I was read in paper in searchable encryption that encrypt bloom filter index in the following way:
1- generate secret key to encrypt bloom filter and query is:
the secret key sk (M1, M2, s ), where M1, M2 ∊ Rm×m are invertible matrices and s∊{0,1}m is a vector.
2- then encrypt bloom filter as following: split bloom filter i into two vector i',i"
, set i=i'=i" if s is one; else i'=1/2 i+ r and i"=1/2i-r , as r is a random number. Then encrypt i',i" with transpose of two matrix M1 and M2 .
secondly, encrypt query in the following way:
1-split query bloom filter into two vectors q',q"
set q=q'=q" if s is zero; else q'=1/2 i+ r and q"=1/2i-r , as r is a random number. Then encrypt q',q" with inverse of two matrix M1 and M2 .
what i want to ask why multiply bloom filter index by transpose of matrix and query by inverse of matrix and the way used to split vectors?
I think you have three questions? Amal Hashim
In Q1, you say about the transpose, this is not transpose. But it just split the Index I.
In Q2, you say about the inverse, this is not inverse. But it is Query encryption.
In Q3, you say the way of splitting the vector (i) Index_Enc (SK, I), (ii) Query_Enc(SK, Q).
Shamsher Ullah , ok, you are right. what i want to know about all this, it is better to encrypt index and query with the same technique, so when the comparison is done, query will find the corresponding index.
Shamsher Ullah , when represent an index for data as encrypted bloom filters and query as another encrypted bloom filter. when trying to search over this index bloom filter by this query. how find the right encrypted bloom filter in index satisfying that encrypted query if each of them encrypted by different way.
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