PHE (partially homomorphic encryption) schemes are in general more efficient than SHE and FHE, mainly because they are homomorphic w.r.t to only one type of operation: addition or multiplication. SHE ...

As @Raoul722 pointed out the polynomial should be irreducible. One should also add the fact that in the original Ring-LWE article security proofs hold by sampling the error with a spherical ...

There is an Eurocrypt'15 paper published by Albrecht et al. which creates a cipher minimizing the number of multiplications needed to produce an encryption. This cipher is called LowMC and it can also ...

The way this is currently done within SPDZ is using a primitive which allows to truncate a secret shared value $[s]$ by a publicly known power of $2$. You can see the code here. In SPDZ, $k$ bit ...

Ok, so the question is how is AES implemented within SPDZ. I'm going to explain the big picture and then whoever is interested in details should check out the original paper here or the code here. ...

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 ...

You can do this slightly better with an additional $\mathcal{0}(2^{56})$ memory and with $\mathcal{0}(2^{56})$ time. You can notice that the relation $c \leftarrow E_{k_1}(E_{k_2}(m))$ can be ...

Recently a method of doing share conversions for generic field or rings has been done here. Basically this paper offers a solution of converting a sharing of $a \in F_p$ i.e. $[a]_p$ into a sharing of ...

Have a look in the SCALE-MAMBA documentation at 11.10.3 section where it explains how one implements $\mathsf{ArcTan}([x])$ where x is a shared fixed point value. Regarding your case specifically, ...

Answer for question 1: According to this paper popular FHE schemes like BGV, NTRU and so on support plaintexts from a ring $R_p = Z_p[X]/\langle f(x) \rangle$ where $n = deg(f)$. The main trick is ...
When you compose $2$ interactive systems $\mathcal{IS}_1$ and $\mathcal{IS}_2$ into $\mathcal{IS}_1 \circ \mathcal{IS}_2$, the book indicates that you're simply connecting the matching ports between ...