Problem - Kevin Tafuro

RSA. For example, public key certificates encode the public exponent within
them, and it is almost universally one of these three values. These numbers are
common because it’s fast to multiply other numbers with these numbers, particularly
in hardware. This number is stored in the RSA object, and it is used for
both encryption and decryption operations.
cb
Callback function; when called, it allows for monitoring the progress of generating
a prime. It is passed directly to the function’s internal call to BN_generate_
prime( ), as discussed in Recipe 7.4.
cb_arg
Application-specific argument that is passed directly to the callback function, if
one is specified.
If you need to generate an “n-bit” key manually, you can do so as follows:
1. Choose two random primes p and q, both of length n/2, using the techniques
discussed in Recipe 7.5. Ideally, both primes will have their two most significant
bits set to ensure that the public key (derived from these primes) is exactly n bits
long.
2. Compute n, the product of p and q. This is the public key.
3. Compute d, the inverse of the chosen exponent, modulo (p –1)× (q – 1). This is
generally done using the extended Euclidean algorithm, which is outside the
scope of this book. See the Handbook of Applied Cryptography by Alfred J. Menezes,
Paul C. Van Oorschot, and Scott A. Vanstone for a good discussion of the
extended Euclidean algorithm.
4. Optionally, precompute some values that will significantly speed up private key
operations (decryption and signing): d mod (p – 1), d mod (q – 1), and the
inverse of q mod p (again using the extended Euclidean algorithm).
Here’s an example, using the OpenSSLBIGNUM library, of computing all the values
you need for a key, given two primes p and q:
#include
typedef struct {
BIGNUM *n;
unsigned long e; /* This number should generally be small. */
} RSA_PUBKEY;
typedef struct {
BIGNUM *n;
BIGNUM *d; /* The actual private key. */
/* These aren't necessary, but speed things up if used. If you do use them,
you don't need to keep n or d around. */
BIGNUM *p;
BIGNUM *q;
328 | Chapter 7: Public Key Cryptography
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