Security of Homomorphic encryption schemes Usually for cryptosystems the security is denoted as a $2^n$-bit security such as 256-bit, 1024-bit, 2048-bit etc whereas I came across homomorphic schemes mentioning 80-bit and 96-bit security.

Is this secure enough? Why does it not follow the $2^n$-bit security?
Why does it not follow the $2^n$-bit security?


They follow the usual way of describing schemes, i.e., $n$ bits of security means $2^n$ operations to the best attack. So, taking $n = 80$, you impose "an effort" of $2^{80}$ to the attacker.


  Is this secure enough?


This is a tricky question. That depends on what you want to do with the scheme and how powerful the attacker is supposed to be.

Anyway, I think the main reason to have $n = 80 $ in this kind of paper, is that homomorphic encryption schemes are very expensive and authors just want to show a proof of concept. Anyone that wants to use these cryptosystems is free to instantiate them with larger values of $n$.