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# Query Composition

The database elements in EllipticPIR is arranged as a hypercube with dimension `d`. For instance, if `d = 3` and the number of database elements `n = 1,000,000`, the dataset is arrange as 3-d cube with `100 x 100 x 100` elements for each edge.

The query will select the position on that hypercube. For `d = 3` case, you should select the `x`, `y` and `z` coordinates of the hypercube in your query.

Once you determine the `(x, y, z)` tuble, next you should create an encrypted query.

You will **generate a private** key `sk` that can be ephemeral per query (you can reuse the private key for multiple queries, but there are no such requirement). **You don't have to submit your public key** to the server. There is no such API.

Then, create an array of EC-ElGamal encrypted message array for each coordinates. For `x`-coordinate, you will create an array of EC-ElGamal encrypted messages with the length equal to the element count on the `x`-edge of the hypercube. The encrypted array is

`[Enc(0), .., Enc(0), Enc(1), Enc(0), .., Enc(0)]`

where only the `x`-th message is one and zeros for non `x`-th.

This will continue to y, z, .. to reach to the dimension. Thus the final query is

`[`\
  `[Enc(0), .., Enc(0), Enc(1), Enc(0), .., Enc(0)],`\
  `..,`\
  `[Enc(0), .., Enc(0), Enc(1), Enc(0), .., Enc(0)]`\
`].`

The total number of encrypted messages will be `O(n^(1/d))`. This will be both the computational complexity of the query generation process and the outbound network traffic to the server.