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Then, you can encrypt each component $(c_0,c_1)$ using Paillier again. There is a natural generalization of Paillier to longer plaintexts, the Damgård–Jurik cryptosystem. … It allows to encrypt plaintexts from $\mathbb{Z}_{n^s}$, with a ciphertext in $\mathbb{Z}_{n^{s+1}}$, for any $s$ (Paillier is just the case $s=1$). …

Yes, it is often necessary to consider overflows in Paillier encryption. … The signing process is essentially performed homomorphically and interactively, inside a Paillier ciphertext. …

I do not think what you want is possible with any simple solution - by simple, I mean computationally less expensive than downloading and decrypting all the ciphertexts. Basically, multiplicative homo …

The construction from the Paillier cryptosysem is way more involved and was presented at the CRYPTO conference in august this year. … If the messages can be large, then the LWE-based or the Paillier-based instantiations must be used. …

Yes, both will give the same result. However, taking mod after each multiplication is far more efficient: if you do not take modulos during intermediate multiplications, the size of the strings you ar …

The Paillier cryptosystem allows to encrypt integers modulo $n$. Therefore, if $m$ is bigger than $n$, encrypting it will lose most of the message - only $m \bmod n$ is retrieved through decryption. … You can for example write $m$ in base $n$, as $m = \sum_i m_i n^{i}$, and encrypt the $m_i$'s separately with Paillier. …

There are secure two-party protocols to securely compute, given Paillier encryptions of $x$ and $y$ respectively, a Paillier encryption of $x\cdot y$, where the two parties have shares of the secret Paillier … This is a simple standard protocol to interactively multiply Paillier encrypted values. …

Knowing the secret key in the Paillier encryption scheme is equivalent to knowing the factorization, hence the exact same protocol can be used to prove knowledge of the Paillier secret key. …