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Cryptography in C and C++, Second Edition by Michael Welschenbach

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Chapter 12. Large Random Numbers

Mathematics is full of pseudorandomness—plenty enough to supply all would-be creators for all time.

—D. R. Hofstadter, Gödel, Escher, Bach

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.

—John von Neumann,

Sequences of "random" numerical values are used in many statistical procedures, in numerical mathematics, in physics, and also in number-theoretic applications to replace statistical observations or to automate the input of variable quantities. Random numbers are used:

  • to select random samples from a larger set,

  • in cryptography to generate keys and in running security protocols,

  • as initial values in procedures to generate prime numbers,

  • to test computer programs ...

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