Custom index comparator in MongoDB - mongodb

Question

I'm working with a dataset composed by probabilistic encrypted elements indistinguishable from random samples. This way, sequential encryptions of the same number results in different ciphertexts. However, these still comparable through a special function that applies algorithms like SHA256 to compare two ciphertexts.
I want to add a list of the described ciphertexts to a MongoDB database and index it using a tree-based structure (i.e.: AVL). I can't simply apply the default indexing of the database because, as described, the records must be comparable using the special function.
An example: Suppose I have a database db and a collection c composed by the following document type:
{
"_id":ObjectId,
"r":string
}
Moreover, let F(int,string,string) be the following function:
F(h,l,r) = ( SHA256(l | r) + h ) % 3
where the operator | is a standard concatenation function.
I want to execute the following query in an efficient way, such as in a collection with some suitable indexing:
db.c.find( { F(h,l,r) :{ $eq: 0 } } )
for h and l chosen arbitrarily but not constants. I.e.: Suppose I want to find all records that satisfy F(h1,l1,r), for some pair (h1, l1). Later, in another moment, I want to do the same but using (h2, l2) such that h1 != h2 and l1 != l2. h and l may assume any value in the set of integers.
How can I do that?

Answer 1

You can execute this query use the operator $where, but this way can't use index. So, for query performance it's dependents on the size of your dataset.
db.c.find({$where: function() { return F(1, "bb", this.r) == 0; }})
Before execute the code above, you need store your function F on the mongodb server:
db.system.js.save({
_id: "F",
value: function(h, l, r) {
// the body of function
}
})
Links:
store javascript function on server

Answer 2

I've tried a solution that store the result of the function in your collection, so I changed the schema, like below:
{
"_id": ObjectId,
"r": {
"_key": F(H, L, value),
"value": String
}
}
The field r._key is value of F(h,l,r) with constant h and l, and the field r.value is original r field.
So you can create index on field r._key and your query condition will be:
db.c.find( { "r._key" : 0 } )