the display unit if the discernible pattern exists, and alternatively the discernible pattern is not detected on the display unit.

According to yet another embodiment of the present invention, there is provided a device for detecting a pattern in a sequence of numbers, the device comprising: (a) an input port for receiving the sequence of numbers; (b) a processor for determining a visual character according to at least a portion of the sequence of numbers; and (c) a display unit for displaying the visual character, such that if a plurality of visual characters are determined according to the at least a portion of the sequence of numbers, a discernible pattern is detected on the display unit if the discernible pattern exists, and alternatively such that the discernible pattern is not detected on the display unit.

Hereinafter, the term "computer network" refers to a connection between any two computers which permits the transmission of data. Hereinafter, the term "computer" includes, but is not limited to, personal computers (PC) having an operating system such as DOS, Windows™, OS/2™ or Linux; Mackintosh™ computers; computers having JAVA™-OS as the operating system; and graphical workstations such as the computers of Sun Microsystems ™ and Silicon Graphics™, and other computers having some version of the UNIX operating system such as AIX or SOLARIS™ of Sun Microsystems™; or any other known and available operating system. Hereinafter, the term "Windows™" includes but is not limited to Windows95™, Windows 3.x™ in which "x" is an integer such as "1", Windows NT™, Windows98™, Windows CE™ and any upgraded versions of these operating systems by Microsoft Inc. (Seattle, Washington, USA). Hereinafter, the term "true random number" refers to a number which is stochastically random, in the sense that it is not capable of being repeatedly regenerated at will. The term "pseudorandom number" refers to a number which is produced according to a mathematical algorithm and which can theoretically be repeatedly regenerated. The term "pseudorandom number generator" refers to a mathematical algorithm according to which a computer is able to generate a pseudorandom number. One characteristic of such a pseudorandom number generator is that a seed is used to generate the sequence of pseudorandom numbers. The seed is automatically changed every time a pseudorandom number is generated because the same seed will always cause the same sequence of pseudorandom numbers to be generated for a particular pseudorandom number generator.

Hereinafter, the term "display unit" includes but is not limited to a printer; a display screen including, but not limited to, a plasma screen, an LCD screen, a CRT, any type of computer monitor screen, or any other technology for visual display of images; and an apparatus featuring a software program which is capable of pattern recognition and/or image analysis in an image, with the results of the analysis being output for visual inspection.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, wherein:

FIGS. 1A and IB are flow charts of an exemplary method for detecting a discernible pattern in the sequence of numbers according to the present invention;

FIGS. 2A-2G are exemplary displays on a display unit after four separate performances of the method according to the present invention, Figures 2 A and 2B being an analysis of the output of a simple pseudorandom number generator in color, Figure 2C being an analysis of the output of a pseudorandom number generator included with a release of the PASCAL programming language shown in color, Figure 2D being an analysis of a plaintext file in color, Figure 2E being an analysis of the output of a cryptography method performed on the text of Figure 2D in color, and Figures 2F and 2G being analyses of the output of other typical pseudorandom number generators shown in black and white;

FIG. 3 is an exemplary block diagram of an illustrative system for detecting a discernible pattern in the sequence of numbers according to the present invention; and

FIG. 4 is an exemplary block diagram of an illustrative device for detecting a discernible pattern in the sequence of numbers according to the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention is of a system and method for determining whether a sequence of numbers has a discernible pattern. The present invention features a software program for displaying a plurality of visual characters on a computer screen or other display unit, each visual character being chosen according to at least two of the numbers from the sequence of numbers to be analyzed. As a window is moved along the sequence of numbers, a corresponding visual character is displayed on the screen. Thus, a visual pattern which may be present, because of any statistical or deterministic relationship between the numbers, is substantially immediately visually discernible to the human eye.

The principles and operation of a method and a system for visually detecting a discernible pattern in a sequence of numbers according to the present invention may be better understood with reference to the drawings and the accompanying description, it being understood that these drawings are given for illustrative purposes only and are not meant to be limiting.

Referring now to the drawings, Figure 1 A depicts an illustrative method for determining whether a sequence of numbers contains a discernible pattern according to the present invention, the steps of the method being operated by a data processor. In step one, a sequence of numbers is provided. In step two, a window is moved along the sequence of numbers. The window includes at least two of the numbers of the sequence each time. The operation of the window from step two is shown in greater detail with reference to Figure IB below.

In step three, a visual character is selected according to the plurality of numbers in the window and is displayed on the display unit, such that for each location of the window, one visual character is displayed on the display unit. Preferably, the visual character is displayed on a display screen, although the visual character could also be displayed on a printer by printing onto paper, for example. The visual characters themselves are described in greater detail below.

In step four, the window is shifted by one position along the sequence of numbers, and step three is repeated. For example, if the sequence of numbers included "41-23-56-78", and the first location of the window included the numbers "41-23-56", then shifting the window by one position along the sequence of numbers would cause the window to include "23-56-78", and so forth. Preferably, steps three and four are repeated until the window has moved substantially along the length of substantially the entire sequence of numbers. Figure IB shows the operation of the window from step two of Figure

1A in greater detail. The steps of the operation of the window are designated with Roman numerals to indicate that this process is being described independently of the description for Figure 1 A. In step I, the window is shown in the first position, such that the numbers "41-23-56" are included. In step II, the window has been shifted by one position, now including the numbers "23- 56-78". In step III, the window has again been shifted by one position, thereby including the numbers "56-78-91". These steps can be repeated substantially as many times as desired, until preferably substantially all of the numbers in the sequence have been included in a window at least once. Of course, the window could be altered to include a group of a plurality of numbers of substantially any desired size.

As these steps are repeated, the display screen or other display unit displays an increasingly larger number of visual characters, corresponding to the numbers of the sequence captured by the window at each position. The examples described herein employ a colored dot as the visual character, it being understood that this is for the purposes of illustration only and is not meant to be limiting in any way.

If there is a discernible pattern of these visual characters, the human eye is very sensitive for detecting such a pattern. Furthermore, statistical tests are limited to correlations between numbers in the sequence which are essentially linear, while the human eye can detect various patterns, including non-linear patterns.

The exact nature of these patterns depends upon the visual characters. For example, if the visual character includes color as part of the definition, then a sequence of sufficiently random numbers should produce a "white" screen. By contrast, any pattern in the sequence of numbers, linear or non-linear, causes an apparent pattern of shapes and/or colors to appear on the display unit, thereby indicating that the sequence of numbers is not sufficiently random. The visual characters themselves can be selected in a number of ways, in particular according to the number of numbers from the sequence being displayed in the window. For example, if only two numbers are in the window at any one time, then these two numbers can represent an "x" coordinate and a "y" coordinate, such that the visual character is a point in two-dimensional space determined according to the "x" and the "y" coordinates. Alternatively and preferably, if the window includes three numbers at any one time, then the three numbers can represent an "x" coordinate, a "y" coordinate and a color for the third number, such that the visual character is a point in two-dimensional space determined according to the "x" and the "y" coordinates, with a color, for example. Alternatively and more preferably, if the window includes three numbers at any one time, then the three numbers can represent an "x" coordinate, a "y" coordinate and a "z" coordinate, for example. If the window includes four numbers at any one time, then the four numbers can represent an "x" coordinate, a "y" coordinate, a "z" coordinate and a color, for example. Other embodiments of the visual characters are also possible, beyond windows of two, three or four numbers. For example, if a window which includes more than four numbers is desired, then at least two separate displays could be constructed. Each display would be displayed alone on the display unit, but would quickly be interchanged with other displays. Thus, again any discernible pattern could be detected according to the display on the display unit such as the computer display screen, since such a pattern would emerge from the rapid interchange of the different displays on the display unit.

For any of the above embodiments, if the size of the individual numbers in the sequence of numbers was too large, each individual number could be partitioned into a plurality of smaller numbers of the desired size, and the steps of the method performed substantially as described above.

Figures 2A-2G show seven illustrative displays on a display unit after seven different sequences of numbers have been analyzed. The first two displays, shown in Figures 2 A and 2B, were obtained by analyzing two different sequences of numbers generated by two runs with a simple pseudorandom number generator. The simple pseudorandom number generator generated the string of numbers by manipulating a seed S according to the equation (S * c) + a in order to generate the new seed, in which a and c were constants. Every time the seed was changed according to the formula above, the first byte of the new seed was output as the next number in the string.

The analysis of the resulting string of generated numbers was as follows. First, the string of numbers was analyzed according to four standard statistical tests to detect non-random behavior. In the first test, the deviation of the mean of the entire string of numbers from the theoretical mean was determined. Since each number was a byte of the output number, the value of each number could have been from 0 to 255. Therefore, theoretically the mean should have been 127.5 and the deviation from the theoretical mean should have been 0. In the second test, the ratio of the standard deviation in the string of numbers and the theoretical standard deviation was determined. If the string of numbers were exhibiting random behavior, the ratio should have been 1. In the third test, the correlation between each pair of adjacent numbers was examined. Theoretically, such correlation should have been 0 for a string of random numbers. In the fourth test, the correlation between each pair of numbers separated by one number was examined. Again, theoretically such correlation should have been 0 for a string of random numbers. Thus, as described in more detail below, the strings of random numbers passed the statistical tests yet failed according to the method of the present invention. For performing an analysis according to the method of the present invention, the window included three numbers at a time, representing the "x" coordinate, the "y" coordinate and color, respectively, such that the visual character was a point in two-dimensional space with a color. The visual character was displayed on a computer screen as the display unit. As can clearly be seen in Figures 2 A and 2B, a highly visually discernible pattern is visible on the computer screen. For example, in Figure 2A, a regular grid pattern of clusters of colored dots is clearly visible. In Figure 2B, the display shows a regular pattern of diagonal stripes of colored dots, alternating between stripes of dots of a lighter color and stripes of dots of a darker color. Therefore, in these two runs, the output of the pseudorandom number generator clearly was not random, and had an easily discernible pattern of output numbers.

Surprisingly, the output of this pseudorandom number generator passed the tests to determine whether the pseudorandom numbers being produced were sufficiently random. For the first run, the string featured 13298 numbers. For the first test, the result was -0.0007, as opposed to the theoretical result of 0. For the second test, the result was 1.0335, as opposed to the theoretical result of 1. For the third test, the result was 0.0107, as opposed to the theoretical result of 0. For the fourth test, the result was 0.0116, again as opposed to the theoretical result of 0. For the second run of the pseudorandom number generator, the results of the four tests were -0.2532, 1.0029, -0.0056 and - 0.0116, respectively. Thus, although the simple pseudorandom number generator was able to "pass" the four statistical tests, and to produce strings of apparently random numbers, the method of the present invention was able to detect a strong discernible pattern within the strings of numbers, indicating a non-random correlation between the numbers.

Figure 2C shows the display obtained from the analysis of a string of numbers generated by the pseudorandom number generator packaged with the Turbo™ PASCAL compiler of Borland, Inc. The output of this pseudorandom number generator was also apparently random according to the statistical tests described above (data not shown). However, Figure 2C shows that a pattern is still discernible, with groups of colored dots in discernible shapes distributed about the display. Thus, even though the output of this generator does not have such a strong pattern, the method of the present invention is able to detect that it is not completely random.

Figure 2D shows the display obtained from the analysis of plaintext, transformed into numbers according to the ASCII value of the characters. The color display clearly shows a discernible pattern, which is not surprising since the plaintext was natural language text and would therefore be expected to have a pattern. After a cryptographical method operated by the word processing program Q-text™ was performed on this plaintext, the resultant output string of numbers was also analyzed according to the method of the present invention, as shown in Figure 2E. Again, the color display shows a clearly discernible pattern, which demonstrates that the cryptographic method employed may be susceptible to attack.

Figures 2F and 2G are black and white displays of analyses of the output of two typical pseudorandom number generators. The analyses were performed according to the method of the present invention, as described previously.

These displays are shown to demonstrate that the visual character of the present invention may optionally be restricted to display in black and white, rather than color.

Therefore, clearly the method of the present invention is able to visually detect whether a sequence of numbers is sufficiently random, and hence preferably the usefulness of the pseudorandom number generator which was used to generate the sequence of numbers, by determining whether a visual pattern is discernible to the human eye.

The present invention could also be embodied as a system, an example of which is shown in Figure 3. A system 10 for determining whether a sequence of numbers is sufficiently random includes a number receiver 12 for receiving the sequence of numbers. Number receiver 12 then passes a predetermined number of numbers from the sequence to a window 14. The predetermined number of numbers is then used to determine a visual character 16. Visual character 16 is then displayed on a display unit 18, which is preferably a display screen, but is alternatively a printer printing to paper, for example.

As noted previously, preferably window 14 includes two, three or four numbers each time, and more preferably three numbers. Preferably visual character 16 is a point in two or three dimensional space, more preferably featuring a color. For the preferred embodiment, if the sequence of numbers is sufficiently random, then display unit 18 should appear to be substantially entirely of a "white" color. Alternatively, if a pattern is discernible, then the sequence of numbers is not sufficiently random. Thus, the usefulness of the pseudorandom number generator could also be determined according to whether a pattern was discernible on display unit 18.

In addition, the present invention could be embodied as a device, as shown in Figure 4. A device 20 for detecting a pattern in a sequence of numbers features a data processor 22 and a non- volatile memory 24. Non- volatile memory 24 stores a software program for being operated by data processor 22, such that the steps of the method of the present invention are performed. Device 20 also features a display unit 26 for displaying the results of the method, substantially as previously described. Device 20 has an input port 28 for receiving the string of random numbers. In the preferred embodiment shown in Figure 4, input port 28 is connected to a communication line or port 30, a portion of which is shown for the purposes of illustration, such that the string of random numbers could be encrypted data which is being sent over a communication line, for example. Of course, device 20 could receive such a string of random numbers in substantially any other manner possible. The system, method and device of the present invention could also be used in many other ways, other than those described above. For example, another use for the system, method or device of the present invention is for the analysis of encrypted text, which is essentially a string of numbers. As shown in Figure 2E, the method, device and system of the present invention can be used for the analysis of encrypted text, which is the output of an encryption algorithm. If the output of the encryption algorithm is not random, such that there is a discernible pattern within the string of output numbers, the algorithm may be more vulnerable to being broken. Thus, if the output of the encryption method has a discernible pattern, the usefulness of the encryption method would be reduced since the method might be more vulnerable to being broken.

Yet another use of the method, device and system of the present invention would be to test the usefulness of access control methods. These methods often rely upon strings of numbers as codes or passwords to determine access to a controlled space, such as a room, for example. The output of such methods should also be random, again to avoid breakage of the access control method by an unauthorized party. Thus, if the output of the access control method has a discernible pattern, the usefulness of the access control method would be reduced since the method might be more vulnerable to being broken.

It will be appreciated that the above descriptions are intended only to serve as examples, and that many other embodiments are possible within the spirit and the scope of the present invention.

Claims

WHAT IS CLAIMED IS:

1. A method for detecting a pattern in a sequence of numbers with a display unit, the method comprising the steps of:

(a) providing a window, said window including a plurality of numbers from the sequence of numbers;

(b) determining a visual character according to said plurality of numbers in said window;

(c) displaying said visual character on the display unit;

(d) advancing said window one number in the sequence of numbers; and

(e) repeating steps (b), (c) and (d) for at least a portion of the sequence of numbers, such that if a pattern is discernible on the display unit, the pattern is detected.

2. The method of claim 1, wherein step (e) is repeated for substantially the entirety of the sequence of random numbers.

3. The method of claim 1 , wherein said plurality of numbers is two numbers.

4. The method of claim 3, wherein said visual character is determined according to said two numbers, one of said two numbers representing an "x" coordinate and another of said two numbers representing a "y" coordinate, such that said visual character is a point in two-dimensional space on the display unit.

5. The method of claim 1 , wherein said plurality of numbers is three numbers.

6. The method of claim 5, wherein said visual character is determined according to said three numbers, one of said two numbers representing an "x" coordinate, another of said two numbers representing a "y" coordinate and yet another of said numbers representing a color, such that said visual character is a point with a color in two-dimensional space on the display unit.

7. The method of claim 1, wherein said plurality of numbers is four numbers.

8. The method of claim 7, wherein said visual character is determined according to said four numbers, one of said two numbers representing an "x" coordinate, another of said two numbers representing a "y" coordinate, yet another of said numbers representing a "z" coordinate and a still another of said numbers representing a color, such that said visual character is a point with a color in three-dimensional space on the display unit.

9. The method of claim 1, wherein said plurality of numbers is at least four numbers.

10. The method of claim 9, wherein said visual character is determined according to said at least four numbers, one of said two numbers representing an "x" coordinate, another of said two numbers representing a "y" coordinate and yet another of said numbers representing a color, still another number determining a display of said visual character, such that a plurality of said displays are displayed on the display screen and such that said visual character is a point with a color in an interchanging plurality of displays in three-dimensional space on the display unit.

11. The method of claim 1 , wherein the display unit is a display screen.

12. The method of claim 1 , wherein the display unit is a printer.

13. The method of claim 1, wherein the sequence of numbers is produced by a pseudorandom number generator, such that a usefulness of said pseudorandom number generator is determined according to whether the discernible pattern was detected.

14. The method of claim 1, wherein the sequence of numbers is produced according to an encryption method, such that a usefulness of said encryption method is determined according to whether the discernible pattern was detected.

15. The method of claim 1 , wherein the sequence of numbers is produced according to an access control method, such that a usefulness of said access control method is determined according to whether the discernible pattern was detected.

16. A system for detecting a pattern in a sequence of numbers, the system comprising:

(a) a number receiver for receiving the sequence of numbers;

(b) a window for receiving a plurality of numbers from said number receiver;

(c) a visual character for being determined according to said plurality of numbers in said window; and (d) a display unit for displaying said visual character, such that if a plurality of visual characters are determined according to at least a portion of the sequence of numbers, the pattern is detected on the display unit if the pattern exists, and alternatively such that the pattern is not detected on the display unit.

17. A device for detecting a pattern in a sequence of numbers, the device comprising:

(a) an input port for receiving the sequence of numbers;

(b) a processor for determining a visual character according to at least a portion of the sequence of numbers; and

(c) a display unit for displaying said visual character, such that if a plurality of visual characters are determined according to said at least a portion of the sequence of numbers, a discernible pattern is detected on the display unit if the pattern exists, and alternatively such that the pattern is not detected on the display unit.