Cryptographic Applications - Introduction to Cryptography with Java Applets - page 314

FIGURE 16.3

FIGURE 16.4

16.4

RANDOM NUMBER GENERATION
Many cryptosystems depend on the ability to generate random numbers, where random
means in the sense that the values could not be easily predicted by an adversary. Perhaps sur-
prisingly, this is difficult to do in practice. Without special hardware, a computer cannot
truly generate random numbers; they can merely produce what we call pseudorandom num-
bers based on some deterministic mathematical algorithm, and an initial number called a
seed. If either the seed or the transformation is not chosen carefully enough, an adversary
can predict, to a high degree of accuracy, the pseudorandom numbers produced.

E XAMPLE . Conventional random number generators are insufficient for protecting the secrecy
of the numbers they generate. An example is a linear congruential generator, which pro-
duces a sequence

x 1 , x 2 , ... of pseudorandom numbers given by the affine transformation

x n ax n 1 +

b (mod m ) n ≥ 1, 0 ≤ x n < m .