Secure Key Exchange over an Insecure Medium with Public Key Cryptography - Implementing SSL/TLS Using Cryptography and PKI - page 97

1111(15)
1111(15)
11110(30)
As you can see, the result fi ts into fi ve bits. Also notice that although if you
add four bits to four bits and they overfl ow, they wrap. The wrapped result is
the lower four bits of the correct response. Therefore, you can just add the two
ints, keep track of whether they overfl owed, and carry this overfl ow (of one bit)
into the next addition.
Notice that sum — the temporary workspace for each addition operation — is
itself an int . You check for overfl ow by comparing it to MAXCHAR (0xFF). Although
the Intel instruction set does keep track of whether or not an operation — such
as an add — overfl owed and updates an overfl ow bit (also called a carry bit),
the C language has never standardized access to such a bit, in spite of the fact
that every microprocessor or microcontroller defi nes one. Because you don't
have access to the overfl ow bit, you have to check for it on each add operation.
The only other point to notice is that you must continue until you've looped
through all of the bytes of h1 . You can't stop after you hit the last (actually, the
fi rst because you're working backward) byte of h2 because there may be a carry
bit that needs to be propagated backward. In one extreme case, which actually
does occur in cryptographic applications, h1 may be 0x01FFFFFEFF and h2
may be 0x0100. In this case, each byte of h1 overfl ows all the way to the very
fi rst. Thus, the while loop continues until i is 0, even if there's nothing left to
do with h2 (for example, j = 0 ).
Finally, there's a possibility that you can get to the end of the add operation
and still have a carry bit left over. If this is the case, you need to expand h1 by
exactly one char and set its lower-order bit to 1 as shown in Listing 3-5.
Listing 3-5: “huge.c” add (overfl ow expansion)
// Still overflowed; allocate more space
if ( carry )
{
expand( h1 );
}
Here you call the function expand , shown in listing 3-6, which is defi ned for
precisely this purpose.
Listing 3-6: “huge.c” expand
/**
* Extend the space for h by 1 char and set the LSB of that int
* to 1.
*/
void expand( huge *h )
(Continued)