The leftmost four bits define the sign.
The leftmost bit is treated as the most significant bit.
Let be the leftmost bits of , where is the bit length of the group order .
Let be the leftmost bits of .
In the end, if then those two leftmost bits will be 11 and Bob will answer that .
And so now k and k have a unique location, being distinguished by the first two leftmost bits.
The leftmost four bits are considered ample headroom for calculations.
Shift b one bit to the right, discarding the rightmost bit, and making the leftmost bit have a value of zero.
Keep track of whether the leftmost bit of a is set to one and call this value carry.
Shift a one bit to the left, discarding the leftmost bit, and making the new rightmost bit zero.