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Update README.md

fixing latex syntax in readme.
Sebastian Angel 2 years ago
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      README.md

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README.md

@@ -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