Authenticating Communications Using Digital Signatures - Implementing SSL/TLS Using Cryptography and PKI - page 218

Generating ECC Keypairs
One point glossed over thus far is that of the elliptic-curve parameters themselves.
In fact, generating elliptic-curve parameters is so complex, so time consuming,
and so hard to get right that the NIST publishes a list of approved named curves
for use in elliptic curve operations. Of course, the actual keypairs — the secret
integer and the public point — are generated per-user from the parameters.
Generating a keypair is actually pretty simple: Pick a random large integer d
and multiply it by the point G . The result of the multiplication is the public key,
and d is the private key.
To illustrate how to use this, you can borrow an elliptic curve from RFC 4754
that includes some ECDSA examples. The test routine is shown in Listing 4-41.
Listing 4-41: “ecdsa.c” test routine
#ifdef TEST_ECDSA
int main( int argc, char *argv[ ] )
{
// ECC parameters
unsigned char P[] = {
0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
};
unsigned char b[] = {
0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55, 0x76,
0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6, 0x3B, 0xCE,
0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B
};
unsigned char q[] = {
0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, 0xA7, 0x17, 0x9E, 0x84, 0xF3, 0xB9,
0xCA, 0xC2, 0xFC, 0x63, 0x25, 0x51
};
unsigned char gx[] = {
0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, 0xE6, 0xE5,
0x63,
0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, 0x2D, 0xEB, 0x33, 0xA0, 0xF4,
0xA1,
0x39, 0x45, 0xD8, 0x98, 0xC2, 0x96
};
unsigned char gy[] = {
0x4F, 0xE3, 0x42, 0xE2, 0xFE, 0x1A, 0x7F, 0x9B, 0x8E, 0xE7, 0xEB, 0x4A, 0x7C,
0x0F, 0x9E, 0x16, 0x2B, 0xCE, 0x33, 0x57, 0x6B, 0x31, 0x5E, 0xCE, 0xCB, 0xB6,
0x40, 0x68, 0x37, 0xBF, 0x51, 0xF5
};
// key
unsigned char w[] = { 0xDC, 0x51, 0xD3, 0x86, 0x6A, 0x15, 0xBA, 0xCD, 0xE3,
0x3D, 0x96, 0xF9, 0x92, 0xFC, 0xA9, 0x9D, 0xA7, 0xE6, 0xEF, 0x09, 0x34, 0xE7,