Problem - Kevin Tafuro

In addition, you might wish to test a number to see if it is prime. The API for that
one is a bit complex:
int BN_is_prime(BIGNUM *bn, int numchecks, void (*callback)(int, int, void *),
BN_CTX *ctx, void *cb_arg);
int BN_is_prime_fasttest(BIGNUM *bn, int numchecks,
void (*callback)(int, int, void *), BN_CTX *ctx,
void *cb_arg);
These functions do not guarantee that the number is prime. OpenSSLuses the
Rabin-Miller primality test, which is an iterative, probabilistic algorithm, where the
probability that the algorithm is right increases dramatically with every iteration. The
checks argument specifies how many iterations to use. We strongly recommend
using the built-in constant BN_prime_checks, which makes probability of the result
being wrong negligible. When using that value, the odds of the result being wrong
are 1 in 280. This function requires you to pass in a pointer to an initialized BN_CTX object, which
it uses as scratch space.
Prime number testing isn’t that cheap. BN_is_prime_fasttest( ) explicitly tries factoring
by a bunch of small primes, which speeds things up when the value you’re checking
might not be prime (which is the case when you’re generating a random prime).
Because testing the primality of a number can be quite expensive, OpenSSLprovides
a way to monitor status by using the callback and cb_arg arguments. In addition,
because the primality-testing algorithm consists of performing a fixed number of iterations,
this callback can be useful for implementing a status meter of some sort.
If you define the callback, it is called after each iteration. The first argument is always
1, the second is always the iteration number (starting with 0), and the third is the
value of cb_arg (this can be used to identify the calling thread if multiple threads are
sharing the same callback).
Math operations on BIGNUM objects
Yes, we saved the best for last. Table 7-2 lists the math operations supported by
OpenSSL’s BIGNUM library.
Table 7-2. Math operations supported by OpenSSL’s BIGNUM library
Function Description Limitations Comments
int BN_add(BIGNUM *r, BIGNUM
*a, BIGNUM *b);
r = a+b
int BN_sub(BIGNUM *r, BIGNUM
*a, BIGNUM *b);
int BN_mul(BIGNUM *r, BIGNUM
*a, BIGNUM *b, BN_CTX *ctx);
r = a-b r≠a and r≠b Values may be the same, but
the objects may not be.
r = a×b Use BN_lshift or BN_lshift1
instead to multiply by a
known power of 2 (it’s
faster).
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