Calculating pow(a,b) mod n

Question

I want to calculate a^b mod n for use in RSA decryption. My code (below) returns incorrect answers. What is wrong with it?

unsigned long i         


        

Answer 1

Are you trying to calculate (a^b)%n, or a^(b%n) ?

If you want the first one, then your code only works when b is an even number, because of that b/2. The "if b%n==1" is incorrect because you don't care about b%n here, but rather about b%2.

If you want the second one, then the loop is wrong because you're looping b/2 times instead of (b%n)/2 times.

Either way, your function is unnecessarily complex. Why do you loop until b/2 and try to multiply in 2 a's each time? Why not just loop until b and mulitply in one a each time. That would eliminate a lot of unnecessary complexity and thus eliminate potential errors. Are you thinking that you'll make the program faster by cutting the number of times through the loop in half? Frankly, that's a bad programming practice: micro-optimization. It doesn't really help much: You still multiply by a the same number of times, all you do is cut down on the number of times testing the loop. If b is typically small (like one or two digits), it's not worth the trouble. If b is large -- if it can be in the millions -- then this is insufficient, you need a much more radical optimization.

Also, why do the %n each time through the loop? Why not just do it once at the end?