What would be a typical value for the security parameter of the Fully Homomorphic Encryption over the Integers scheme? The parameters of the Fully Homomorphic Encryption scheme by Dijk et.al are chosen according to the value of the security parameter ${\lambda}$, section 3 of the aforementioned article. 

What is the security parameter for this scheme ? It represents the bits of security the scheme has ? If so, what would be a secure value right now ?
For the first part of the question, I couldn't find where the authors Quantify their security, what I understood that they build their scheme based on the hardness of GCD problem.

As for the second part, According to NIST recommendation which is a non-regulatory federal agency within the U.S. Commerce Department's Technology Administration. a secure value is estimated to be 112 and this won't be broken before 2030.  For other security estimates according to different schemes you can refer to https://www.keylength.com/