Random number table
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 a student of Karl Pearson's 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 set about to develop a large table of random numbers for use with the Monte Carlo method, and using a hardware random number generator produced A Million Random Digits with 100,000 Normal Deviates. The RAND table used electronic simulation of a roulette 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 punch cards, which allowed for its use in computers. In the 1950s, a hardware random number generator named ERNIE was used to draw British lottery numbers.
The first "testing" of random numbers 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.
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. But note that any published table (and in fact any previously prepared table at all) are unusable for cryptographic purposes since the existence of the public (or private) table provides a way for an attacker to break any cryptosystem using the random numbers as an input. In short, the numbers in such tables are not unpredictable; they can be stolen or copied by an attacker.