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The requirement is that your element $g$ is in $\mathbb{Z}_{n^2}^*$ and not in $(\mathbb{Z}_{n}^*)^2$. The set $\mathbb{Z}_{n^2}^*$ is the set of integers smaller than $n^2$ that are relatively prime to $n^2$, i.e., you require an element $g$ from $\mathbb{Z}_{n^2}$ such that $\gcd(g,n^2)=1$. $(\mathbb{Z}_{n}^*)^2$ on the other hand is the set of pairs ...

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The answer is yes. Say we have an FHE scheme that supports addition and multiplication over an underlying field (so we are not limited to just 0,1). As in your question, assume we want to compute $Y=2^C$ where $C$ is encrypted and $Y$ is encrypted such that $y=D(Y)=2^m$. We can do this using a basic square and multiply algorithm. Assume that we can do a bit ...

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The addition and Multiplication are at bit level , which are nothing but XOR and AND gates. Where XOR is bit level addition and AND is bit level multiplication. Since XOR and AND form universal gates, In theory all operations like all possible arthimetic operations could be done . More here Can Add and Multiply On Cipher Text achieve all operations?

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Here’s is a crypto analysis on Porticor system. From my point of view the system is almost useless in a cloud environment because its security can only be proved on a semi-honest model, witch means you have to trust Porticor and your cloud provider… not very likely in a post-NSA era. I'm not an cryptographer, but I've implemented a PHE schema used on ...

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If you want to minimize computation time and are willing to use a protocol that involves many rounds of interaction, and if it is OK to disclose the offer of the winning ISP (not just its identity) and of all other ISPs that tied with it, here is one protocol. In an initial phase, each ISP does the following: Convert the 8-bit value $x$ to a $2^8$-bit ...

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I would suggest looking into sharemind. Their setup is a little different from VIFF, there are 3 computation servers and everyone shares their inputs with the computation servers. As long as the computation servers don't collude, privacy is guaranteed. They have also optimized many things. So it may work better for you. That said, there are some ...

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