Random Number Generation

By: Jesse Miller

Random numbers play an important role in the use of encryption for various network security applications security applications. A number of network security algorithms based on cryptography make use of random numbers.

The use of random numbers for the nonce frustrates opponent`s efforts to determine or guess the nonce. Session key generation is done by a key distribution center or by one of the principals. Generation of keys for the RSA public-key encryption algorithm uses random numbers.

These applications give rise to two distinct and not necessarily compatible requirements for a sequence of random numbers, randomness and unpredictability.

Traditionally, the concern in the generation of a sequence of allegedly random numbers has been that the sequence of numbers be random in some well-defined statistical sense. The following two criteria are used to validate that a sequence of numbers is random.

The distribution of numbers in the sequence should be uniform. The frequency of occurrence of each of the numbers should be approximately the same. No one value in the sequence can be inferred from the others. There is no test to prove independence. There are well defined tests for determining that a sequence of numbers matches a particular distribution, such as the uniform distribution.

Use of a sequence of the numbers that appear statistically random often occurs in the design of algorithms related to cryptography. If the sequence is sufficiently long, the primality of a number can be determined with near certainty.

This type of approach is known as randomization which crops up frequently in the design of algorithms.

In applications such as reciprocal authentication and session key generation, the requirement is not so much that the sequence of numbers be statistically random but that the successive members of the sequence are unpredictable. Each number is statistically independent of other numbers in the sequence and therefore unpredictable.

True random numbers are rarely used. Sequences of numbers that appear to be random are generated by some algorithm. Care must be taken that an opponent not be able to predict future elements of the sequence on the basis of earlier elements.

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Source of true random numbers are hard to come by. Physical noise generators, such as pulse detectors of ionizing radiation events, gas discharge tubes, and leaky capacitors, are one potential source. These devices are of limited utility in network security applications.
Concept of numbers generated by a deterministic algorithm is uneasy.

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