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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 ?

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    $\begingroup$ You may like to have a look at the following paper: "Fully Homomophic Encryption over the Integers Revisited". It gives a reduction from AGCD to DLWE and discusses the possible values for parameters of AGCD on Section 2. Here is the link to the paper: link.springer.com/chapter/10.1007%2F978-3-662-46800-5_20 $\endgroup$ – Luckyluck63 Apr 12 '16 at 3:16
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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/

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