How to calculate the mod value of a rational/irrational value? We have a course in network security this semester and we are being taught RSA algorithm. I came across a typical math problem that I was unable to solve here. $$D*E \equiv 1 \mod{\phi(n)}$$ This became $$D \equiv E^{-1} \mod{\phi(n)}$$ How do you solve this ??? My lect gave this specific example $$D \equiv 7^{-1} \mod{160}$$ and the solution for $D$ was $23$! How did she arrive at this.

**Hint**

$7D = 1 \mod 160$

**Sol'n**

> $7D = 1 \mod 160$ and $D = 23 \Longrightarrow 23*7 \mod 160$ satisfies this.