How does the Efficient Fully Homomorphic Encryption from (Standard) LWE work? I am interesting to learn the low level implementation of Efficient Fully Homomorphic Encryption from (Standard) LWE and I am wondering if anyone can answer the following questions:


Does the BV scheme work on binary numbers (0,1) or not? 
Does the BV scheme encrypt and decrypt each bit separately?  
Is there any difference between the original paper of BV andthe updated version in terms of encryption and decryption processes?
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 the message $m$ $\in \{0,1,...t-1\}^n$)

The BGV scheme instantiated with the LWE problem is the same as in BV.
The main difference in BGV is that the scheme supports a more general context, namely it could be also instantiated with the Ring-LWE problem providing a more efficient circuit (inner operations are done inside a ring $R$ instead from $Z_q$ as in LWE).