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2.5.2 What is random number generation?

Random number generation is used in a wide variety of cryptographic operations, such as key generation and challenge/response protocols. A random number generator is a function that outputs a sequence of 0s and 1s such that at any point, the next bit cannot be predicted based on the previous bits. However, true random number generation is difficult to do on a computer, since computers are deterministic devices. Thus, if the same random generator is run twice, identical results are received. True random number generators are in use, but they can be difficult to build. They typically take input from something in the physical world, such as the rate of neutron emission from a radioactive substance or a user's idle mouse movements.

Because of these difficulties, random number generation on a computer is usually only pseudo-random number generation. A pseudo-random number generator produces a sequence of bits that has a random looking distribution. With each different seed (a typically random stream of bits used to generate a usually longer pseudo-random stream), the pseudo-random number generator generates a different pseudo-random sequence. With a relatively small random seed a pseudo-random number generator can produce a long apparently random string.

Pseudo-random number generators are often based on cryptographic functions like block ciphers or stream ciphers. For instance, iterated DES encryption starting with a 56-bit seed produces a pseudo-random sequence.

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