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Does the limited range of the values, makes cracking the Paillier cryptosystem easier? That depends. I'm assuming that you are generating good, large random $r$ values, just reusing them for the same plaintexts. The main problem with this is that you loose semantic security. It however does not lead to a key leakage attack (AFAIK). So, your question is ...

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With version 1, you are essentially using an additively homomorphic substitution cipher. I understand that the database is quite large, but the number of different values small. This (typically) means that statistical analysis can be used to derive a lot of information, especially if the attacker has some auxiliary information which is often the case. This ...

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The BV scheme presented in the article works for plaintext messages in $GF(2)$ (that is $m$ $\in$ $\{0,1\}$) but can be extended to support encrypting messages that are in $GF(t)$ where $t$ is prime with the modulus $Z_q$. This means that if you want to encrypt a message in $\{0,1\}^n$ you have to do it for each bit separately in $GF(2)$ (or in $GF(t)$ and ...

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There has been work on using garbled circuits while also hiding the function. This can be done via implementing a universal circuit inside the garbled circuit. However, the standard garbled circuit does reveal the topology of the circuit. Also, when considering malicious security, the most efficient method is cut-and-choose, and this reveals the actual ...

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yes in general garbled circuits allow hiding of data from other party. Secure Two party computation is all about a known function which both the parties agree upon priorly (For example, in millionaire's problem, it is comparison) and Subsequently hiding their particular inputs from other

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No, because the guy who can only decrypt in the target group $G_1$ can take any ciphertext in $G$, use the pairing to map it to $G_1$ and then decrypt in $G_1$ (here I assume the full scheme where the message is a number and not a group element). You could do it the other way round, i.e., let the guy only decrypt in $G$ and not in $G_1$, by giving him not ...

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Yes, for example CryptDB uses the Paillier cryptosystem to implement homomorphic encryption for columns that require it. See CryptDB: Protecting Confidentiality with Encrypted Query Processing (pdf) for a description. Whether you consider that use "effective" is another matter. Earlier this month there was a back and forth between the CryptDB developers and ...

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The connection between SMC, FHE techniques has been established recently (1) We present a computationally secure MPC protocol for threshold adversaries which is parametrized by a value L. When L = 2 we obtain a classical form of MPC protocol in which interaction is required for multiplications, as L increases interaction is reduced in that one requires ...

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No, a cryptosystem can't do what's asked. Proof: if one can precisely answer queries of the form "how many data points up to a distance of $3$ starting from an origin point = $n$" (a subset of what's wanted) for any value of $n$ with $|n|\le m+3$, and each point has integer value $v$ with $|v|\le m$, then one can find exactly the value of all the points in ...

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