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Update README.md

fixing latex syntax in readme.
Sebastian Angel 2 years ago
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1 changed files with 13 additions and 13 deletions
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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
 ## 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 
 This means that if your database has, say, 1 KB elements, then you can pack 10 
 such elements into a single BFV plaintext. 
 such elements into a single BFV plaintext. 
 On the other hand, if your database has, say, 20 KB elements, then you will 
 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.
 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
 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,
 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
 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). 
 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
 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
 # Changelog