fixing latex syntax in readme. Sebastian Angel 1 year ago
 @@ -39,33 +39,33 @@ You can also look at the tests in the test folder.    ## Default parameters   -$$N$$ indicates the degree of the BFV polynomials. Default is 4096. +*N* indicates the degree of the BFV polynomials. Default is 4096.   -$$t$$ indicates the plaintext modulus, but we specify $$logt$$ instead. Default is 20. +*t* indicates the plaintext modulus, but we specify *log t* instead. Default is 20.   -Each BFV ciphertext can encrypt $$\log{t}\cdot N \approx 10 KB$$ bits of information. +Each BFV ciphertext can encrypt log t * N, which is approximately 10 KB bits of information.    This means that if your database has, say, 1 KB elements, then you can pack 10   such elements into a single BFV plaintext.   On the other hand, if your database has, say, 20 KB elements, then you will   need two BFV plaintexts to represent each of your elements.   -$$d$$ represents the recursion level. When the number of BFV plaintexts needed +*d* represents the recursion level. When the number of BFV plaintexts needed  to represent your database (see above for how to map the number of database  elements of a given size to the number of BFV plaintexts) is smaller than N, -then setting $$d = 1$$ minimizes communication costs. However, you can also set -$$d = 2$$ which doubles the size of the query and increases the size of the +then setting *d = 1* minimizes communication costs. However, you can also set +*d = 2* which doubles the size of the query and increases the size of the  response by roughly a factor of 4, but in some cases might reduce computational  costs a little bit (because the oblivious expansion procedure is cheaper).    -When the number of BFV plaintexts is much greater than N, then $$d = 2$$ -minimizes communication costs. You can read the paper to understand how $$d$$ -affects communication costs. In general, the query consists of $$d$$ BFV -ciphertexts and can index a database with $$N^d$$ BFV plaintexts; the response -consists of $$F^{d-1}$$ ciphertexts, where $$F$$ is the ciphertext +When the number of BFV plaintexts is much greater than N, then *d = 2* +minimizes communication costs. You can read the paper to understand how *d* +affects communication costs. In general, the query consists of *d* BFV +ciphertexts and can index a database with *N^d* BFV plaintexts; the response +consists of *F^(d-1)* ciphertexts, where *F* is the ciphertext  expansion factor. In the current implementation which uses recursive -modulo swithcing, $$F$$ is around 4. We have not identified any setting where -$$d > 2$$ is beneficial. +modulo swithcing, *F* is around 4. We have not identified any setting where +*d > 2* is beneficial.      # Changelog