They are not very random for that purpose; see Knuth [1]. Examples of acceptable uses of these random bits are: (i) multiplying a signal randomly by ±1 at a rapid “chip rate,” so as to spread its spectrum uniformly (but recoverably) across some desired bandpass | 300 Chapter 7. Random Numbers random floating-point number. They are not very random for that purpose see Knuth 1 . Examples of acceptable uses of these random bits are i multiplying a signal randomly by 1 at a rapid chip rate so as to spread its spectrum uniformly but recoverably across some desired bandpass or ii Monte Carlo exploration of a binary tree where decisions as to whether to branch left or right are to be made randomly. Now we do not want you to go through life thinking that there is something special about the primitive polynomial of degree 18 used in the above examples. We chose 18 because 218 is small enough for you to verify our claims directly by numerical experiment. The accompanying table 2 lists one primitive polynomial for each degree up to 100. In fact there exist many such for each degree. For example see for a complete table up to degree 10. CITED REFERENCES AND FURTHER READING Knuth . 1981 SeminumericalAlgorithms 2nd ed. vol. 2 of TheArtofComputerProgramming Reading MA Addison-Wesley pp. 29ff. 1 Horowitz P. and Hill W 1989 TheArt ofElectronics 2nd ed. Cambridge Cambridge University Press . Tausworthe . 1965 Mathematics of Computation vol. 19 pp. 201-209. Watson . 1962 Mathematics of Computation vol. 16 pp. 368-369. 2 Random Sequences Based on Data Encryption In Numerical Recipes first edition we described howto use the Data Encryption Standard DES 1-3 for the generation of random numbers. Unfortunately when implemented in software in a high-level language like C DES is very slow so excruciatingly slow in fact that our previous implementation can be viewed as more mischievous than useful. Here we give a much faster and simpler algorithm which though it may not be secure in the cryptographic sense generates about equally good random numbers. DES like its progenitor cryptographic system LUCIFER is a so-called block product cipher 4 . It acts on 64 bits of input by iteratively applying 16 times in fact a kind of .
