Random number generator

Details Random number generator Random number generator

1999-03-17

2003-03-25

Mai, Tan V. (Department: 2124)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

C708S003000

Reexamination Certificate

active

06539410

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to random number generators and in particular to random number generators based on detection of quantum phenomena.
2. Description of the Related Art
A random number generator is a device which produces a stream of random numbers or numbers that are nearly random, and not always the same number. A number in this stream is said to be fully random if it has no “memory” of what has gone before it. Statistically speaking, its conditional probability distribution given the past, being independent of its past, equals its unconditional probability distribution. Moreover, it is usually desirable that, for each integer n≧1, the so-called marginal distribution of the n
th
number in the stream have the same distribution as the first one. The numbers are then said to be stationary (or have identical distributions). For simplicity, all sequences of truly random numbers are generally to be interpreted as being fully random and stationary, and as possibly having equally likely occurrences of each number being produced, as the context might hopefully indicate. It has proved to be very difficult to produce truly random numbers. While people may be capable of producing somewhat random numbers by picking numbers out one at a time, they certainly cannot do so fast enough to meet the requirements of modern usage. Therefore, for all practical purposes, machines are used to produce random numbers.
Most machines and methods heretofore employed for producing random numbers are either “deterministic” they follow a fixed, totally predictable recipe—or else are still far from truly random. Some devices produce nearly truly random numbers, but they are subject to being skewed by external influences or are very delicate and expensive to maintain. For many purposes an approximation of randomness has turned out to be acceptable. For an increasing number of other purposes, something closely approximating true randomness is a necessity.
Random numbers are most commonly thought of as having security applications such as for sending encryted messages. Random numbers are useful for security purposes because they create inherently unpredictable sequences which cannot be easily duplicated, studiously replicated or discovered by accident. For many lower security applications, a random number generator with a reasonable degree of randomness will suffice. Higher security applications demand a greater degree of true randomness.
Another problem that exists with current random number generators, apart from the “level of randomness” of the numbers that they are able to produce, is that sufficient numbers of random numbers cannot be produced quickly enough for contemporary applications. This is significant in security applications where messages are encoded with a string of random numbers by adding a bit in the string to each bit in the message. The result appears to be nonsense to any recipient until it is decoded by subtracting out the string to recover the message. Ideally, the random number string should be as long as the message itself. In practice, a string—known as a “key”—is used repeatedly and it is hoped the string cannot be discovered. The length of the key is critically important because each additional random bit in the string doubles the security level of the cipher. Naturally, if production of sufficient numbers of random numbers were possible and practical, the level of security enjoyed for encrypted messages would increase exponentially.
In addition to security applications, random numbers are increasingly essential for scientific investigations including studies of physical laws, investigations and constructions of probability distributions, analyses of the performance of mathematical algorithms in principle and as applied practically to devices, and notably for development of artificial intelligence. Random number generators are used in the assessment of the performance of machines to help construct a large variety of representative situations. The sampling thus obtained provides feedback which is used to learn more about the, process or operation being studied. As with security applications, problems exist regarding the availability of a sufficient volume of random numbers and with the true randomness of the numbers produced. In a growing number of areas of scientific inquiry, the ability to produce large numbers of random numbers can be critical. Certain research, such as large-scale Monte Carlo simulations, requires millions of random numbers to yield useful information. In sensitive analyses where essentially true randomness in a sampling is necessary to obtain sound results, any significant lack of randomness can unacceptably skew test data and frustrate the research.
In part due to the need for large numbers of random numbers, the technique of producing “pseudo-random” numbers evolved. Pseudo-random numbers are generated using an arithmetical algorithm having an output of numbers which can pass many statistical tests of randomness. Another important aspect of arithmetically produced random numbers is that they can be replicated. This is useful for purposes of testing and analyses, but potentially disastrous for security applications. While pseudo-random numbers are statistically random for most applications, and have the application specific advantage of being reproducible, they suffer from one major flaw—they repeat. For example, a popular pseudorandom number generator is the linear-congruential generator. The linear-congruential generator of degree k produces non-negative integers less than some given integer m, where m≧2. At some point, if the generator is asked to produce m
k
+k integers, its last k integers must have already occurred previously. Since each integer produced by the generator is based on the same algorithm, and is therefore dependent on the previous k integers, this leads into a cycle of repetition that the generator cannot escape. In this sense, each pseudo-random number generator has a finite period. The best linear-congruential generators have a period exceeding 2 billion. Shift-register algorithms have been used to greatly extend the period of the generator. Even so, the fact remains that, regardless of the length of the period of a pseudo-random number generator, the numbers which are the product of the technique are ultimately deterministic and certainly not truly random.
Most machines are understood to function in the realm of classical mechanics according to the physical laws stated by Newton. The Newtonian world (including the essentially mechanistic world of Maxwell's equations concerning the behavior of electricity and magnetism) has at its core, the feature and key premise that if all the initial conditions (positions, velocities, charges, etc.) of the components of an isolated physical system are known, all of its future behavior can be known and predicted. It is therefore ultimately deterministic, the generation of truly random numbers or random behavior therefrom being inherently impossible.
Moving closer to the observation of quantum phenomena, many devices have been constructed that take sample measurements of a physical process (sometimes a macroscopic, but sometimes a microscopic process). The measurements are converted into a sequence of elements, each element hopefully having little or no memory (but whether these elements actually lack memory of any of their predecessors depends both on the measuring apparatus and the physical process). Production of random numbers from a physical process creates a string of numbers which, even if not purely random, may seem to be highly so and is largely unrepeatable. This lack of repeatability is a liability in scientific applications, but can be circumvented by recording and/or storing the actual numbers generated if it is not too costly. Conversely, lack of repeatability itself is not necessarily a disadvantage and may well be an asset in security applications and the investigation of artificial intelligence.
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