# Problem with Chaum`s Untraceable Electronic Cash

For example according to protocol I need calculate this:

$$b=F^{(1/h)} \bmod pq.$$

Where $$p$$ and $$q$$ are prime numbers. I have $$F$$ and $$h$$. But how can I calculate $$b$$?

I tried to do this:

$$\text{temp} = h^{-1} \bmod((p-1)*(q-1))$$

and then

$$b=F^{\text{temp}} \bmod pq$$

But the problem is that

$$h^{-1} \bmod((p-1)*(q-1))$$

does not always exist, sometimes $$\text{GCD}(h,(p-1)*(q-1))$$ is not $$1$$.

Is it supposed to be like that or do I need to calculate it in a different way?

• What values of $F, h, p, q$ have you tried? – an4s Apr 28 '19 at 1:48
• I guess, $h$ should be selected so that it has an inverse element? maybe it's selected by some party at its discretion? – Mikhail Koipish May 1 '19 at 10:34