# Example of FHEI scheme?

I am reading this paper Toward Secure Multikeyword Top-k Retrieval over Encrypted Cloud Data.

I am trying to work out an example of the FHEI (Fully homomorphic Encryption over Integers) scheme mentioned on the paper, but unable to prove it. Can anyone explain the scheme with a working example?

Edit 1: I am unable to understand how to choose value of $r$ for equation $(pq + r)$. I am getting expected solution when using $r = 0$, but any other value of $r$ in range of ($-2^ρ, 2^ρ$) gives incorrect solution.

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But what did you not understand? That scheme is almost the same of the one in FHE over Integers, by Gentry, Dijk, Halevi, and Vaikuntanathan (eprint.iacr.org/2009/616). So, maybe it will be useful take a look in their paper... – Vitor Jan 14 at 12:39
I am reading this paper also. Problem is that I am trying to solve an example, but I am not getting expected answer. How should I choose values for parameters - ρ, λ, μ, η, γ ? And what is the role of security parameter λ? – Anurag Jan 14 at 17:28
On the section 3 the authors explain how to choose those params: "A convenient parameter set to keep in mind is ρ=λ, ρ'=2λ, η=O(λ²), γ=O(λ^5) and τ=γ+λ". So, once you fix a value to λ, you may use this configuration... – Vitor Jan 15 at 18:46
I am trying to work out an example for paper mentioned in question. Is there any restriction on value of parameters that I may be missing? And also for evaluation do I need a circuit or simple bitwise OR/AND/XOR will do? – Anurag Jan 19 at 19:43