49.1 Introduction

There are three different ways to use the interface, with varying demands on the quality of the source and the amount of control over the production process:

• The “no fuss” interface specifies that (random-integer U) produces the next random integer number X such that 0 <= X < U and (random-real) produces the next random real number X such that 0 < X < 1. Details about how these random values are produced may not be very relevant, as long as they appear to be sufficiently random.
• For simulation purposes, on the contrary, it is usually necessary to know that the numbers are produced deterministically by a pseudo–random number generator of high quality and to have explicit access to its state. In addition, one might want to use several independent sources of random numbers at the same time and it can be useful to have some simple form of randomization.
• For security applications a serious form of true randomization is essential, in the sense that it is difficult for an adversary to exploit or introduce imperfections into the distribution of random bits. Moreover, the linear complexity of the stream of random bits is more important than its statistical properties. In these applications, an entropy source (producing truly random bits at a low rate) can be used to randomize a pseudo random number generator to increase the rate of available bits.

Once randomness sources provide the infrastructure to obtain random bits, these can be used to construct other random deviates. Most important are floating point numbers of various distributions and random discrete structures, such as permutations or graphs.