Cryptography: Random Numbers - Criteria for a Random Number

 
Principles of Pseudorandom Number Generation 

•Random numbers play an important role in the use of encryption for various network security applications

•The Use of Random Numbers: A number of network security algorithms and protocols based on cryptography make use of random binary numbers. For example,

–Key distribution

–Session key generation

–Generation of keys for the RSA public-key encryption algorithm

–Generation of a bit stream for symmetric stream encryption

These applications give rise to two distinct and not necessarily compatible requirements for a sequence of random numbers:

•randomness and

•unpredictability

RANDOMNESS 

•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:

–Uniform distribution: The distribution of bits in the sequence should be uniform; that is, the frequency of occurrence of ones and zeros should be approximately equal.

–Independence: No one subsequence in the sequence can be inferred from the others.

UNPREDICTABILITY 

•In applications such as reciprocal authentication, session key generation, and stream ciphers, the requirement is not just that the sequence of numbers be statistically random but that the successive members of the sequence are unpredictable.

•With “true” random sequences, each number is statistically independent of other numbers in the sequence and therefore unpredictable.

•However, true random numbers are seldom used; rather, sequences of numbers that appear to be random are generated by some algorithm.

•In this latter case, care must be taken that an opponent not be able to predict future elements of the sequence on the basis of earlier elements.