Cryptography Reference
In-Depth Information
FIGURE 11.1
The applet called TestPrimeGeneratorApplet generates probable primes of a specified byte
length. It generates random numbers of the requested length, and tests each for primality until
one passes, using the number of tests specified. The screen shot in Figure 11.1 is of the
applet generating a probable prime using Rabin-Miller.
This particular prime is just a probable prime. It was not constructed to be a strong prime,
or a safe prime, though it may be either purely by accident. See the chapters on quadratic
ciphers (Chapter 10) and on exponential congruences (Chapter 13) for an explanation of the
terms strong prime and safe prime.
EXERCISES
1.
Using the Rabin-Miller primality test, determine the probability that the integer is
prime for each of the following numbers. Choose your own bases (as randomly as you
can). You should be able to do the calculations without the aid of a computer.
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