Problem - Kevin Tafuro

Table 7-2. Math operations supported by OpenSSL’s BIGNUM library (continued)
Function Description Limitations Comments
BN_ULONG BN_div_word(BIGNUM
*a, BN_ULONG w);
a = a÷w Returns the remainder.
BN_ULONG BN_mod_word(BIGNUM
*a, BN_ULONG w);
return a mod w
All of the above functions that return an int return 1 on success or 0 on failure. BN_
div_word( ) and BN_mod_word( ) return their result. Note that the type BN_ULONG is simply
a typedef for unsigned long.
See Also
Recipe 11.9
7.5 Generating a Prime Number (Testing for
Primality)
Problem
You need to generate a random prime number or test to see if a number is prime.
Solution
Use the routines provided by your arbitrary-precision math library, or generate a random
odd number and use the Rabin-Miller primality test to see whether the number
generated is actually prime.
Discussion
Good arbitrary-precision math libraries have functions that can automatically generate
primes and determine to a near certainty whether a number is prime. In addition,
these libraries should have functionality that produces “safe” primes (that is, a
prime whose value minus 1 divided by 2 is also prime). You should also be able to
ask for a prime that gives a particular remainder when you divide that prime by a
particular number. The last two pieces of functionality are useful for generating
parameters for Diffie-Hellman key exchange.
The OpenSSLfunctionality for generating and testing primes is discussed in Recipe
7.4.
The most common way primes are generated is by choosing a random odd number
of the desired bit length from a secure pseudo-random source (we discuss pseudo-
Generating a Prime Number (Testing for Primality) | 323
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