Random number tables have been used in
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
for tasks such as selected
random
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. ...
samples. This was much more effective than manually selecting the random samples (with dice, cards, etc.). Nowadays, tables of random numbers have been replaced by computational
random number generator
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular ou ...
s.
If carefully prepared, the filtering and testing processes remove any noticeable bias or asymmetry from the hardware-generated original numbers so that such tables provide the most "reliable" random numbers available to the casual user.
Any published (or otherwise accessible) random data table is unsuitable for cryptographic purposes since the accessibility of the numbers makes them effectively predictable, and hence their effect on a
cryptosystem
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption).
Typically, a cryptosystem consists of three algorithms: one for key generation, one ...
is also predictable. By way of contrast, genuinely random numbers that are only accessible to the intended encoder and decoder allow literally unbreakable encryption of a similar or lesser amount of meaningful data (using a simple
exclusive OR
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (on ...
operation) in a method known as the
one-time pad
The one-time pad (OTP) is an encryption technique that cannot be Cryptanalysis, cracked in cryptography. It requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent. In this technique, ...
, which has often insurmountable problems that are barriers to implementing this method correctly.
History
Tables of random numbers have the desired properties no matter how chosen from the table: by row, column, diagonal or irregularly. The first such table was published by
L.H.C. Tippett in 1927, and since then a number of other such tables were developed. The first tables were generated through a variety of ways—one (by
L.H.C. Tippett) took its numbers "at random" from census registers, another (by
R.A. Fisher and
Francis Yates) used numbers taken "at random" from logarithm tables, and in 1939 a set of 100,000 digits were published by
M.G. Kendall and
B. Babington Smith produced by a specialized machine in conjunction with a human operator. In the mid-1940s, the
RAND Corporation
The RAND Corporation, doing business as RAND, is an American nonprofit global policy think tank, research institute, and public sector consulting firm. RAND engages in research and development (R&D) in several fields and industries. Since the ...
set about to develop a large table of random numbers for use with the
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
, and using a
hardware random number generator
In computing, a hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator is a device that generates random numbers from a physical process c ...
produced ''
A Million Random Digits with 100,000 Normal Deviates
''A Million Random Digits with 100,000 Normal Deviates'' is a random number book by the RAND Corporation, originally published in 1955. The book, consisting primarily of a random number table, was an important
20th century work in the field ...
''. The RAND table used electronic simulation of a
roulette
Roulette (named after the French language, French word meaning "little wheel") is a casino game which was likely developed from the Italy, Italian game Biribi. In the game, a player may choose to place a bet on a single number, various grouping ...
wheel attached to a computer, the results of which were then carefully filtered and tested before being used to generate the table. The RAND table was an important breakthrough in delivering random numbers because such a large and carefully prepared table had never before been available (the largest previously published table was ten times smaller in size), and because it was also available on
IBM
International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...
punched card
A punched card (also punch card or punched-card) is a stiff paper-based medium used to store digital information via the presence or absence of holes in predefined positions. Developed over the 18th to 20th centuries, punched cards were widel ...
s, which allowed for its use in
computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
s. In the 1950s, a hardware random number generator named
ERNIE
Ernie is a masculine given name, frequently a short form (hypocorism) of Ernest, Ernald, Ernesto, or Verner. It may refer to:
People
* Ernie Accorsi (born 1941), American football executive
* Ernie Adams (disambiguation)
* Ernie Afaganis ...
was used to draw British premium bond numbers.
The first "testing" of random numbers for
statistical randomness
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice, dice roll or the digits of pi, π exhibit statistical randomness.
Statistical randomne ...
was developed by
M.G. Kendall and
B. Babington Smith in the late 1930s, and was based upon looking for certain types of probabilistic expectations in a given sequence. The simplest test looked to make sure that roughly equal numbers of 1s, 2s, 3s, etc. were present; more complicated tests looked for the number of digits between successive 0s and compared the total counts with their expected probabilities. Over the years more complicated tests were developed. Kendall and Smith also created the notion of "
local randomness", whereby a given set of random numbers would be broken down and tested in segments. In their set of 100,000 numbers, for example, two of the thousands were somewhat less "locally random" than the rest, but the set as a whole would pass its tests. Kendall and Smith advised their readers not to use those particular thousands by themselves as a consequence.
Published tables still have niche uses, particularly in the performance of
experimental music
Experimental music is a general label for any music or music genre that pushes existing boundaries and genre definitions. Experimental compositional practice is defined broadly by exploratory sensibilities radically opposed to, and questioning of, ...
pieces that call for them, such as ''Vision'' (1959) and ''Poem'' (1960) by
La Monte Young
La Monte Thornton Young (born October 14, 1935) is an American composer, musician, and performance artist recognized as one of the first American minimalist composers and a central figure in Fluxus and post-war avant-garde music. He is best k ...
.
See also
* ''
A Million Random Digits with 100,000 Normal Deviates
''A Million Random Digits with 100,000 Normal Deviates'' is a random number book by the RAND Corporation, originally published in 1955. The book, consisting primarily of a random number table, was an important
20th century work in the field ...
''
*
Kish grid
References
External links
Data from ''A Million Random Digits With 100,000 Normal Deviates''by the RAND Corporation
{{Authority control
Random number generation