Secure Key Exchange over an Insecure Medium with Public Key Cryptography - Implementing SSL/TLS Using Cryptography and PKI - page 96

Listing 3-4: “huge.c” add routine (addition loop)

i = h1->size;
j = h2->size;

do
{
i--;
if ( j )
{
j--;
sum = h1->rep[ i ] + h2->rep[ j ] + carry;
}
else
{
sum = h1->rep[ i ] + carry;
}
carry = sum > 0xFF;
h1->rep[ i ] = sum;
}
while ( i );

Most signifi cantly, start at the end of each array, which, again, could be two
different sizes, although h2 is guaranteed to be equal to or smaller in length
than h1 . Each char can be added independently, working right-to-left, keeping
track of overfl ow at each step, and propagating it backward to the subsequent
char , as shown in fi gure 3-2.

i = 4 i = 5

j = 4 j = 5

h1->rep x x x x x x

h2->rep x x x x x + x +

x x sum x x sum

carry carry

Figure 3-2: Large number addition

Note that the overfl ow cannot be more than one bit. To convince yourself that
this is true, consider adding two four-bit numbers. The largest such (unsigned)
number is 15 ( bi nary 1111). If you add 15 and 15, you get: