# 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.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.ellipticpir.com/technology/query-composition.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.