# Time required for mod operation [closed]

Let $x,y,n$ be $1234567809, 12345, 9087654321$. My laptop can perform 1 64-bit mod operation in 1 microsecond. Estimate the number of seconds needed for each of the following:

1. Find $x^y \pmod{n}$
2. Find $t$ such that $x^t \equiv 2672633475 \pmod{n}$.

I guess around 10^45 digits, am I right and how do I calculate time from here?

## closed as unclear what you're asking by Evil, Rick Decker, David Richerby, Yuval Filmus, hengxinApr 25 '17 at 7:32

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• What did you try? Where did you get stuck? We're happy to help with conceptual questions but just answering homework-style exercises for you is unlikely to really help you. – David Richerby Apr 24 '17 at 16:08
• Welcome to Computer Science! Don't use images as main content of your post. This makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and mathematics (note that you can use LaTeX) and don't forget to give proper attribution to your sources! – Raphael Apr 24 '17 at 18:38

Hint: If you want to calculate $1234567809^{12345}$ modulo 9087654321, you do not start by calculating $1234567809^{12345}$. After every operation, you reduce the result modulo 9087654321.
Hint 2: You can calculate $x^{12345}$ with about 25 multiplications, not 12345.